Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.3% → 40.4%

Time: 2.3min

Alternatives: 42

Speedup: 3.5×

• 88.4% 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: 30.3% 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: 40.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := k \cdot y2 - j \cdot y3\\ t_4 := y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - \left(a \cdot t_2 - y4 \cdot t_3\right)\right)\\ t_5 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot t_3\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;j \leq -1.32 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.2 \cdot 10^{-87}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq -6.6 \cdot 10^{-174}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -2.9 \cdot 10^{-230}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{-306}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{-242}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{-166}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-133}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{+93}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot t_2 + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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))) (* y3 (- (* y0 y5) (* y1 y4))))
           (* x (- (* i y1) (* b y0))))))
        (t_2 (- (* x y2) (* z y3)))
        (t_3 (- (* k y2) (* j y3)))
        (t_4 (* y1 (- (* i (- (* x j) (* z k))) (- (* a t_2) (* y4 t_3)))))
        (t_5
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 t_3))
           (* c (- (* y y3) (* t y2)))))))
   (if (<= j -1.32e+14)
     t_1
     (if (<= j -2.2e-87)
       t_5
       (if (<= j -6.6e-174)
         (* i (* y5 (- (* y k) (* t j))))
         (if (<= j -2.9e-230)
           t_4
           (if (<= j 6.5e-306)
             (* a (* y5 (- (* t y2) (* y y3))))
             (if (<= j 2.4e-242)
               t_5
               (if (<= j 1.35e-166)
                 t_4
                 (if (<= j 2.3e-133)
                   (* c (* z (- (* t i) (* y0 y3))))
                   (if (<= j 2.8e+93)
                     (*
                      y0
                      (+
                       (+ (* c t_2) (* y5 (- (* j y3) (* k y2))))
                       (* b (- (* z k) (* x j)))))
                     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))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (k * y2) - (j * y3);
	double t_4 = y1 * ((i * ((x * j) - (z * k))) - ((a * t_2) - (y4 * t_3)));
	double t_5 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (j <= -1.32e+14) {
		tmp = t_1;
	} else if (j <= -2.2e-87) {
		tmp = t_5;
	} else if (j <= -6.6e-174) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (j <= -2.9e-230) {
		tmp = t_4;
	} else if (j <= 6.5e-306) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (j <= 2.4e-242) {
		tmp = t_5;
	} else if (j <= 1.35e-166) {
		tmp = t_4;
	} else if (j <= 2.3e-133) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else if (j <= 2.8e+93) {
		tmp = y0 * (((c * t_2) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
    t_2 = (x * y2) - (z * y3)
    t_3 = (k * y2) - (j * y3)
    t_4 = y1 * ((i * ((x * j) - (z * k))) - ((a * t_2) - (y4 * t_3)))
    t_5 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))))
    if (j <= (-1.32d+14)) then
        tmp = t_1
    else if (j <= (-2.2d-87)) then
        tmp = t_5
    else if (j <= (-6.6d-174)) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (j <= (-2.9d-230)) then
        tmp = t_4
    else if (j <= 6.5d-306) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (j <= 2.4d-242) then
        tmp = t_5
    else if (j <= 1.35d-166) then
        tmp = t_4
    else if (j <= 2.3d-133) then
        tmp = c * (z * ((t * i) - (y0 * y3)))
    else if (j <= 2.8d+93) then
        tmp = y0 * (((c * t_2) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))))
    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))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (k * y2) - (j * y3);
	double t_4 = y1 * ((i * ((x * j) - (z * k))) - ((a * t_2) - (y4 * t_3)));
	double t_5 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (j <= -1.32e+14) {
		tmp = t_1;
	} else if (j <= -2.2e-87) {
		tmp = t_5;
	} else if (j <= -6.6e-174) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (j <= -2.9e-230) {
		tmp = t_4;
	} else if (j <= 6.5e-306) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (j <= 2.4e-242) {
		tmp = t_5;
	} else if (j <= 1.35e-166) {
		tmp = t_4;
	} else if (j <= 2.3e-133) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else if (j <= 2.8e+93) {
		tmp = y0 * (((c * t_2) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	} 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))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
	t_2 = (x * y2) - (z * y3)
	t_3 = (k * y2) - (j * y3)
	t_4 = y1 * ((i * ((x * j) - (z * k))) - ((a * t_2) - (y4 * t_3)))
	t_5 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))))
	tmp = 0
	if j <= -1.32e+14:
		tmp = t_1
	elif j <= -2.2e-87:
		tmp = t_5
	elif j <= -6.6e-174:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif j <= -2.9e-230:
		tmp = t_4
	elif j <= 6.5e-306:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif j <= 2.4e-242:
		tmp = t_5
	elif j <= 1.35e-166:
		tmp = t_4
	elif j <= 2.3e-133:
		tmp = c * (z * ((t * i) - (y0 * y3)))
	elif j <= 2.8e+93:
		tmp = y0 * (((c * t_2) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))))
	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(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(Float64(k * y2) - Float64(j * y3))
	t_4 = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) - Float64(Float64(a * t_2) - Float64(y4 * t_3))))
	t_5 = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * t_3)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	tmp = 0.0
	if (j <= -1.32e+14)
		tmp = t_1;
	elseif (j <= -2.2e-87)
		tmp = t_5;
	elseif (j <= -6.6e-174)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (j <= -2.9e-230)
		tmp = t_4;
	elseif (j <= 6.5e-306)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (j <= 2.4e-242)
		tmp = t_5;
	elseif (j <= 1.35e-166)
		tmp = t_4;
	elseif (j <= 2.3e-133)
		tmp = Float64(c * Float64(z * Float64(Float64(t * i) - Float64(y0 * y3))));
	elseif (j <= 2.8e+93)
		tmp = Float64(y0 * Float64(Float64(Float64(c * t_2) + Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2)))) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))));
	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))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	t_2 = (x * y2) - (z * y3);
	t_3 = (k * y2) - (j * y3);
	t_4 = y1 * ((i * ((x * j) - (z * k))) - ((a * t_2) - (y4 * t_3)));
	t_5 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))));
	tmp = 0.0;
	if (j <= -1.32e+14)
		tmp = t_1;
	elseif (j <= -2.2e-87)
		tmp = t_5;
	elseif (j <= -6.6e-174)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (j <= -2.9e-230)
		tmp = t_4;
	elseif (j <= 6.5e-306)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (j <= 2.4e-242)
		tmp = t_5;
	elseif (j <= 1.35e-166)
		tmp = t_4;
	elseif (j <= 2.3e-133)
		tmp = c * (z * ((t * i) - (y0 * y3)));
	elseif (j <= 2.8e+93)
		tmp = y0 * (((c * t_2) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	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[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t$95$2), $MachinePrecision] - N[(y4 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.32e+14], t$95$1, If[LessEqual[j, -2.2e-87], t$95$5, If[LessEqual[j, -6.6e-174], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.9e-230], t$95$4, If[LessEqual[j, 6.5e-306], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.4e-242], t$95$5, If[LessEqual[j, 1.35e-166], t$95$4, If[LessEqual[j, 2.3e-133], N[(c * N[(z * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.8e+93], N[(y0 * N[(N[(N[(c * t$95$2), $MachinePrecision] + N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -1.32e14 or 2.79999999999999989e93 < 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. Taylor expanded in j around inf 64.8%

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

      1. +-commutative 64.8%

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

      2. mul-1-neg 64.8%

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

      3. unsub-neg 64.8%

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

      4. *-commutative 64.8%

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

   4. Simplified 64.8%

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

   if -1.32e14 < j < -2.19999999999999988e-87 or 6.5000000000000004e-306 < j < 2.4000000000000001e-242

   1. Initial program 47.3%

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

   2. Taylor expanded in y4 around inf 61.0%

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

   if -2.19999999999999988e-87 < j < -6.6000000000000002e-174

   1. Initial program 41.5%

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

   2. Taylor expanded in y5 around inf 41.3%

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

      1. mul-1-neg 41.3%

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

      2. associate-*r* 35.5%

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

      3. *-commutative 35.5%

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

   4. Simplified 35.5%

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

   5. Taylor expanded in i around inf 53.8%

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

   if -6.6000000000000002e-174 < j < -2.90000000000000005e-230 or 2.4000000000000001e-242 < j < 1.35000000000000003e-166

   1. Initial program 37.5%

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

   2. Taylor expanded in y1 around -inf 66.7%

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

      1. mul-1-neg 66.7%

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

      2. *-commutative 66.7%

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

      3. distribute-rgt-neg-in 66.7%

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

   4. Simplified 66.7%

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

   if -2.90000000000000005e-230 < j < 6.5000000000000004e-306

   1. Initial program 42.1%

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

   2. Taylor expanded in y5 around inf 26.3%

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

      1. mul-1-neg 26.3%

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

      2. associate-*r* 34.6%

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

      3. *-commutative 34.6%

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

   4. Simplified 34.6%

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

   5. Taylor expanded in a around inf 67.5%

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

      1. *-commutative 67.5%

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

   7. Simplified 67.5%

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

   if 1.35000000000000003e-166 < j < 2.3e-133

   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. Taylor expanded in c around inf 11.9%

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

      1. +-commutative 11.9%

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

      2. mul-1-neg 11.9%

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

      3. unsub-neg 11.9%

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

      4. *-commutative 11.9%

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

      5. *-commutative 11.9%

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

      6. *-commutative 11.9%

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

      7. *-commutative 11.9%

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

   4. Simplified 11.9%

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

   5. Taylor expanded in z around inf 56.4%

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

      1. distribute-lft-out-- 56.4%

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

      2. *-commutative 56.4%

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

   7. Simplified 56.4%

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

   if 2.3e-133 < j < 2.79999999999999989e93

   1. Initial program 38.8%

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

   2. Taylor expanded in y0 around inf 60.4%

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

      1. +-commutative 60.4%

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

      2. mul-1-neg 60.4%

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

      3. unsub-neg 60.4%

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

      4. *-commutative 60.4%

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

      5. *-commutative 60.4%

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

      6. *-commutative 60.4%

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

      7. *-commutative 60.4%

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

   4. Simplified 60.4%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.32 \cdot 10^{+14}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -2.2 \cdot 10^{-87}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq -6.6 \cdot 10^{-174}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -2.9 \cdot 10^{-230}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - \left(a \cdot \left(x \cdot y2 - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{-306}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{-242}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{-166}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - \left(a \cdot \left(x \cdot y2 - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-133}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{+93}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]

Alternative 2: 53.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y4) - (i * y5);
	double t_2 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (((c * y0) - (a * y1)) * ((x * y2) - (z * y3)))) + (t_1 * ((t * j) - (y * k)))) + (((c * y4) - (a * y5)) * ((y * y3) - (t * y2)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)));
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = j * (((t * t_1) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	}
	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 * y4) - (i * y5);
	double t_2 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (((c * y0) - (a * y1)) * ((x * y2) - (z * y3)))) + (t_1 * ((t * j) - (y * k)))) + (((c * y4) - (a * y5)) * ((y * y3) - (t * y2)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)));
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = j * (((t * t_1) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	}
	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 * b) - (c * i)) * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (((c * y0) - (a * y1)) * ((x * y2) - (z * y3)))) + (t_1 * ((t * j) - (y * k)))) + (((c * y4) - (a * y5)) * ((y * y3) - (t * y2)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)))
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = j * (((t * t_1) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
	return tmp

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (b * y4) - (i * y5);
	t_2 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (((c * y0) - (a * y1)) * ((x * y2) - (z * y3)))) + (t_1 * ((t * j) - (y * k)))) + (((c * y4) - (a * y5)) * ((y * y3) - (t * y2)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)));
	tmp = 0.0;
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = j * (((t * t_1) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 88.6%

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

   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. Taylor expanded in j around inf 42.4%

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

      1. +-commutative 42.4%

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

      2. mul-1-neg 42.4%

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

      3. unsub-neg 42.4%

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

      4. *-commutative 42.4%

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

   4. Simplified 42.4%

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

4. Final simplification 60.6%

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

Alternative 3: 37.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := c \cdot y4 - a \cdot y5\\ t_3 := j \cdot y3 - k \cdot y2\\ t_4 := y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot t_3\right)\right)\\ t_5 := y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot t_3\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_6 := y1 \cdot y4 - y0 \cdot y5\\ t_7 := \left(k \cdot y2 - j \cdot y3\right) \cdot t_6 + \left(x \cdot \left(y2 \cdot t_1\right) + t_2 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+266}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-7}:\\ \;\;\;\;y3 \cdot \left(y \cdot t_2 + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-60}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot t_6 + x \cdot t_1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-232}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-274}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-239}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-61}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+142}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1)))
        (t_2 (- (* c y4) (* a y5)))
        (t_3 (- (* j y3) (* k y2)))
        (t_4
         (*
          y5
          (+
           (* a (- (* t y2) (* y y3)))
           (+ (* i (- (* y k) (* t j))) (* y0 t_3)))))
        (t_5
         (*
          y0
          (+
           (+ (* c (- (* x y2) (* z y3))) (* y5 t_3))
           (* b (- (* z k) (* x j))))))
        (t_6 (- (* y1 y4) (* y0 y5)))
        (t_7
         (+
          (* (- (* k y2) (* j y3)) t_6)
          (+ (* x (* y2 t_1)) (* t_2 (- (* y y3) (* t y2)))))))
   (if (<= y -1.1e+266)
     t_4
     (if (<= y -8.6e-7)
       (*
        y3
        (+
         (* y t_2)
         (+ (* j (- (* y0 y5) (* y1 y4))) (* z (- (* a y1) (* c y0))))))
       (if (<= y -5.5e-60)
         (* y2 (+ (+ (* k t_6) (* x t_1)) (* t (- (* a y5) (* c y4)))))
         (if (<= y -5.6e-232)
           t_5
           (if (<= y -7.8e-274)
             t_7
             (if (<= y 2.6e-239)
               t_5
               (if (<= y 9e-61)
                 t_4
                 (if (<= y 2.5e+142)
                   t_7
                   (* (* y c) (- (* y3 y4) (* x i)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (c * y4) - (a * y5);
	double t_3 = (j * y3) - (k * y2);
	double t_4 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * t_3)));
	double t_5 = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * t_3)) + (b * ((z * k) - (x * j))));
	double t_6 = (y1 * y4) - (y0 * y5);
	double t_7 = (((k * y2) - (j * y3)) * t_6) + ((x * (y2 * t_1)) + (t_2 * ((y * y3) - (t * y2))));
	double tmp;
	if (y <= -1.1e+266) {
		tmp = t_4;
	} else if (y <= -8.6e-7) {
		tmp = y3 * ((y * t_2) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else if (y <= -5.5e-60) {
		tmp = y2 * (((k * t_6) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	} else if (y <= -5.6e-232) {
		tmp = t_5;
	} else if (y <= -7.8e-274) {
		tmp = t_7;
	} else if (y <= 2.6e-239) {
		tmp = t_5;
	} else if (y <= 9e-61) {
		tmp = t_4;
	} else if (y <= 2.5e+142) {
		tmp = t_7;
	} else {
		tmp = (y * c) * ((y3 * y4) - (x * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_1 = (c * y0) - (a * y1)
    t_2 = (c * y4) - (a * y5)
    t_3 = (j * y3) - (k * y2)
    t_4 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * t_3)))
    t_5 = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * t_3)) + (b * ((z * k) - (x * j))))
    t_6 = (y1 * y4) - (y0 * y5)
    t_7 = (((k * y2) - (j * y3)) * t_6) + ((x * (y2 * t_1)) + (t_2 * ((y * y3) - (t * y2))))
    if (y <= (-1.1d+266)) then
        tmp = t_4
    else if (y <= (-8.6d-7)) then
        tmp = y3 * ((y * t_2) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
    else if (y <= (-5.5d-60)) then
        tmp = y2 * (((k * t_6) + (x * t_1)) + (t * ((a * y5) - (c * y4))))
    else if (y <= (-5.6d-232)) then
        tmp = t_5
    else if (y <= (-7.8d-274)) then
        tmp = t_7
    else if (y <= 2.6d-239) then
        tmp = t_5
    else if (y <= 9d-61) then
        tmp = t_4
    else if (y <= 2.5d+142) then
        tmp = t_7
    else
        tmp = (y * c) * ((y3 * y4) - (x * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (c * y4) - (a * y5);
	double t_3 = (j * y3) - (k * y2);
	double t_4 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * t_3)));
	double t_5 = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * t_3)) + (b * ((z * k) - (x * j))));
	double t_6 = (y1 * y4) - (y0 * y5);
	double t_7 = (((k * y2) - (j * y3)) * t_6) + ((x * (y2 * t_1)) + (t_2 * ((y * y3) - (t * y2))));
	double tmp;
	if (y <= -1.1e+266) {
		tmp = t_4;
	} else if (y <= -8.6e-7) {
		tmp = y3 * ((y * t_2) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else if (y <= -5.5e-60) {
		tmp = y2 * (((k * t_6) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	} else if (y <= -5.6e-232) {
		tmp = t_5;
	} else if (y <= -7.8e-274) {
		tmp = t_7;
	} else if (y <= 2.6e-239) {
		tmp = t_5;
	} else if (y <= 9e-61) {
		tmp = t_4;
	} else if (y <= 2.5e+142) {
		tmp = t_7;
	} else {
		tmp = (y * c) * ((y3 * y4) - (x * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * y0) - (a * y1)
	t_2 = (c * y4) - (a * y5)
	t_3 = (j * y3) - (k * y2)
	t_4 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * t_3)))
	t_5 = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * t_3)) + (b * ((z * k) - (x * j))))
	t_6 = (y1 * y4) - (y0 * y5)
	t_7 = (((k * y2) - (j * y3)) * t_6) + ((x * (y2 * t_1)) + (t_2 * ((y * y3) - (t * y2))))
	tmp = 0
	if y <= -1.1e+266:
		tmp = t_4
	elif y <= -8.6e-7:
		tmp = y3 * ((y * t_2) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
	elif y <= -5.5e-60:
		tmp = y2 * (((k * t_6) + (x * t_1)) + (t * ((a * y5) - (c * y4))))
	elif y <= -5.6e-232:
		tmp = t_5
	elif y <= -7.8e-274:
		tmp = t_7
	elif y <= 2.6e-239:
		tmp = t_5
	elif y <= 9e-61:
		tmp = t_4
	elif y <= 2.5e+142:
		tmp = t_7
	else:
		tmp = (y * c) * ((y3 * y4) - (x * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y0) - Float64(a * y1))
	t_2 = Float64(Float64(c * y4) - Float64(a * y5))
	t_3 = Float64(Float64(j * y3) - Float64(k * y2))
	t_4 = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * t_3))))
	t_5 = Float64(y0 * Float64(Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y5 * t_3)) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))))
	t_6 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_7 = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * t_6) + Float64(Float64(x * Float64(y2 * t_1)) + Float64(t_2 * Float64(Float64(y * y3) - Float64(t * y2)))))
	tmp = 0.0
	if (y <= -1.1e+266)
		tmp = t_4;
	elseif (y <= -8.6e-7)
		tmp = Float64(y3 * Float64(Float64(y * t_2) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (y <= -5.5e-60)
		tmp = Float64(y2 * Float64(Float64(Float64(k * t_6) + Float64(x * t_1)) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y <= -5.6e-232)
		tmp = t_5;
	elseif (y <= -7.8e-274)
		tmp = t_7;
	elseif (y <= 2.6e-239)
		tmp = t_5;
	elseif (y <= 9e-61)
		tmp = t_4;
	elseif (y <= 2.5e+142)
		tmp = t_7;
	else
		tmp = Float64(Float64(y * c) * Float64(Float64(y3 * y4) - Float64(x * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (c * y0) - (a * y1);
	t_2 = (c * y4) - (a * y5);
	t_3 = (j * y3) - (k * y2);
	t_4 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * t_3)));
	t_5 = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * t_3)) + (b * ((z * k) - (x * j))));
	t_6 = (y1 * y4) - (y0 * y5);
	t_7 = (((k * y2) - (j * y3)) * t_6) + ((x * (y2 * t_1)) + (t_2 * ((y * y3) - (t * y2))));
	tmp = 0.0;
	if (y <= -1.1e+266)
		tmp = t_4;
	elseif (y <= -8.6e-7)
		tmp = y3 * ((y * t_2) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	elseif (y <= -5.5e-60)
		tmp = y2 * (((k * t_6) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	elseif (y <= -5.6e-232)
		tmp = t_5;
	elseif (y <= -7.8e-274)
		tmp = t_7;
	elseif (y <= 2.6e-239)
		tmp = t_5;
	elseif (y <= 9e-61)
		tmp = t_4;
	elseif (y <= 2.5e+142)
		tmp = t_7;
	else
		tmp = (y * c) * ((y3 * y4) - (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y0 * N[(N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * t$95$6), $MachinePrecision] + N[(N[(x * N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.1e+266], t$95$4, If[LessEqual[y, -8.6e-7], N[(y3 * N[(N[(y * t$95$2), $MachinePrecision] + 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]), $MachinePrecision], If[LessEqual[y, -5.5e-60], N[(y2 * N[(N[(N[(k * t$95$6), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.6e-232], t$95$5, If[LessEqual[y, -7.8e-274], t$95$7, If[LessEqual[y, 2.6e-239], t$95$5, If[LessEqual[y, 9e-61], t$95$4, If[LessEqual[y, 2.5e+142], t$95$7, N[(N[(y * c), $MachinePrecision] * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.0999999999999999e266 or 2.60000000000000003e-239 < y < 9e-61

   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. Taylor expanded in y5 around -inf 58.8%

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

   if -1.0999999999999999e266 < y < -8.6000000000000002e-7

   1. Initial program 38.5%

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

   2. Taylor expanded in y3 around -inf 57.0%

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

   if -8.6000000000000002e-7 < y < -5.4999999999999997e-60

   1. Initial program 24.4%

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

   2. Taylor expanded in y2 around inf 69.3%

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

   if -5.4999999999999997e-60 < y < -5.59999999999999985e-232 or -7.79999999999999971e-274 < y < 2.60000000000000003e-239

   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. Taylor expanded in y0 around inf 59.9%

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

      1. +-commutative 59.9%

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

      2. mul-1-neg 59.9%

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

      3. unsub-neg 59.9%

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

      4. *-commutative 59.9%

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

      5. *-commutative 59.9%

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

      6. *-commutative 59.9%

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

      7. *-commutative 59.9%

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

   4. Simplified 59.9%

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

   if -5.59999999999999985e-232 < y < -7.79999999999999971e-274 or 9e-61 < y < 2.5000000000000001e142

   1. Initial program 39.1%

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

   2. Taylor expanded in y2 around inf 59.8%

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

      1. *-commutative 59.8%

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

   4. Simplified 59.8%

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

   if 2.5000000000000001e142 < y

   1. Initial program 20.8%

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

   2. Taylor expanded in c around inf 35.5%

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

      1. +-commutative 35.5%

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

      2. mul-1-neg 35.5%

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

      3. unsub-neg 35.5%

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

      4. *-commutative 35.5%

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

      5. *-commutative 35.5%

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

      6. *-commutative 35.5%

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

      7. *-commutative 35.5%

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

   4. Simplified 35.5%

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

   5. Taylor expanded in y around -inf 71.2%

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

      1. associate-*r* 65.5%

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

      2. +-commutative 65.5%

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

      3. mul-1-neg 65.5%

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

      4. unsub-neg 65.5%

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

      5. *-commutative 65.5%

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

   7. Simplified 65.5%

      \[\leadsto \color{blue}{\left(c \cdot y\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+266}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-7}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-60}:\\ \;\;\;\;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(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-232}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-274}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(c \cdot y4 - a \cdot y5\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-239}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-61}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+142}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(c \cdot y4 - a \cdot y5\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \end{array} \]

Alternative 4: 37.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ t_2 := j \cdot y3 - k \cdot y2\\ t_3 := y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot t_2\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_4 := y \cdot k - t \cdot j\\ t_5 := y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot t_4 + y0 \cdot t_2\right)\right)\\ t_6 := c \cdot y4 - a \cdot y5\\ t_7 := t_6 \cdot \left(y \cdot y3 - t \cdot y2\right)\\ t_8 := t_1 + \left(\left(i \cdot y5\right) \cdot t_4 + t_7\right)\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{+264}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+33}:\\ \;\;\;\;y3 \cdot \left(y \cdot t_6 + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-58}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-225}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-274}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-238}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-60}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+142}:\\ \;\;\;\;t_1 + \left(x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t_7\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5))))
        (t_2 (- (* j y3) (* k y2)))
        (t_3
         (*
          y0
          (+
           (+ (* c (- (* x y2) (* z y3))) (* y5 t_2))
           (* b (- (* z k) (* x j))))))
        (t_4 (- (* y k) (* t j)))
        (t_5 (* y5 (+ (* a (- (* t y2) (* y y3))) (+ (* i t_4) (* y0 t_2)))))
        (t_6 (- (* c y4) (* a y5)))
        (t_7 (* t_6 (- (* y y3) (* t y2))))
        (t_8 (+ t_1 (+ (* (* i y5) t_4) t_7))))
   (if (<= y -1.45e+264)
     t_5
     (if (<= y -1.9e+33)
       (*
        y3
        (+
         (* y t_6)
         (+ (* j (- (* y0 y5) (* y1 y4))) (* z (- (* a y1) (* c y0))))))
       (if (<= y -3.5e-58)
         t_8
         (if (<= y -1.6e-225)
           t_3
           (if (<= y -1.25e-274)
             t_8
             (if (<= y 7.2e-238)
               t_3
               (if (<= y 1.05e-60)
                 t_5
                 (if (<= y 3.3e+142)
                   (+ t_1 (+ (* x (* y2 (- (* c y0) (* a y1)))) t_7))
                   (* (* y c) (- (* y3 y4) (* x i)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5));
	double t_2 = (j * y3) - (k * y2);
	double t_3 = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * t_2)) + (b * ((z * k) - (x * j))));
	double t_4 = (y * k) - (t * j);
	double t_5 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_4) + (y0 * t_2)));
	double t_6 = (c * y4) - (a * y5);
	double t_7 = t_6 * ((y * y3) - (t * y2));
	double t_8 = t_1 + (((i * y5) * t_4) + t_7);
	double tmp;
	if (y <= -1.45e+264) {
		tmp = t_5;
	} else if (y <= -1.9e+33) {
		tmp = y3 * ((y * t_6) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else if (y <= -3.5e-58) {
		tmp = t_8;
	} else if (y <= -1.6e-225) {
		tmp = t_3;
	} else if (y <= -1.25e-274) {
		tmp = t_8;
	} else if (y <= 7.2e-238) {
		tmp = t_3;
	} else if (y <= 1.05e-60) {
		tmp = t_5;
	} else if (y <= 3.3e+142) {
		tmp = t_1 + ((x * (y2 * ((c * y0) - (a * y1)))) + t_7);
	} else {
		tmp = (y * c) * ((y3 * y4) - (x * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_1 = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))
    t_2 = (j * y3) - (k * y2)
    t_3 = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * t_2)) + (b * ((z * k) - (x * j))))
    t_4 = (y * k) - (t * j)
    t_5 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_4) + (y0 * t_2)))
    t_6 = (c * y4) - (a * y5)
    t_7 = t_6 * ((y * y3) - (t * y2))
    t_8 = t_1 + (((i * y5) * t_4) + t_7)
    if (y <= (-1.45d+264)) then
        tmp = t_5
    else if (y <= (-1.9d+33)) then
        tmp = y3 * ((y * t_6) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
    else if (y <= (-3.5d-58)) then
        tmp = t_8
    else if (y <= (-1.6d-225)) then
        tmp = t_3
    else if (y <= (-1.25d-274)) then
        tmp = t_8
    else if (y <= 7.2d-238) then
        tmp = t_3
    else if (y <= 1.05d-60) then
        tmp = t_5
    else if (y <= 3.3d+142) then
        tmp = t_1 + ((x * (y2 * ((c * y0) - (a * y1)))) + t_7)
    else
        tmp = (y * c) * ((y3 * y4) - (x * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5));
	double t_2 = (j * y3) - (k * y2);
	double t_3 = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * t_2)) + (b * ((z * k) - (x * j))));
	double t_4 = (y * k) - (t * j);
	double t_5 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_4) + (y0 * t_2)));
	double t_6 = (c * y4) - (a * y5);
	double t_7 = t_6 * ((y * y3) - (t * y2));
	double t_8 = t_1 + (((i * y5) * t_4) + t_7);
	double tmp;
	if (y <= -1.45e+264) {
		tmp = t_5;
	} else if (y <= -1.9e+33) {
		tmp = y3 * ((y * t_6) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else if (y <= -3.5e-58) {
		tmp = t_8;
	} else if (y <= -1.6e-225) {
		tmp = t_3;
	} else if (y <= -1.25e-274) {
		tmp = t_8;
	} else if (y <= 7.2e-238) {
		tmp = t_3;
	} else if (y <= 1.05e-60) {
		tmp = t_5;
	} else if (y <= 3.3e+142) {
		tmp = t_1 + ((x * (y2 * ((c * y0) - (a * y1)))) + t_7);
	} else {
		tmp = (y * c) * ((y3 * y4) - (x * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))
	t_2 = (j * y3) - (k * y2)
	t_3 = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * t_2)) + (b * ((z * k) - (x * j))))
	t_4 = (y * k) - (t * j)
	t_5 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_4) + (y0 * t_2)))
	t_6 = (c * y4) - (a * y5)
	t_7 = t_6 * ((y * y3) - (t * y2))
	t_8 = t_1 + (((i * y5) * t_4) + t_7)
	tmp = 0
	if y <= -1.45e+264:
		tmp = t_5
	elif y <= -1.9e+33:
		tmp = y3 * ((y * t_6) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
	elif y <= -3.5e-58:
		tmp = t_8
	elif y <= -1.6e-225:
		tmp = t_3
	elif y <= -1.25e-274:
		tmp = t_8
	elif y <= 7.2e-238:
		tmp = t_3
	elif y <= 1.05e-60:
		tmp = t_5
	elif y <= 3.3e+142:
		tmp = t_1 + ((x * (y2 * ((c * y0) - (a * y1)))) + t_7)
	else:
		tmp = (y * c) * ((y3 * y4) - (x * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5)))
	t_2 = Float64(Float64(j * y3) - Float64(k * y2))
	t_3 = Float64(y0 * Float64(Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y5 * t_2)) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))))
	t_4 = Float64(Float64(y * k) - Float64(t * j))
	t_5 = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(i * t_4) + Float64(y0 * t_2))))
	t_6 = Float64(Float64(c * y4) - Float64(a * y5))
	t_7 = Float64(t_6 * Float64(Float64(y * y3) - Float64(t * y2)))
	t_8 = Float64(t_1 + Float64(Float64(Float64(i * y5) * t_4) + t_7))
	tmp = 0.0
	if (y <= -1.45e+264)
		tmp = t_5;
	elseif (y <= -1.9e+33)
		tmp = Float64(y3 * Float64(Float64(y * t_6) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (y <= -3.5e-58)
		tmp = t_8;
	elseif (y <= -1.6e-225)
		tmp = t_3;
	elseif (y <= -1.25e-274)
		tmp = t_8;
	elseif (y <= 7.2e-238)
		tmp = t_3;
	elseif (y <= 1.05e-60)
		tmp = t_5;
	elseif (y <= 3.3e+142)
		tmp = Float64(t_1 + Float64(Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + t_7));
	else
		tmp = Float64(Float64(y * c) * Float64(Float64(y3 * y4) - Float64(x * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5));
	t_2 = (j * y3) - (k * y2);
	t_3 = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * t_2)) + (b * ((z * k) - (x * j))));
	t_4 = (y * k) - (t * j);
	t_5 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * t_4) + (y0 * t_2)));
	t_6 = (c * y4) - (a * y5);
	t_7 = t_6 * ((y * y3) - (t * y2));
	t_8 = t_1 + (((i * y5) * t_4) + t_7);
	tmp = 0.0;
	if (y <= -1.45e+264)
		tmp = t_5;
	elseif (y <= -1.9e+33)
		tmp = y3 * ((y * t_6) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	elseif (y <= -3.5e-58)
		tmp = t_8;
	elseif (y <= -1.6e-225)
		tmp = t_3;
	elseif (y <= -1.25e-274)
		tmp = t_8;
	elseif (y <= 7.2e-238)
		tmp = t_3;
	elseif (y <= 1.05e-60)
		tmp = t_5;
	elseif (y <= 3.3e+142)
		tmp = t_1 + ((x * (y2 * ((c * y0) - (a * y1)))) + t_7);
	else
		tmp = (y * c) * ((y3 * y4) - (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y0 * N[(N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * t$95$4), $MachinePrecision] + N[(y0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$6 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$1 + N[(N[(N[(i * y5), $MachinePrecision] * t$95$4), $MachinePrecision] + t$95$7), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.45e+264], t$95$5, If[LessEqual[y, -1.9e+33], N[(y3 * N[(N[(y * t$95$6), $MachinePrecision] + 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]), $MachinePrecision], If[LessEqual[y, -3.5e-58], t$95$8, If[LessEqual[y, -1.6e-225], t$95$3, If[LessEqual[y, -1.25e-274], t$95$8, If[LessEqual[y, 7.2e-238], t$95$3, If[LessEqual[y, 1.05e-60], t$95$5, If[LessEqual[y, 3.3e+142], N[(t$95$1 + N[(N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$7), $MachinePrecision]), $MachinePrecision], N[(N[(y * c), $MachinePrecision] * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.4499999999999999e264 or 7.20000000000000021e-238 < y < 1.04999999999999996e-60

   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. Taylor expanded in y5 around -inf 58.8%

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

   if -1.4499999999999999e264 < y < -1.90000000000000001e33

   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. Taylor expanded in y3 around -inf 57.9%

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

   if -1.90000000000000001e33 < y < -3.4999999999999999e-58 or -1.59999999999999987e-225 < y < -1.25e-274

   1. Initial program 35.1%

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

   2. Taylor expanded in y5 around inf 62.4%

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

      1. mul-1-neg 62.4%

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

      2. associate-*r* 65.9%

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

      3. *-commutative 65.9%

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

   4. Simplified 65.9%

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

   if -3.4999999999999999e-58 < y < -1.59999999999999987e-225 or -1.25e-274 < y < 7.20000000000000021e-238

   1. Initial program 37.9%

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

   2. Taylor expanded in y0 around inf 61.0%

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

      1. +-commutative 61.0%

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

      2. mul-1-neg 61.0%

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

      3. unsub-neg 61.0%

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

      4. *-commutative 61.0%

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

      5. *-commutative 61.0%

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

      6. *-commutative 61.0%

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

      7. *-commutative 61.0%

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

   4. Simplified 61.0%

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

   if 1.04999999999999996e-60 < y < 3.3000000000000002e142

   1. Initial program 41.0%

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

   2. Taylor expanded in y2 around inf 55.1%

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

      1. *-commutative 55.1%

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

   4. Simplified 55.1%

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

   if 3.3000000000000002e142 < y

   1. Initial program 20.8%

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

   2. Taylor expanded in c around inf 35.5%

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

      1. +-commutative 35.5%

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

      2. mul-1-neg 35.5%

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

      3. unsub-neg 35.5%

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

      4. *-commutative 35.5%

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

      5. *-commutative 35.5%

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

      6. *-commutative 35.5%

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

      7. *-commutative 35.5%

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

   4. Simplified 35.5%

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

   5. Taylor expanded in y around -inf 71.2%

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

      1. associate-*r* 65.5%

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

      2. +-commutative 65.5%

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

      3. mul-1-neg 65.5%

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

      4. unsub-neg 65.5%

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

      5. *-commutative 65.5%

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

   7. Simplified 65.5%

      \[\leadsto \color{blue}{\left(c \cdot y\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+264}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+33}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-58}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(i \cdot y5\right) \cdot \left(y \cdot k - t \cdot j\right) + \left(c \cdot y4 - a \cdot y5\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-225}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-274}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(i \cdot y5\right) \cdot \left(y \cdot k - t \cdot j\right) + \left(c \cdot y4 - a \cdot y5\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-238}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-60}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+142}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(c \cdot y4 - a \cdot y5\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \end{array} \]

Alternative 5: 36.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot y3 - t \cdot y2\\ t_2 := c \cdot y4 - a \cdot y5\\ t_3 := j \cdot y3 - k \cdot y2\\ t_4 := y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot t_3\right)\right)\\ t_5 := y0 \cdot y5 - y1 \cdot y4\\ t_6 := y1 \cdot y4 - y0 \cdot y5\\ t_7 := \left(k \cdot y2 - j \cdot y3\right) \cdot t_6\\ t_8 := x \cdot y2 - z \cdot y3\\ \mathbf{if}\;y \leq -2 \cdot 10^{+261}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+39}:\\ \;\;\;\;y3 \cdot \left(y \cdot t_2 + \left(j \cdot t_5 + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-95}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot t_6 + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-184}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot t_5\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-274}:\\ \;\;\;\;t_7 + c \cdot \left(\left(y0 \cdot t_8 + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot t_1\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-239}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot t_8 + y5 \cdot t_3\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-62}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+142}:\\ \;\;\;\;t_7 + \left(x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t_2 \cdot t_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y y3) (* t y2)))
        (t_2 (- (* c y4) (* a y5)))
        (t_3 (- (* j y3) (* k y2)))
        (t_4
         (*
          y5
          (+
           (* a (- (* t y2) (* y y3)))
           (+ (* i (- (* y k) (* t j))) (* y0 t_3)))))
        (t_5 (- (* y0 y5) (* y1 y4)))
        (t_6 (- (* y1 y4) (* y0 y5)))
        (t_7 (* (- (* k y2) (* j y3)) t_6))
        (t_8 (- (* x y2) (* z y3))))
   (if (<= y -2e+261)
     t_4
     (if (<= y -6.8e+39)
       (* y3 (+ (* y t_2) (+ (* j t_5) (* z (- (* a y1) (* c y0))))))
       (if (<= y -9.5e-95)
         (*
          k
          (+
           (+ (* y2 t_6) (* y (- (* i y5) (* b y4))))
           (* z (- (* b y0) (* i y1)))))
         (if (<= y -2.7e-184)
           (*
            j
            (+
             (+ (* t (- (* b y4) (* i y5))) (* y3 t_5))
             (* x (- (* i y1) (* b y0)))))
           (if (<= y -1.6e-274)
             (+
              t_7
              (* c (+ (+ (* y0 t_8) (* i (- (* z t) (* x y)))) (* y4 t_1))))
             (if (<= y 3.6e-239)
               (* y0 (+ (+ (* c t_8) (* y5 t_3)) (* b (- (* z k) (* x j)))))
               (if (<= y 1.35e-62)
                 t_4
                 (if (<= y 3.8e+142)
                   (+ t_7 (+ (* x (* y2 (- (* c y0) (* a y1)))) (* t_2 t_1)))
                   (* (* y c) (- (* y3 y4) (* x i)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * y3) - (t * y2);
	double t_2 = (c * y4) - (a * y5);
	double t_3 = (j * y3) - (k * y2);
	double t_4 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * t_3)));
	double t_5 = (y0 * y5) - (y1 * y4);
	double t_6 = (y1 * y4) - (y0 * y5);
	double t_7 = ((k * y2) - (j * y3)) * t_6;
	double t_8 = (x * y2) - (z * y3);
	double tmp;
	if (y <= -2e+261) {
		tmp = t_4;
	} else if (y <= -6.8e+39) {
		tmp = y3 * ((y * t_2) + ((j * t_5) + (z * ((a * y1) - (c * y0)))));
	} else if (y <= -9.5e-95) {
		tmp = k * (((y2 * t_6) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	} else if (y <= -2.7e-184) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * t_5)) + (x * ((i * y1) - (b * y0))));
	} else if (y <= -1.6e-274) {
		tmp = t_7 + (c * (((y0 * t_8) + (i * ((z * t) - (x * y)))) + (y4 * t_1)));
	} else if (y <= 3.6e-239) {
		tmp = y0 * (((c * t_8) + (y5 * t_3)) + (b * ((z * k) - (x * j))));
	} else if (y <= 1.35e-62) {
		tmp = t_4;
	} else if (y <= 3.8e+142) {
		tmp = t_7 + ((x * (y2 * ((c * y0) - (a * y1)))) + (t_2 * t_1));
	} else {
		tmp = (y * c) * ((y3 * y4) - (x * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_1 = (y * y3) - (t * y2)
    t_2 = (c * y4) - (a * y5)
    t_3 = (j * y3) - (k * y2)
    t_4 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * t_3)))
    t_5 = (y0 * y5) - (y1 * y4)
    t_6 = (y1 * y4) - (y0 * y5)
    t_7 = ((k * y2) - (j * y3)) * t_6
    t_8 = (x * y2) - (z * y3)
    if (y <= (-2d+261)) then
        tmp = t_4
    else if (y <= (-6.8d+39)) then
        tmp = y3 * ((y * t_2) + ((j * t_5) + (z * ((a * y1) - (c * y0)))))
    else if (y <= (-9.5d-95)) then
        tmp = k * (((y2 * t_6) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
    else if (y <= (-2.7d-184)) then
        tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * t_5)) + (x * ((i * y1) - (b * y0))))
    else if (y <= (-1.6d-274)) then
        tmp = t_7 + (c * (((y0 * t_8) + (i * ((z * t) - (x * y)))) + (y4 * t_1)))
    else if (y <= 3.6d-239) then
        tmp = y0 * (((c * t_8) + (y5 * t_3)) + (b * ((z * k) - (x * j))))
    else if (y <= 1.35d-62) then
        tmp = t_4
    else if (y <= 3.8d+142) then
        tmp = t_7 + ((x * (y2 * ((c * y0) - (a * y1)))) + (t_2 * t_1))
    else
        tmp = (y * c) * ((y3 * y4) - (x * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * y3) - (t * y2);
	double t_2 = (c * y4) - (a * y5);
	double t_3 = (j * y3) - (k * y2);
	double t_4 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * t_3)));
	double t_5 = (y0 * y5) - (y1 * y4);
	double t_6 = (y1 * y4) - (y0 * y5);
	double t_7 = ((k * y2) - (j * y3)) * t_6;
	double t_8 = (x * y2) - (z * y3);
	double tmp;
	if (y <= -2e+261) {
		tmp = t_4;
	} else if (y <= -6.8e+39) {
		tmp = y3 * ((y * t_2) + ((j * t_5) + (z * ((a * y1) - (c * y0)))));
	} else if (y <= -9.5e-95) {
		tmp = k * (((y2 * t_6) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	} else if (y <= -2.7e-184) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * t_5)) + (x * ((i * y1) - (b * y0))));
	} else if (y <= -1.6e-274) {
		tmp = t_7 + (c * (((y0 * t_8) + (i * ((z * t) - (x * y)))) + (y4 * t_1)));
	} else if (y <= 3.6e-239) {
		tmp = y0 * (((c * t_8) + (y5 * t_3)) + (b * ((z * k) - (x * j))));
	} else if (y <= 1.35e-62) {
		tmp = t_4;
	} else if (y <= 3.8e+142) {
		tmp = t_7 + ((x * (y2 * ((c * y0) - (a * y1)))) + (t_2 * t_1));
	} else {
		tmp = (y * c) * ((y3 * y4) - (x * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y * y3) - (t * y2)
	t_2 = (c * y4) - (a * y5)
	t_3 = (j * y3) - (k * y2)
	t_4 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * t_3)))
	t_5 = (y0 * y5) - (y1 * y4)
	t_6 = (y1 * y4) - (y0 * y5)
	t_7 = ((k * y2) - (j * y3)) * t_6
	t_8 = (x * y2) - (z * y3)
	tmp = 0
	if y <= -2e+261:
		tmp = t_4
	elif y <= -6.8e+39:
		tmp = y3 * ((y * t_2) + ((j * t_5) + (z * ((a * y1) - (c * y0)))))
	elif y <= -9.5e-95:
		tmp = k * (((y2 * t_6) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
	elif y <= -2.7e-184:
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * t_5)) + (x * ((i * y1) - (b * y0))))
	elif y <= -1.6e-274:
		tmp = t_7 + (c * (((y0 * t_8) + (i * ((z * t) - (x * y)))) + (y4 * t_1)))
	elif y <= 3.6e-239:
		tmp = y0 * (((c * t_8) + (y5 * t_3)) + (b * ((z * k) - (x * j))))
	elif y <= 1.35e-62:
		tmp = t_4
	elif y <= 3.8e+142:
		tmp = t_7 + ((x * (y2 * ((c * y0) - (a * y1)))) + (t_2 * t_1))
	else:
		tmp = (y * c) * ((y3 * y4) - (x * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * y3) - Float64(t * y2))
	t_2 = Float64(Float64(c * y4) - Float64(a * y5))
	t_3 = Float64(Float64(j * y3) - Float64(k * y2))
	t_4 = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * t_3))))
	t_5 = Float64(Float64(y0 * y5) - Float64(y1 * y4))
	t_6 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_7 = Float64(Float64(Float64(k * y2) - Float64(j * y3)) * t_6)
	t_8 = Float64(Float64(x * y2) - Float64(z * y3))
	tmp = 0.0
	if (y <= -2e+261)
		tmp = t_4;
	elseif (y <= -6.8e+39)
		tmp = Float64(y3 * Float64(Float64(y * t_2) + Float64(Float64(j * t_5) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (y <= -9.5e-95)
		tmp = Float64(k * Float64(Float64(Float64(y2 * t_6) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))));
	elseif (y <= -2.7e-184)
		tmp = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * t_5)) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y <= -1.6e-274)
		tmp = Float64(t_7 + Float64(c * Float64(Float64(Float64(y0 * t_8) + Float64(i * Float64(Float64(z * t) - Float64(x * y)))) + Float64(y4 * t_1))));
	elseif (y <= 3.6e-239)
		tmp = Float64(y0 * Float64(Float64(Float64(c * t_8) + Float64(y5 * t_3)) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y <= 1.35e-62)
		tmp = t_4;
	elseif (y <= 3.8e+142)
		tmp = Float64(t_7 + Float64(Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t_2 * t_1)));
	else
		tmp = Float64(Float64(y * c) * Float64(Float64(y3 * y4) - Float64(x * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y * y3) - (t * y2);
	t_2 = (c * y4) - (a * y5);
	t_3 = (j * y3) - (k * y2);
	t_4 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * t_3)));
	t_5 = (y0 * y5) - (y1 * y4);
	t_6 = (y1 * y4) - (y0 * y5);
	t_7 = ((k * y2) - (j * y3)) * t_6;
	t_8 = (x * y2) - (z * y3);
	tmp = 0.0;
	if (y <= -2e+261)
		tmp = t_4;
	elseif (y <= -6.8e+39)
		tmp = y3 * ((y * t_2) + ((j * t_5) + (z * ((a * y1) - (c * y0)))));
	elseif (y <= -9.5e-95)
		tmp = k * (((y2 * t_6) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	elseif (y <= -2.7e-184)
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * t_5)) + (x * ((i * y1) - (b * y0))));
	elseif (y <= -1.6e-274)
		tmp = t_7 + (c * (((y0 * t_8) + (i * ((z * t) - (x * y)))) + (y4 * t_1)));
	elseif (y <= 3.6e-239)
		tmp = y0 * (((c * t_8) + (y5 * t_3)) + (b * ((z * k) - (x * j))));
	elseif (y <= 1.35e-62)
		tmp = t_4;
	elseif (y <= 3.8e+142)
		tmp = t_7 + ((x * (y2 * ((c * y0) - (a * y1)))) + (t_2 * t_1));
	else
		tmp = (y * c) * ((y3 * y4) - (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * t$95$6), $MachinePrecision]}, Block[{t$95$8 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+261], t$95$4, If[LessEqual[y, -6.8e+39], N[(y3 * N[(N[(y * t$95$2), $MachinePrecision] + N[(N[(j * t$95$5), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.5e-95], N[(k * N[(N[(N[(y2 * t$95$6), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.7e-184], N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * t$95$5), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.6e-274], N[(t$95$7 + N[(c * N[(N[(N[(y0 * t$95$8), $MachinePrecision] + N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e-239], N[(y0 * N[(N[(N[(c * t$95$8), $MachinePrecision] + N[(y5 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e-62], t$95$4, If[LessEqual[y, 3.8e+142], N[(t$95$7 + N[(N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * c), $MachinePrecision] * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y < -1.9999999999999999e261 or 3.6000000000000001e-239 < y < 1.3500000000000001e-62

   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. Taylor expanded in y5 around -inf 58.8%

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

   if -1.9999999999999999e261 < y < -6.7999999999999998e39

   1. Initial program 36.2%

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

   2. Taylor expanded in y3 around -inf 58.3%

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

   if -6.7999999999999998e39 < y < -9.49999999999999998e-95

   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. Taylor expanded in k around inf 57.7%

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

      1. sub-neg 57.7%

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

      2. +-commutative 57.7%

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

      3. mul-1-neg 57.7%

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

      4. unsub-neg 57.7%

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

      5. *-commutative 57.7%

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

      6. mul-1-neg 57.7%

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

      7. remove-double-neg 57.7%

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

   4. Simplified 57.7%

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

   if -9.49999999999999998e-95 < y < -2.7000000000000001e-184

   1. Initial program 31.6%

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

   2. Taylor expanded in j around inf 63.7%

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

      1. +-commutative 63.7%

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

      2. mul-1-neg 63.7%

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

      3. unsub-neg 63.7%

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

      4. *-commutative 63.7%

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

   4. Simplified 63.7%

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

   if -2.7000000000000001e-184 < y < -1.59999999999999989e-274

   1. Initial program 35.6%

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

   2. Taylor expanded in c around inf 65.3%

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

      1. +-commutative 65.3%

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

      2. mul-1-neg 65.3%

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

      3. unsub-neg 65.3%

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

      4. *-commutative 65.3%

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

      5. *-commutative 65.3%

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

      6. *-commutative 65.3%

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

      7. *-commutative 65.3%

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

   4. Simplified 65.3%

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

   if -1.59999999999999989e-274 < y < 3.6000000000000001e-239

   1. Initial program 39.1%

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

   2. Taylor expanded in y0 around inf 67.2%

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

      1. +-commutative 67.2%

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

      2. mul-1-neg 67.2%

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

      3. unsub-neg 67.2%

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

      4. *-commutative 67.2%

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

      5. *-commutative 67.2%

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

      6. *-commutative 67.2%

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

      7. *-commutative 67.2%

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

   4. Simplified 67.2%

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

   if 1.3500000000000001e-62 < y < 3.7999999999999999e142

   1. Initial program 41.0%

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

   2. Taylor expanded in y2 around inf 55.1%

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

      1. *-commutative 55.1%

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

   4. Simplified 55.1%

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

   if 3.7999999999999999e142 < y

   1. Initial program 20.8%

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

   2. Taylor expanded in c around inf 35.5%

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

      1. +-commutative 35.5%

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

      2. mul-1-neg 35.5%

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

      3. unsub-neg 35.5%

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

      4. *-commutative 35.5%

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

      5. *-commutative 35.5%

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

      6. *-commutative 35.5%

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

      7. *-commutative 35.5%

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

   4. Simplified 35.5%

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

   5. Taylor expanded in y around -inf 71.2%

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

      1. associate-*r* 65.5%

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

      2. +-commutative 65.5%

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

      3. mul-1-neg 65.5%

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

      4. unsub-neg 65.5%

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

      5. *-commutative 65.5%

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

   7. Simplified 65.5%

      \[\leadsto \color{blue}{\left(c \cdot y\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+261}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+39}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-95}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-184}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-274}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-239}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-62}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+142}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + \left(c \cdot y4 - a \cdot y5\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \end{array} \]

Alternative 6: 39.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\\ t_2 := j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_3 := y0 \cdot \left(t_1 + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;j \leq -2.45 \cdot 10^{+92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-23}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq -3.25 \cdot 10^{-87}:\\ \;\;\;\;y0 \cdot t_1\\ \mathbf{elif}\;j \leq -1.2 \cdot 10^{-131}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{-213}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 1.06 \cdot 10^{-292}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-253}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-193}:\\ \;\;\;\;y \cdot \left(i \cdot \left(k \cdot y5\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-133}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 6.8 \cdot 10^{+94}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (+ (* c (- (* x y2) (* z y3))) (* y5 (- (* j y3) (* k y2)))))
        (t_2
         (*
          j
          (+
           (+ (* t (- (* b y4) (* i y5))) (* y3 (- (* y0 y5) (* y1 y4))))
           (* x (- (* i y1) (* b y0))))))
        (t_3 (* y0 (+ t_1 (* b (- (* z k) (* x j)))))))
   (if (<= j -2.45e+92)
     t_2
     (if (<= j -3.7e-23)
       (* y1 (+ (* i (- (* x j) (* z k))) (* y4 (- (* k y2) (* j y3)))))
       (if (<= j -3.25e-87)
         (* y0 t_1)
         (if (<= j -1.2e-131)
           (* i (* y5 (- (* y k) (* t j))))
           (if (<= j -1.8e-213)
             t_3
             (if (<= j 1.06e-292)
               (* a (* y5 (- (* t y2) (* y y3))))
               (if (<= j 6.2e-253)
                 t_3
                 (if (<= j 2.3e-193)
                   (* y (+ (* i (* k y5)) (* y3 (- (* c y4) (* a y5)))))
                   (if (<= j 1.7e-133)
                     (* c (* z (- (* t i) (* y0 y3))))
                     (if (<= j 6.8e+94) t_3 t_2))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)));
	double t_2 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	double t_3 = y0 * (t_1 + (b * ((z * k) - (x * j))));
	double tmp;
	if (j <= -2.45e+92) {
		tmp = t_2;
	} else if (j <= -3.7e-23) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3))));
	} else if (j <= -3.25e-87) {
		tmp = y0 * t_1;
	} else if (j <= -1.2e-131) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (j <= -1.8e-213) {
		tmp = t_3;
	} else if (j <= 1.06e-292) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (j <= 6.2e-253) {
		tmp = t_3;
	} else if (j <= 2.3e-193) {
		tmp = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))));
	} else if (j <= 1.7e-133) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else if (j <= 6.8e+94) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))
    t_2 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
    t_3 = y0 * (t_1 + (b * ((z * k) - (x * j))))
    if (j <= (-2.45d+92)) then
        tmp = t_2
    else if (j <= (-3.7d-23)) then
        tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3))))
    else if (j <= (-3.25d-87)) then
        tmp = y0 * t_1
    else if (j <= (-1.2d-131)) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (j <= (-1.8d-213)) then
        tmp = t_3
    else if (j <= 1.06d-292) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (j <= 6.2d-253) then
        tmp = t_3
    else if (j <= 2.3d-193) then
        tmp = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))))
    else if (j <= 1.7d-133) then
        tmp = c * (z * ((t * i) - (y0 * y3)))
    else if (j <= 6.8d+94) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)));
	double t_2 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	double t_3 = y0 * (t_1 + (b * ((z * k) - (x * j))));
	double tmp;
	if (j <= -2.45e+92) {
		tmp = t_2;
	} else if (j <= -3.7e-23) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3))));
	} else if (j <= -3.25e-87) {
		tmp = y0 * t_1;
	} else if (j <= -1.2e-131) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (j <= -1.8e-213) {
		tmp = t_3;
	} else if (j <= 1.06e-292) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (j <= 6.2e-253) {
		tmp = t_3;
	} else if (j <= 2.3e-193) {
		tmp = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))));
	} else if (j <= 1.7e-133) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else if (j <= 6.8e+94) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))
	t_2 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
	t_3 = y0 * (t_1 + (b * ((z * k) - (x * j))))
	tmp = 0
	if j <= -2.45e+92:
		tmp = t_2
	elif j <= -3.7e-23:
		tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3))))
	elif j <= -3.25e-87:
		tmp = y0 * t_1
	elif j <= -1.2e-131:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif j <= -1.8e-213:
		tmp = t_3
	elif j <= 1.06e-292:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif j <= 6.2e-253:
		tmp = t_3
	elif j <= 2.3e-193:
		tmp = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))))
	elif j <= 1.7e-133:
		tmp = c * (z * ((t * i) - (y0 * y3)))
	elif j <= 6.8e+94:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))))
	t_2 = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_3 = Float64(y0 * Float64(t_1 + Float64(b * Float64(Float64(z * k) - Float64(x * j)))))
	tmp = 0.0
	if (j <= -2.45e+92)
		tmp = t_2;
	elseif (j <= -3.7e-23)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3)))));
	elseif (j <= -3.25e-87)
		tmp = Float64(y0 * t_1);
	elseif (j <= -1.2e-131)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (j <= -1.8e-213)
		tmp = t_3;
	elseif (j <= 1.06e-292)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (j <= 6.2e-253)
		tmp = t_3;
	elseif (j <= 2.3e-193)
		tmp = Float64(y * Float64(Float64(i * Float64(k * y5)) + Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5)))));
	elseif (j <= 1.7e-133)
		tmp = Float64(c * Float64(z * Float64(Float64(t * i) - Float64(y0 * y3))));
	elseif (j <= 6.8e+94)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)));
	t_2 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	t_3 = y0 * (t_1 + (b * ((z * k) - (x * j))));
	tmp = 0.0;
	if (j <= -2.45e+92)
		tmp = t_2;
	elseif (j <= -3.7e-23)
		tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3))));
	elseif (j <= -3.25e-87)
		tmp = y0 * t_1;
	elseif (j <= -1.2e-131)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (j <= -1.8e-213)
		tmp = t_3;
	elseif (j <= 1.06e-292)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (j <= 6.2e-253)
		tmp = t_3;
	elseif (j <= 2.3e-193)
		tmp = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))));
	elseif (j <= 1.7e-133)
		tmp = c * (z * ((t * i) - (y0 * y3)));
	elseif (j <= 6.8e+94)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y0 * N[(t$95$1 + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.45e+92], t$95$2, If[LessEqual[j, -3.7e-23], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.25e-87], N[(y0 * t$95$1), $MachinePrecision], If[LessEqual[j, -1.2e-131], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.8e-213], t$95$3, If[LessEqual[j, 1.06e-292], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.2e-253], t$95$3, If[LessEqual[j, 2.3e-193], N[(y * N[(N[(i * N[(k * y5), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.7e-133], N[(c * N[(z * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.8e+94], t$95$3, t$95$2]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if j < -2.4500000000000001e92 or 6.8000000000000004e94 < j

   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. Taylor expanded in j around inf 68.6%

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

      1. +-commutative 68.6%

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

      2. mul-1-neg 68.6%

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

      3. unsub-neg 68.6%

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

      4. *-commutative 68.6%

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

   4. Simplified 68.6%

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

   if -2.4500000000000001e92 < j < -3.7000000000000003e-23

   1. Initial program 21.7%

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

   2. Taylor expanded in y1 around -inf 48.6%

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

      1. mul-1-neg 48.6%

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

      2. *-commutative 48.6%

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

      3. distribute-rgt-neg-in 48.6%

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

   4. Simplified 48.6%

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

   5. Taylor expanded in a around 0 52.9%

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

   if -3.7000000000000003e-23 < j < -3.2500000000000001e-87

   1. Initial program 49.8%

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

   2. Taylor expanded in c around inf 38.8%

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

      1. +-commutative 38.8%

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

      2. mul-1-neg 38.8%

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

      3. unsub-neg 38.8%

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

      4. *-commutative 38.8%

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

      5. *-commutative 38.8%

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

      6. *-commutative 38.8%

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

      7. *-commutative 38.8%

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

   4. Simplified 38.8%

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

   5. Taylor expanded in y0 around inf 51.4%

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

      1. +-commutative 51.4%

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

      2. mul-1-neg 51.4%

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

      3. *-commutative 51.4%

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

      4. *-commutative 51.4%

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

      5. *-commutative 51.4%

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

      6. unsub-neg 51.4%

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

      7. *-commutative 51.4%

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

      8. *-commutative 51.4%

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

      9. *-commutative 51.4%

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

      10. *-commutative 51.4%

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

   7. Simplified 51.4%

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

   if -3.2500000000000001e-87 < j < -1.2e-131

   1. Initial program 45.1%

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

   2. Taylor expanded in y5 around inf 66.6%

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

      1. mul-1-neg 66.6%

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

      2. associate-*r* 55.6%

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

      3. *-commutative 55.6%

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

   4. Simplified 55.6%

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

   5. Taylor expanded in i around inf 78.2%

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

   if -1.2e-131 < j < -1.8e-213 or 1.05999999999999997e-292 < j < 6.19999999999999991e-253 or 1.70000000000000003e-133 < j < 6.8000000000000004e94

   1. Initial program 40.3%

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

   2. Taylor expanded in y0 around inf 58.3%

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

      1. +-commutative 58.3%

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

      2. mul-1-neg 58.3%

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

      3. unsub-neg 58.3%

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

      4. *-commutative 58.3%

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

      5. *-commutative 58.3%

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

      6. *-commutative 58.3%

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

      7. *-commutative 58.3%

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

   4. Simplified 58.3%

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

   if -1.8e-213 < j < 1.05999999999999997e-292

   1. Initial program 37.7%

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

   2. Taylor expanded in y5 around inf 33.7%

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

      1. mul-1-neg 33.7%

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

      2. associate-*r* 37.9%

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

      3. *-commutative 37.9%

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

   4. Simplified 37.9%

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

   5. Taylor expanded in a around inf 47.2%

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

      1. *-commutative 47.2%

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

   7. Simplified 47.2%

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

   if 6.19999999999999991e-253 < j < 2.30000000000000009e-193

   1. Initial program 50.0%

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

   2. Taylor expanded in y5 around inf 57.5%

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

      1. mul-1-neg 57.5%

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

      2. associate-*r* 50.4%

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

      3. *-commutative 50.4%

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

   4. Simplified 50.4%

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

   5. Taylor expanded in y around -inf 72.2%

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

   if 2.30000000000000009e-193 < j < 1.70000000000000003e-133

   1. Initial program 40.0%

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

   2. Taylor expanded in c around inf 13.9%

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

      1. +-commutative 13.9%

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

      2. mul-1-neg 13.9%

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

      3. unsub-neg 13.9%

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

      4. *-commutative 13.9%

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

      5. *-commutative 13.9%

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

      6. *-commutative 13.9%

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

      7. *-commutative 13.9%

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

   4. Simplified 13.9%

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

   5. Taylor expanded in z around inf 54.0%

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

      1. distribute-lft-out-- 54.0%

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

      2. *-commutative 54.0%

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

   7. Simplified 54.0%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-1 \cdot \left(y3 \cdot y0 - i \cdot t\right)\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.45 \cdot 10^{+92}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-23}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq -3.25 \cdot 10^{-87}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq -1.2 \cdot 10^{-131}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{-213}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 1.06 \cdot 10^{-292}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-253}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-193}:\\ \;\;\;\;y \cdot \left(i \cdot \left(k \cdot y5\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-133}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 6.8 \cdot 10^{+94}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]

Alternative 7: 40.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_2 := y1 \cdot y4 - y0 \cdot y5\\ t_3 := k \cdot y2 - j \cdot y3\\ t_4 := y2 \cdot \left(k \cdot t_2 + c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{if}\;j \leq -6.5 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.35 \cdot 10^{-23}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot t_3\right)\\ \mathbf{elif}\;j \leq -3 \cdot 10^{-82}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq -1.16 \cdot 10^{-131}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -2.4 \cdot 10^{-179}:\\ \;\;\;\;t_3 \cdot t_2 + t \cdot \left(i \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{-134}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-100}:\\ \;\;\;\;y \cdot \left(i \cdot \left(k \cdot y5\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{+54}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq 8.6 \cdot 10^{+87}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(-x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          j
          (+
           (+ (* t (- (* b y4) (* i y5))) (* y3 (- (* y0 y5) (* y1 y4))))
           (* x (- (* i y1) (* b y0))))))
        (t_2 (- (* y1 y4) (* y0 y5)))
        (t_3 (- (* k y2) (* j y3)))
        (t_4 (* y2 (+ (* k t_2) (* c (- (* x y0) (* t y4)))))))
   (if (<= j -6.5e+90)
     t_1
     (if (<= j -2.35e-23)
       (* y1 (+ (* i (- (* x j) (* z k))) (* y4 t_3)))
       (if (<= j -3e-82)
         (* y0 (+ (* c (- (* x y2) (* z y3))) (* y5 (- (* j y3) (* k y2)))))
         (if (<= j -1.16e-131)
           (* i (* y5 (- (* y k) (* t j))))
           (if (<= j -2.4e-179)
             (+ (* t_3 t_2) (* t (* i (- (* z c) (* j y5)))))
             (if (<= j 1.65e-134)
               t_4
               (if (<= j 4.8e-100)
                 (* y (+ (* i (* k y5)) (* y3 (- (* c y4) (* a y5)))))
                 (if (<= j 2.3e+54)
                   t_4
                   (if (<= j 8.6e+87) (* a (* y1 (- (* x 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 * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	double t_2 = (y1 * y4) - (y0 * y5);
	double t_3 = (k * y2) - (j * y3);
	double t_4 = y2 * ((k * t_2) + (c * ((x * y0) - (t * y4))));
	double tmp;
	if (j <= -6.5e+90) {
		tmp = t_1;
	} else if (j <= -2.35e-23) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * t_3));
	} else if (j <= -3e-82) {
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2))));
	} else if (j <= -1.16e-131) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (j <= -2.4e-179) {
		tmp = (t_3 * t_2) + (t * (i * ((z * c) - (j * y5))));
	} else if (j <= 1.65e-134) {
		tmp = t_4;
	} else if (j <= 4.8e-100) {
		tmp = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))));
	} else if (j <= 2.3e+54) {
		tmp = t_4;
	} else if (j <= 8.6e+87) {
		tmp = a * (y1 * -(x * 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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
    t_2 = (y1 * y4) - (y0 * y5)
    t_3 = (k * y2) - (j * y3)
    t_4 = y2 * ((k * t_2) + (c * ((x * y0) - (t * y4))))
    if (j <= (-6.5d+90)) then
        tmp = t_1
    else if (j <= (-2.35d-23)) then
        tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * t_3))
    else if (j <= (-3d-82)) then
        tmp = y0 * ((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2))))
    else if (j <= (-1.16d-131)) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (j <= (-2.4d-179)) then
        tmp = (t_3 * t_2) + (t * (i * ((z * c) - (j * y5))))
    else if (j <= 1.65d-134) then
        tmp = t_4
    else if (j <= 4.8d-100) then
        tmp = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))))
    else if (j <= 2.3d+54) then
        tmp = t_4
    else if (j <= 8.6d+87) then
        tmp = a * (y1 * -(x * 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 * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	double t_2 = (y1 * y4) - (y0 * y5);
	double t_3 = (k * y2) - (j * y3);
	double t_4 = y2 * ((k * t_2) + (c * ((x * y0) - (t * y4))));
	double tmp;
	if (j <= -6.5e+90) {
		tmp = t_1;
	} else if (j <= -2.35e-23) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * t_3));
	} else if (j <= -3e-82) {
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2))));
	} else if (j <= -1.16e-131) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (j <= -2.4e-179) {
		tmp = (t_3 * t_2) + (t * (i * ((z * c) - (j * y5))));
	} else if (j <= 1.65e-134) {
		tmp = t_4;
	} else if (j <= 4.8e-100) {
		tmp = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))));
	} else if (j <= 2.3e+54) {
		tmp = t_4;
	} else if (j <= 8.6e+87) {
		tmp = a * (y1 * -(x * 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 * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
	t_2 = (y1 * y4) - (y0 * y5)
	t_3 = (k * y2) - (j * y3)
	t_4 = y2 * ((k * t_2) + (c * ((x * y0) - (t * y4))))
	tmp = 0
	if j <= -6.5e+90:
		tmp = t_1
	elif j <= -2.35e-23:
		tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * t_3))
	elif j <= -3e-82:
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2))))
	elif j <= -1.16e-131:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif j <= -2.4e-179:
		tmp = (t_3 * t_2) + (t * (i * ((z * c) - (j * y5))))
	elif j <= 1.65e-134:
		tmp = t_4
	elif j <= 4.8e-100:
		tmp = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))))
	elif j <= 2.3e+54:
		tmp = t_4
	elif j <= 8.6e+87:
		tmp = a * (y1 * -(x * 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(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_2 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_3 = Float64(Float64(k * y2) - Float64(j * y3))
	t_4 = Float64(y2 * Float64(Float64(k * t_2) + Float64(c * Float64(Float64(x * y0) - Float64(t * y4)))))
	tmp = 0.0
	if (j <= -6.5e+90)
		tmp = t_1;
	elseif (j <= -2.35e-23)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(y4 * t_3)));
	elseif (j <= -3e-82)
		tmp = Float64(y0 * Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2)))));
	elseif (j <= -1.16e-131)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (j <= -2.4e-179)
		tmp = Float64(Float64(t_3 * t_2) + Float64(t * Float64(i * Float64(Float64(z * c) - Float64(j * y5)))));
	elseif (j <= 1.65e-134)
		tmp = t_4;
	elseif (j <= 4.8e-100)
		tmp = Float64(y * Float64(Float64(i * Float64(k * y5)) + Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5)))));
	elseif (j <= 2.3e+54)
		tmp = t_4;
	elseif (j <= 8.6e+87)
		tmp = Float64(a * Float64(y1 * Float64(-Float64(x * 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 * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	t_2 = (y1 * y4) - (y0 * y5);
	t_3 = (k * y2) - (j * y3);
	t_4 = y2 * ((k * t_2) + (c * ((x * y0) - (t * y4))));
	tmp = 0.0;
	if (j <= -6.5e+90)
		tmp = t_1;
	elseif (j <= -2.35e-23)
		tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * t_3));
	elseif (j <= -3e-82)
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2))));
	elseif (j <= -1.16e-131)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (j <= -2.4e-179)
		tmp = (t_3 * t_2) + (t * (i * ((z * c) - (j * y5))));
	elseif (j <= 1.65e-134)
		tmp = t_4;
	elseif (j <= 4.8e-100)
		tmp = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))));
	elseif (j <= 2.3e+54)
		tmp = t_4;
	elseif (j <= 8.6e+87)
		tmp = a * (y1 * -(x * 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[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y2 * N[(N[(k * t$95$2), $MachinePrecision] + N[(c * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6.5e+90], t$95$1, If[LessEqual[j, -2.35e-23], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3e-82], N[(y0 * N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.16e-131], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.4e-179], N[(N[(t$95$3 * t$95$2), $MachinePrecision] + N[(t * N[(i * N[(N[(z * c), $MachinePrecision] - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.65e-134], t$95$4, If[LessEqual[j, 4.8e-100], N[(y * N[(N[(i * N[(k * y5), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.3e+54], t$95$4, If[LessEqual[j, 8.6e+87], N[(a * N[(y1 * (-N[(x * y2), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if j < -6.5000000000000001e90 or 8.6000000000000002e87 < j

   1. Initial program 28.3%

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

   2. Taylor expanded in j around inf 67.9%

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

      1. +-commutative 67.9%

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

      2. mul-1-neg 67.9%

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

      3. unsub-neg 67.9%

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

      4. *-commutative 67.9%

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

   4. Simplified 67.9%

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

   if -6.5000000000000001e90 < j < -2.35e-23

   1. Initial program 21.7%

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

   2. Taylor expanded in y1 around -inf 48.6%

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

      1. mul-1-neg 48.6%

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

      2. *-commutative 48.6%

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

      3. distribute-rgt-neg-in 48.6%

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

   4. Simplified 48.6%

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

   5. Taylor expanded in a around 0 52.9%

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

   if -2.35e-23 < j < -2.9999999999999999e-82

   1. Initial program 49.8%

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

   2. Taylor expanded in c around inf 38.8%

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

      1. +-commutative 38.8%

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

      2. mul-1-neg 38.8%

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

      3. unsub-neg 38.8%

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

      4. *-commutative 38.8%

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

      5. *-commutative 38.8%

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

      6. *-commutative 38.8%

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

      7. *-commutative 38.8%

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

   4. Simplified 38.8%

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

   5. Taylor expanded in y0 around inf 51.4%

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

      1. +-commutative 51.4%

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

      2. mul-1-neg 51.4%

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

      3. *-commutative 51.4%

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

      4. *-commutative 51.4%

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

      5. *-commutative 51.4%

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

      6. unsub-neg 51.4%

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

      7. *-commutative 51.4%

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

      8. *-commutative 51.4%

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

      9. *-commutative 51.4%

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

      10. *-commutative 51.4%

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

   7. Simplified 51.4%

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

   if -2.9999999999999999e-82 < j < -1.15999999999999993e-131

   1. Initial program 45.1%

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

   2. Taylor expanded in y5 around inf 66.6%

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

      1. mul-1-neg 66.6%

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

      2. associate-*r* 55.6%

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

      3. *-commutative 55.6%

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

   4. Simplified 55.6%

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

   5. Taylor expanded in i around inf 78.2%

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

   if -1.15999999999999993e-131 < j < -2.4e-179

   1. Initial program 44.4%

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

   2. Taylor expanded in t around inf 77.8%

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

   3. Taylor expanded in i around inf 56.6%

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

      1. +-commutative 56.6%

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

      2. mul-1-neg 56.6%

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

      3. unsub-neg 56.6%

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

      4. *-commutative 56.6%

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

   5. Simplified 56.6%

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

   if -2.4e-179 < j < 1.6500000000000001e-134 or 4.8000000000000005e-100 < j < 2.29999999999999994e54

   1. Initial program 40.0%

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

   2. Taylor expanded in c around inf 50.1%

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

      1. +-commutative 50.1%

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

      2. mul-1-neg 50.1%

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

      3. unsub-neg 50.1%

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

      4. *-commutative 50.1%

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

      5. *-commutative 50.1%

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

      6. *-commutative 50.1%

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

      7. *-commutative 50.1%

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

   4. Simplified 50.1%

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

   5. Taylor expanded in y2 around inf 50.3%

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

   if 1.6500000000000001e-134 < j < 4.8000000000000005e-100

   1. Initial program 40.6%

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

   2. Taylor expanded in y5 around inf 41.0%

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

      1. mul-1-neg 41.0%

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

      2. associate-*r* 41.0%

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

      3. *-commutative 41.0%

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

   4. Simplified 41.0%

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

   5. Taylor expanded in y around -inf 80.1%

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

   if 2.29999999999999994e54 < j < 8.6000000000000002e87

   1. Initial program 40.0%

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

   2. Taylor expanded in y1 around -inf 40.8%

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

      1. mul-1-neg 40.8%

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

      2. *-commutative 40.8%

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

      3. distribute-rgt-neg-in 40.8%

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

   4. Simplified 40.8%

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

   5. Taylor expanded in a around inf 80.5%

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

      1. associate-*r* 80.5%

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

      2. neg-mul-1 80.5%

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

   7. Simplified 80.5%

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

   8. Taylor expanded in x around inf 80.5%

      \[\leadsto \left(-a\right) \cdot \left(y1 \cdot \color{blue}{\left(x \cdot y2\right)}\right) \]
3. Recombined 8 regimes into one program.

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.5 \cdot 10^{+90}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -2.35 \cdot 10^{-23}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq -3 \cdot 10^{-82}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq -1.16 \cdot 10^{-131}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -2.4 \cdot 10^{-179}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(i \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{-134}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-100}:\\ \;\;\;\;y \cdot \left(i \cdot \left(k \cdot y5\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{+54}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 8.6 \cdot 10^{+87}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(-x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]

Alternative 8: 41.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\\ t_2 := j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_3 := y1 \cdot y4 - y0 \cdot y5\\ t_4 := k \cdot t_3\\ t_5 := k \cdot y2 - j \cdot y3\\ \mathbf{if}\;j \leq -5.2 \cdot 10^{+91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -9.6 \cdot 10^{-21}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot t_5\right)\\ \mathbf{elif}\;j \leq -2.5 \cdot 10^{-66}:\\ \;\;\;\;y0 \cdot t_1\\ \mathbf{elif}\;j \leq -1.08 \cdot 10^{-131}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -2.3 \cdot 10^{-180}:\\ \;\;\;\;t_5 \cdot t_3 + t \cdot \left(i \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{-294}:\\ \;\;\;\;y2 \cdot \left(t_4 + c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{-270}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-131}:\\ \;\;\;\;y2 \cdot \left(\left(t_4 + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 8.7 \cdot 10^{+99}:\\ \;\;\;\;y0 \cdot \left(t_1 + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (+ (* c (- (* x y2) (* z y3))) (* y5 (- (* j y3) (* k y2)))))
        (t_2
         (*
          j
          (+
           (+ (* t (- (* b y4) (* i y5))) (* y3 (- (* y0 y5) (* y1 y4))))
           (* x (- (* i y1) (* b y0))))))
        (t_3 (- (* y1 y4) (* y0 y5)))
        (t_4 (* k t_3))
        (t_5 (- (* k y2) (* j y3))))
   (if (<= j -5.2e+91)
     t_2
     (if (<= j -9.6e-21)
       (* y1 (+ (* i (- (* x j) (* z k))) (* y4 t_5)))
       (if (<= j -2.5e-66)
         (* y0 t_1)
         (if (<= j -1.08e-131)
           (* i (* y5 (- (* y k) (* t j))))
           (if (<= j -2.3e-180)
             (+ (* t_5 t_3) (* t (* i (- (* z c) (* j y5)))))
             (if (<= j 5.2e-294)
               (* y2 (+ t_4 (* c (- (* x y0) (* t y4)))))
               (if (<= j 1.75e-270)
                 (* b (* k (- (* z y0) (* y y4))))
                 (if (<= j 2.6e-131)
                   (*
                    y2
                    (+
                     (+ t_4 (* x (- (* c y0) (* a y1))))
                     (* t (- (* a y5) (* c y4)))))
                   (if (<= j 8.7e+99)
                     (* y0 (+ t_1 (* b (- (* z k) (* x j)))))
                     t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)));
	double t_2 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	double t_3 = (y1 * y4) - (y0 * y5);
	double t_4 = k * t_3;
	double t_5 = (k * y2) - (j * y3);
	double tmp;
	if (j <= -5.2e+91) {
		tmp = t_2;
	} else if (j <= -9.6e-21) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * t_5));
	} else if (j <= -2.5e-66) {
		tmp = y0 * t_1;
	} else if (j <= -1.08e-131) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (j <= -2.3e-180) {
		tmp = (t_5 * t_3) + (t * (i * ((z * c) - (j * y5))));
	} else if (j <= 5.2e-294) {
		tmp = y2 * (t_4 + (c * ((x * y0) - (t * y4))));
	} else if (j <= 1.75e-270) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (j <= 2.6e-131) {
		tmp = y2 * ((t_4 + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (j <= 8.7e+99) {
		tmp = y0 * (t_1 + (b * ((z * k) - (x * j))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))
    t_2 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
    t_3 = (y1 * y4) - (y0 * y5)
    t_4 = k * t_3
    t_5 = (k * y2) - (j * y3)
    if (j <= (-5.2d+91)) then
        tmp = t_2
    else if (j <= (-9.6d-21)) then
        tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * t_5))
    else if (j <= (-2.5d-66)) then
        tmp = y0 * t_1
    else if (j <= (-1.08d-131)) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (j <= (-2.3d-180)) then
        tmp = (t_5 * t_3) + (t * (i * ((z * c) - (j * y5))))
    else if (j <= 5.2d-294) then
        tmp = y2 * (t_4 + (c * ((x * y0) - (t * y4))))
    else if (j <= 1.75d-270) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (j <= 2.6d-131) then
        tmp = y2 * ((t_4 + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    else if (j <= 8.7d+99) then
        tmp = y0 * (t_1 + (b * ((z * k) - (x * j))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)));
	double t_2 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	double t_3 = (y1 * y4) - (y0 * y5);
	double t_4 = k * t_3;
	double t_5 = (k * y2) - (j * y3);
	double tmp;
	if (j <= -5.2e+91) {
		tmp = t_2;
	} else if (j <= -9.6e-21) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * t_5));
	} else if (j <= -2.5e-66) {
		tmp = y0 * t_1;
	} else if (j <= -1.08e-131) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (j <= -2.3e-180) {
		tmp = (t_5 * t_3) + (t * (i * ((z * c) - (j * y5))));
	} else if (j <= 5.2e-294) {
		tmp = y2 * (t_4 + (c * ((x * y0) - (t * y4))));
	} else if (j <= 1.75e-270) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (j <= 2.6e-131) {
		tmp = y2 * ((t_4 + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (j <= 8.7e+99) {
		tmp = y0 * (t_1 + (b * ((z * k) - (x * j))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))
	t_2 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
	t_3 = (y1 * y4) - (y0 * y5)
	t_4 = k * t_3
	t_5 = (k * y2) - (j * y3)
	tmp = 0
	if j <= -5.2e+91:
		tmp = t_2
	elif j <= -9.6e-21:
		tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * t_5))
	elif j <= -2.5e-66:
		tmp = y0 * t_1
	elif j <= -1.08e-131:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif j <= -2.3e-180:
		tmp = (t_5 * t_3) + (t * (i * ((z * c) - (j * y5))))
	elif j <= 5.2e-294:
		tmp = y2 * (t_4 + (c * ((x * y0) - (t * y4))))
	elif j <= 1.75e-270:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif j <= 2.6e-131:
		tmp = y2 * ((t_4 + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	elif j <= 8.7e+99:
		tmp = y0 * (t_1 + (b * ((z * k) - (x * j))))
	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(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))))
	t_2 = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_3 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_4 = Float64(k * t_3)
	t_5 = Float64(Float64(k * y2) - Float64(j * y3))
	tmp = 0.0
	if (j <= -5.2e+91)
		tmp = t_2;
	elseif (j <= -9.6e-21)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(y4 * t_5)));
	elseif (j <= -2.5e-66)
		tmp = Float64(y0 * t_1);
	elseif (j <= -1.08e-131)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (j <= -2.3e-180)
		tmp = Float64(Float64(t_5 * t_3) + Float64(t * Float64(i * Float64(Float64(z * c) - Float64(j * y5)))));
	elseif (j <= 5.2e-294)
		tmp = Float64(y2 * Float64(t_4 + Float64(c * Float64(Float64(x * y0) - Float64(t * y4)))));
	elseif (j <= 1.75e-270)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (j <= 2.6e-131)
		tmp = Float64(y2 * Float64(Float64(t_4 + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (j <= 8.7e+99)
		tmp = Float64(y0 * Float64(t_1 + Float64(b * Float64(Float64(z * k) - Float64(x * j)))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)));
	t_2 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	t_3 = (y1 * y4) - (y0 * y5);
	t_4 = k * t_3;
	t_5 = (k * y2) - (j * y3);
	tmp = 0.0;
	if (j <= -5.2e+91)
		tmp = t_2;
	elseif (j <= -9.6e-21)
		tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * t_5));
	elseif (j <= -2.5e-66)
		tmp = y0 * t_1;
	elseif (j <= -1.08e-131)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (j <= -2.3e-180)
		tmp = (t_5 * t_3) + (t * (i * ((z * c) - (j * y5))));
	elseif (j <= 5.2e-294)
		tmp = y2 * (t_4 + (c * ((x * y0) - (t * y4))));
	elseif (j <= 1.75e-270)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (j <= 2.6e-131)
		tmp = y2 * ((t_4 + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	elseif (j <= 8.7e+99)
		tmp = y0 * (t_1 + (b * ((z * k) - (x * j))));
	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[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(k * t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5.2e+91], t$95$2, If[LessEqual[j, -9.6e-21], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.5e-66], N[(y0 * t$95$1), $MachinePrecision], If[LessEqual[j, -1.08e-131], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.3e-180], N[(N[(t$95$5 * t$95$3), $MachinePrecision] + N[(t * N[(i * N[(N[(z * c), $MachinePrecision] - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.2e-294], N[(y2 * N[(t$95$4 + N[(c * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.75e-270], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.6e-131], N[(y2 * N[(N[(t$95$4 + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.7e+99], N[(y0 * N[(t$95$1 + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if j < -5.2000000000000001e91 or 8.6999999999999997e99 < j

   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. Taylor expanded in j around inf 68.6%

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

      1. +-commutative 68.6%

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

      2. mul-1-neg 68.6%

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

      3. unsub-neg 68.6%

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

      4. *-commutative 68.6%

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

   4. Simplified 68.6%

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

   if -5.2000000000000001e91 < j < -9.5999999999999997e-21

   1. Initial program 21.7%

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

   2. Taylor expanded in y1 around -inf 48.6%

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

      1. mul-1-neg 48.6%

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

      2. *-commutative 48.6%

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

      3. distribute-rgt-neg-in 48.6%

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

   4. Simplified 48.6%

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

   5. Taylor expanded in a around 0 52.9%

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

   if -9.5999999999999997e-21 < j < -2.49999999999999981e-66

   1. Initial program 42.6%

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

   2. Taylor expanded in c around inf 43.5%

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

      1. +-commutative 43.5%

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

      2. mul-1-neg 43.5%

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

      3. unsub-neg 43.5%

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

      4. *-commutative 43.5%

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

      5. *-commutative 43.5%

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

      6. *-commutative 43.5%

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

      7. *-commutative 43.5%

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

   4. Simplified 43.5%

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

   5. Taylor expanded in y0 around inf 57.9%

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

      1. +-commutative 57.9%

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

      2. mul-1-neg 57.9%

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

      3. *-commutative 57.9%

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

      4. *-commutative 57.9%

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

      5. *-commutative 57.9%

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

      6. unsub-neg 57.9%

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

      7. *-commutative 57.9%

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

      8. *-commutative 57.9%

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

      9. *-commutative 57.9%

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

      10. *-commutative 57.9%

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

   7. Simplified 57.9%

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

   if -2.49999999999999981e-66 < j < -1.07999999999999996e-131

   1. Initial program 50.6%

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

   2. Taylor expanded in y5 around inf 60.5%

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

      1. mul-1-neg 60.5%

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

      2. associate-*r* 50.6%

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

      3. *-commutative 50.6%

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

   4. Simplified 50.6%

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

   5. Taylor expanded in i around inf 70.5%

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

   if -1.07999999999999996e-131 < j < -2.29999999999999996e-180

   1. Initial program 44.4%

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

   2. Taylor expanded in t around inf 77.8%

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

   3. Taylor expanded in i around inf 56.6%

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

      1. +-commutative 56.6%

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

      2. mul-1-neg 56.6%

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

      3. unsub-neg 56.6%

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

      4. *-commutative 56.6%

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

   5. Simplified 56.6%

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

   if -2.29999999999999996e-180 < j < 5.1999999999999999e-294

   1. Initial program 39.5%

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

   2. Taylor expanded in c around inf 42.9%

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

      1. +-commutative 42.9%

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

      2. mul-1-neg 42.9%

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

      3. unsub-neg 42.9%

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

      4. *-commutative 42.9%

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

      5. *-commutative 42.9%

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

      6. *-commutative 42.9%

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

      7. *-commutative 42.9%

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

   4. Simplified 42.9%

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

   5. Taylor expanded in y2 around inf 46.3%

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

   if 5.1999999999999999e-294 < j < 1.74999999999999997e-270

   1. Initial program 33.1%

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

   2. Taylor expanded in k around inf 33.6%

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

      1. sub-neg 33.6%

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

      2. +-commutative 33.6%

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

      3. mul-1-neg 33.6%

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

      4. unsub-neg 33.6%

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

      5. *-commutative 33.6%

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

      6. mul-1-neg 33.6%

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

      7. remove-double-neg 33.6%

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

   4. Simplified 33.6%

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

   5. Taylor expanded in b around inf 67.6%

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

   if 1.74999999999999997e-270 < j < 2.59999999999999996e-131

   1. Initial program 45.5%

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

   2. Taylor expanded in y2 around inf 56.1%

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

   if 2.59999999999999996e-131 < j < 8.6999999999999997e99

   1. Initial program 38.8%

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

   2. Taylor expanded in y0 around inf 60.4%

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

      1. +-commutative 60.4%

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

      2. mul-1-neg 60.4%

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

      3. unsub-neg 60.4%

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

      4. *-commutative 60.4%

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

      5. *-commutative 60.4%

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

      6. *-commutative 60.4%

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

      7. *-commutative 60.4%

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

   4. Simplified 60.4%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.2 \cdot 10^{+91}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -9.6 \cdot 10^{-21}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq -2.5 \cdot 10^{-66}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq -1.08 \cdot 10^{-131}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -2.3 \cdot 10^{-180}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(i \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{-294}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{-270}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-131}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 8.7 \cdot 10^{+99}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]

Alternative 9: 36.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := y1 \cdot y4 - y0 \cdot y5\\ t_3 := t_1 \cdot t_2\\ t_4 := t_3 + \left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ t_5 := y \cdot \left(i \cdot \left(k \cdot y5\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{if}\;y1 \leq -4.2 \cdot 10^{+137}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -2.2 \cdot 10^{-103}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -1.7 \cdot 10^{-175}:\\ \;\;\;\;t_3 + t \cdot \left(i \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq -4.4 \cdot 10^{-226}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 2.6 \cdot 10^{-201}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y1 \leq 1.8 \cdot 10^{-77}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y1 \leq 2.35 \cdot 10^{+55}:\\ \;\;\;\;y2 \cdot \left(k \cdot t_2 + c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 3.5 \cdot 10^{+76}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y1 \leq 5 \cdot 10^{+106}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y1 \leq 3.6 \cdot 10^{+177}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y2) (* j y3)))
        (t_2 (- (* y1 y4) (* y0 y5)))
        (t_3 (* t_1 t_2))
        (t_4 (+ t_3 (* (* t y5) (- (* a y2) (* i j)))))
        (t_5 (* y (+ (* i (* k y5)) (* y3 (- (* c y4) (* a y5)))))))
   (if (<= y1 -4.2e+137)
     (* a (* y1 (- (* z y3) (* x y2))))
     (if (<= y1 -2.2e-103)
       (* y0 (+ (* c (- (* x y2) (* z y3))) (* y5 (- (* j y3) (* k y2)))))
       (if (<= y1 -1.7e-175)
         (+ t_3 (* t (* i (- (* z c) (* j y5)))))
         (if (<= y1 -4.4e-226)
           (* b (* j (- (* t y4) (* x y0))))
           (if (<= y1 2.6e-201)
             t_4
             (if (<= y1 1.8e-77)
               t_5
               (if (<= y1 2.35e+55)
                 (* y2 (+ (* k t_2) (* c (- (* x y0) (* t y4)))))
                 (if (<= y1 3.5e+76)
                   t_5
                   (if (<= y1 5e+106)
                     t_4
                     (if (<= y1 3.6e+177)
                       (* k (* y0 (- (* z b) (* y2 y5))))
                       (*
                        y1
                        (+ (* i (- (* x j) (* z k))) (* y4 t_1)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = (y1 * y4) - (y0 * y5);
	double t_3 = t_1 * t_2;
	double t_4 = t_3 + ((t * y5) * ((a * y2) - (i * j)));
	double t_5 = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))));
	double tmp;
	if (y1 <= -4.2e+137) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y1 <= -2.2e-103) {
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2))));
	} else if (y1 <= -1.7e-175) {
		tmp = t_3 + (t * (i * ((z * c) - (j * y5))));
	} else if (y1 <= -4.4e-226) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y1 <= 2.6e-201) {
		tmp = t_4;
	} else if (y1 <= 1.8e-77) {
		tmp = t_5;
	} else if (y1 <= 2.35e+55) {
		tmp = y2 * ((k * t_2) + (c * ((x * y0) - (t * y4))));
	} else if (y1 <= 3.5e+76) {
		tmp = t_5;
	} else if (y1 <= 5e+106) {
		tmp = t_4;
	} else if (y1 <= 3.6e+177) {
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	} else {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * t_1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (k * y2) - (j * y3)
    t_2 = (y1 * y4) - (y0 * y5)
    t_3 = t_1 * t_2
    t_4 = t_3 + ((t * y5) * ((a * y2) - (i * j)))
    t_5 = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))))
    if (y1 <= (-4.2d+137)) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (y1 <= (-2.2d-103)) then
        tmp = y0 * ((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2))))
    else if (y1 <= (-1.7d-175)) then
        tmp = t_3 + (t * (i * ((z * c) - (j * y5))))
    else if (y1 <= (-4.4d-226)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y1 <= 2.6d-201) then
        tmp = t_4
    else if (y1 <= 1.8d-77) then
        tmp = t_5
    else if (y1 <= 2.35d+55) then
        tmp = y2 * ((k * t_2) + (c * ((x * y0) - (t * y4))))
    else if (y1 <= 3.5d+76) then
        tmp = t_5
    else if (y1 <= 5d+106) then
        tmp = t_4
    else if (y1 <= 3.6d+177) then
        tmp = k * (y0 * ((z * b) - (y2 * y5)))
    else
        tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * 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 = (k * y2) - (j * y3);
	double t_2 = (y1 * y4) - (y0 * y5);
	double t_3 = t_1 * t_2;
	double t_4 = t_3 + ((t * y5) * ((a * y2) - (i * j)));
	double t_5 = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))));
	double tmp;
	if (y1 <= -4.2e+137) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y1 <= -2.2e-103) {
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2))));
	} else if (y1 <= -1.7e-175) {
		tmp = t_3 + (t * (i * ((z * c) - (j * y5))));
	} else if (y1 <= -4.4e-226) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y1 <= 2.6e-201) {
		tmp = t_4;
	} else if (y1 <= 1.8e-77) {
		tmp = t_5;
	} else if (y1 <= 2.35e+55) {
		tmp = y2 * ((k * t_2) + (c * ((x * y0) - (t * y4))));
	} else if (y1 <= 3.5e+76) {
		tmp = t_5;
	} else if (y1 <= 5e+106) {
		tmp = t_4;
	} else if (y1 <= 3.6e+177) {
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	} else {
		tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * 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 = (k * y2) - (j * y3)
	t_2 = (y1 * y4) - (y0 * y5)
	t_3 = t_1 * t_2
	t_4 = t_3 + ((t * y5) * ((a * y2) - (i * j)))
	t_5 = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))))
	tmp = 0
	if y1 <= -4.2e+137:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif y1 <= -2.2e-103:
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2))))
	elif y1 <= -1.7e-175:
		tmp = t_3 + (t * (i * ((z * c) - (j * y5))))
	elif y1 <= -4.4e-226:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y1 <= 2.6e-201:
		tmp = t_4
	elif y1 <= 1.8e-77:
		tmp = t_5
	elif y1 <= 2.35e+55:
		tmp = y2 * ((k * t_2) + (c * ((x * y0) - (t * y4))))
	elif y1 <= 3.5e+76:
		tmp = t_5
	elif y1 <= 5e+106:
		tmp = t_4
	elif y1 <= 3.6e+177:
		tmp = k * (y0 * ((z * b) - (y2 * y5)))
	else:
		tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * 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(k * y2) - Float64(j * y3))
	t_2 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_3 = Float64(t_1 * t_2)
	t_4 = Float64(t_3 + Float64(Float64(t * y5) * Float64(Float64(a * y2) - Float64(i * j))))
	t_5 = Float64(y * Float64(Float64(i * Float64(k * y5)) + Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5)))))
	tmp = 0.0
	if (y1 <= -4.2e+137)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (y1 <= -2.2e-103)
		tmp = Float64(y0 * Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2)))));
	elseif (y1 <= -1.7e-175)
		tmp = Float64(t_3 + Float64(t * Float64(i * Float64(Float64(z * c) - Float64(j * y5)))));
	elseif (y1 <= -4.4e-226)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y1 <= 2.6e-201)
		tmp = t_4;
	elseif (y1 <= 1.8e-77)
		tmp = t_5;
	elseif (y1 <= 2.35e+55)
		tmp = Float64(y2 * Float64(Float64(k * t_2) + Float64(c * Float64(Float64(x * y0) - Float64(t * y4)))));
	elseif (y1 <= 3.5e+76)
		tmp = t_5;
	elseif (y1 <= 5e+106)
		tmp = t_4;
	elseif (y1 <= 3.6e+177)
		tmp = Float64(k * Float64(y0 * Float64(Float64(z * b) - Float64(y2 * y5))));
	else
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(y4 * 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 = (k * y2) - (j * y3);
	t_2 = (y1 * y4) - (y0 * y5);
	t_3 = t_1 * t_2;
	t_4 = t_3 + ((t * y5) * ((a * y2) - (i * j)));
	t_5 = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))));
	tmp = 0.0;
	if (y1 <= -4.2e+137)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (y1 <= -2.2e-103)
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2))));
	elseif (y1 <= -1.7e-175)
		tmp = t_3 + (t * (i * ((z * c) - (j * y5))));
	elseif (y1 <= -4.4e-226)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y1 <= 2.6e-201)
		tmp = t_4;
	elseif (y1 <= 1.8e-77)
		tmp = t_5;
	elseif (y1 <= 2.35e+55)
		tmp = y2 * ((k * t_2) + (c * ((x * y0) - (t * y4))));
	elseif (y1 <= 3.5e+76)
		tmp = t_5;
	elseif (y1 <= 5e+106)
		tmp = t_4;
	elseif (y1 <= 3.6e+177)
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	else
		tmp = y1 * ((i * ((x * j) - (z * k))) + (y4 * 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[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 * t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + N[(N[(t * y5), $MachinePrecision] * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y * N[(N[(i * N[(k * y5), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -4.2e+137], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.2e-103], N[(y0 * N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.7e-175], N[(t$95$3 + N[(t * N[(i * N[(N[(z * c), $MachinePrecision] - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -4.4e-226], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.6e-201], t$95$4, If[LessEqual[y1, 1.8e-77], t$95$5, If[LessEqual[y1, 2.35e+55], N[(y2 * N[(N[(k * t$95$2), $MachinePrecision] + N[(c * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.5e+76], t$95$5, If[LessEqual[y1, 5e+106], t$95$4, If[LessEqual[y1, 3.6e+177], N[(k * N[(y0 * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y1 < -4.1999999999999998e137

   1. Initial program 36.4%

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

   2. Taylor expanded in y1 around -inf 55.3%

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

      1. mul-1-neg 55.3%

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

      2. *-commutative 55.3%

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

      3. distribute-rgt-neg-in 55.3%

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

   4. Simplified 55.3%

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

   5. Taylor expanded in a around inf 52.5%

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

      1. associate-*r* 52.5%

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

      2. neg-mul-1 52.5%

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

   7. Simplified 52.5%

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

   if -4.1999999999999998e137 < y1 < -2.1999999999999999e-103

   1. Initial program 32.3%

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

   2. Taylor expanded in c around inf 44.7%

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

      1. +-commutative 44.7%

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

      2. mul-1-neg 44.7%

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

      3. unsub-neg 44.7%

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

      4. *-commutative 44.7%

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

      5. *-commutative 44.7%

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

      6. *-commutative 44.7%

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

      7. *-commutative 44.7%

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

   4. Simplified 44.7%

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

   5. Taylor expanded in y0 around inf 52.7%

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

      1. +-commutative 52.7%

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

      2. mul-1-neg 52.7%

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

      3. *-commutative 52.7%

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

      4. *-commutative 52.7%

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

      5. *-commutative 52.7%

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

      6. unsub-neg 52.7%

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

      7. *-commutative 52.7%

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

      8. *-commutative 52.7%

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

      9. *-commutative 52.7%

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

      10. *-commutative 52.7%

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

   7. Simplified 52.7%

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

   if -2.1999999999999999e-103 < y1 < -1.7e-175

   1. Initial program 64.5%

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

   2. Taylor expanded in t around inf 64.9%

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

   3. Taylor expanded in i around inf 71.7%

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

      1. +-commutative 71.7%

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

      2. mul-1-neg 71.7%

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

      3. unsub-neg 71.7%

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

      4. *-commutative 71.7%

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

   5. Simplified 71.7%

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

   if -1.7e-175 < y1 < -4.4e-226

   1. Initial program 50.0%

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

   2. Taylor expanded in j around inf 42.6%

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

      1. +-commutative 42.6%

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

      2. mul-1-neg 42.6%

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

      3. unsub-neg 42.6%

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

      4. *-commutative 42.6%

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

   4. Simplified 42.6%

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

   5. Taylor expanded in b around inf 59.4%

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

   if -4.4e-226 < y1 < 2.59999999999999982e-201 or 3.5e76 < y1 < 4.9999999999999998e106

   1. Initial program 43.0%

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

   2. Taylor expanded in t around inf 49.5%

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

   3. Taylor expanded in y5 around -inf 51.6%

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

      1. mul-1-neg 51.6%

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

      2. associate-*r* 51.6%

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

      3. *-commutative 51.6%

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

      4. *-commutative 51.6%

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

   5. Simplified 51.6%

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

   if 2.59999999999999982e-201 < y1 < 1.8e-77 or 2.35e55 < y1 < 3.5e76

   1. Initial program 31.6%

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

   2. Taylor expanded in y5 around inf 16.5%

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

      1. mul-1-neg 16.5%

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

      2. associate-*r* 16.4%

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

      3. *-commutative 16.4%

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

   4. Simplified 16.4%

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

   5. Taylor expanded in y around -inf 51.2%

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

   if 1.8e-77 < y1 < 2.35e55

   1. Initial program 36.8%

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

   2. Taylor expanded in c around inf 58.3%

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

      1. +-commutative 58.3%

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

      2. mul-1-neg 58.3%

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

      3. unsub-neg 58.3%

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

      4. *-commutative 58.3%

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

      5. *-commutative 58.3%

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

      6. *-commutative 58.3%

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

      7. *-commutative 58.3%

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

   4. Simplified 58.3%

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

   5. Taylor expanded in y2 around inf 63.8%

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

   if 4.9999999999999998e106 < y1 < 3.60000000000000003e177

   1. Initial program 15.3%

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

   2. Taylor expanded in k around inf 46.8%

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

      1. sub-neg 46.8%

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

      2. +-commutative 46.8%

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

      3. mul-1-neg 46.8%

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

      4. unsub-neg 46.8%

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

      5. *-commutative 46.8%

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

      6. mul-1-neg 46.8%

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

      7. remove-double-neg 46.8%

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

   4. Simplified 46.8%

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

   5. Taylor expanded in y0 around inf 62.0%

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

      1. +-commutative 62.0%

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

      2. mul-1-neg 62.0%

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

      3. sub-neg 62.0%

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

      4. *-commutative 62.0%

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

   7. Simplified 62.0%

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

   if 3.60000000000000003e177 < y1

   1. Initial program 12.5%

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

   2. Taylor expanded in y1 around -inf 70.8%

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

      1. mul-1-neg 70.8%

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

      2. *-commutative 70.8%

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

      3. distribute-rgt-neg-in 70.8%

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

   4. Simplified 70.8%

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

   5. Taylor expanded in a around 0 71.2%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -4.2 \cdot 10^{+137}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -2.2 \cdot 10^{-103}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -1.7 \cdot 10^{-175}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(i \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq -4.4 \cdot 10^{-226}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 2.6 \cdot 10^{-201}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;y1 \leq 1.8 \cdot 10^{-77}:\\ \;\;\;\;y \cdot \left(i \cdot \left(k \cdot y5\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 2.35 \cdot 10^{+55}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 3.5 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \left(i \cdot \left(k \cdot y5\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 5 \cdot 10^{+106}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;y1 \leq 3.6 \cdot 10^{+177}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \]

Alternative 10: 42.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_2 := y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_3 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;j \leq -1000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-112}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -1.5 \cdot 10^{-190}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -9.5 \cdot 10^{-223}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 1.8 \cdot 10^{-240}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-131}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 6.7 \cdot 10^{+100}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          j
          (+
           (+ (* t (- (* b y4) (* i y5))) (* y3 (- (* y0 y5) (* y1 y4))))
           (* x (- (* i y1) (* b y0))))))
        (t_2
         (*
          y0
          (+
           (+ (* c (- (* x y2) (* z y3))) (* y5 (- (* j y3) (* k y2))))
           (* b (- (* z k) (* x j))))))
        (t_3
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2)))))))
   (if (<= j -1000000000000.0)
     t_1
     (if (<= j -3.5e-112)
       t_3
       (if (<= j -1.5e-190)
         t_2
         (if (<= j -9.5e-223)
           (* k (* y0 (- (* z b) (* y2 y5))))
           (if (<= j 1.8e-240)
             t_3
             (if (<= j 4.8e-131)
               (*
                y2
                (+
                 (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
                 (* t (- (* a y5) (* c y4)))))
               (if (<= j 6.7e+100) t_2 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	double t_2 = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	double t_3 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (j <= -1000000000000.0) {
		tmp = t_1;
	} else if (j <= -3.5e-112) {
		tmp = t_3;
	} else if (j <= -1.5e-190) {
		tmp = t_2;
	} else if (j <= -9.5e-223) {
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	} else if (j <= 1.8e-240) {
		tmp = t_3;
	} else if (j <= 4.8e-131) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (j <= 6.7e+100) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
    t_2 = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))))
    t_3 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    if (j <= (-1000000000000.0d0)) then
        tmp = t_1
    else if (j <= (-3.5d-112)) then
        tmp = t_3
    else if (j <= (-1.5d-190)) then
        tmp = t_2
    else if (j <= (-9.5d-223)) then
        tmp = k * (y0 * ((z * b) - (y2 * y5)))
    else if (j <= 1.8d-240) then
        tmp = t_3
    else if (j <= 4.8d-131) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    else if (j <= 6.7d+100) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	double t_2 = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	double t_3 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (j <= -1000000000000.0) {
		tmp = t_1;
	} else if (j <= -3.5e-112) {
		tmp = t_3;
	} else if (j <= -1.5e-190) {
		tmp = t_2;
	} else if (j <= -9.5e-223) {
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	} else if (j <= 1.8e-240) {
		tmp = t_3;
	} else if (j <= 4.8e-131) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (j <= 6.7e+100) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
	t_2 = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))))
	t_3 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	tmp = 0
	if j <= -1000000000000.0:
		tmp = t_1
	elif j <= -3.5e-112:
		tmp = t_3
	elif j <= -1.5e-190:
		tmp = t_2
	elif j <= -9.5e-223:
		tmp = k * (y0 * ((z * b) - (y2 * y5)))
	elif j <= 1.8e-240:
		tmp = t_3
	elif j <= 4.8e-131:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	elif j <= 6.7e+100:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_2 = Float64(y0 * Float64(Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2)))) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))))
	t_3 = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	tmp = 0.0
	if (j <= -1000000000000.0)
		tmp = t_1;
	elseif (j <= -3.5e-112)
		tmp = t_3;
	elseif (j <= -1.5e-190)
		tmp = t_2;
	elseif (j <= -9.5e-223)
		tmp = Float64(k * Float64(y0 * Float64(Float64(z * b) - Float64(y2 * y5))));
	elseif (j <= 1.8e-240)
		tmp = t_3;
	elseif (j <= 4.8e-131)
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (j <= 6.7e+100)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	t_2 = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	t_3 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	tmp = 0.0;
	if (j <= -1000000000000.0)
		tmp = t_1;
	elseif (j <= -3.5e-112)
		tmp = t_3;
	elseif (j <= -1.5e-190)
		tmp = t_2;
	elseif (j <= -9.5e-223)
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	elseif (j <= 1.8e-240)
		tmp = t_3;
	elseif (j <= 4.8e-131)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	elseif (j <= 6.7e+100)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y0 * N[(N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1000000000000.0], t$95$1, If[LessEqual[j, -3.5e-112], t$95$3, If[LessEqual[j, -1.5e-190], t$95$2, If[LessEqual[j, -9.5e-223], N[(k * N[(y0 * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.8e-240], t$95$3, If[LessEqual[j, 4.8e-131], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.7e+100], t$95$2, t$95$1]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1e12 or 6.6999999999999997e100 < 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. Taylor expanded in j around inf 64.8%

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

      1. +-commutative 64.8%

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

      2. mul-1-neg 64.8%

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

      3. unsub-neg 64.8%

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

      4. *-commutative 64.8%

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

   4. Simplified 64.8%

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

   if -1e12 < j < -3.49999999999999994e-112 or -9.49999999999999992e-223 < j < 1.7999999999999999e-240

   1. Initial program 43.1%

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

   2. Taylor expanded in y4 around inf 57.5%

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

   if -3.49999999999999994e-112 < j < -1.4999999999999999e-190 or 4.7999999999999999e-131 < j < 6.6999999999999997e100

   1. Initial program 41.5%

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

   2. Taylor expanded in y0 around inf 58.3%

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

      1. +-commutative 58.3%

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

      2. mul-1-neg 58.3%

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

      3. unsub-neg 58.3%

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

      4. *-commutative 58.3%

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

      5. *-commutative 58.3%

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

      6. *-commutative 58.3%

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

      7. *-commutative 58.3%

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

   4. Simplified 58.3%

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

   if -1.4999999999999999e-190 < j < -9.49999999999999992e-223

   1. Initial program 30.7%

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

   2. Taylor expanded in k around inf 39.2%

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

      1. sub-neg 39.2%

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

      2. +-commutative 39.2%

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

      3. mul-1-neg 39.2%

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

      4. unsub-neg 39.2%

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

      5. *-commutative 39.2%

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

      6. mul-1-neg 39.2%

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

      7. remove-double-neg 39.2%

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

   4. Simplified 39.2%

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

   5. Taylor expanded in y0 around inf 48.0%

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

      1. +-commutative 48.0%

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

      2. mul-1-neg 48.0%

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

      3. sub-neg 48.0%

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

      4. *-commutative 48.0%

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

   7. Simplified 48.0%

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

   if 1.7999999999999999e-240 < j < 4.7999999999999999e-131

   1. Initial program 39.1%

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

   2. Taylor expanded in y2 around inf 54.4%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1000000000000:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-112}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq -1.5 \cdot 10^{-190}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -9.5 \cdot 10^{-223}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 1.8 \cdot 10^{-240}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-131}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 6.7 \cdot 10^{+100}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]

Alternative 11: 41.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot y5 - y1 \cdot y4\\ t_2 := b \cdot y4 - i \cdot y5\\ t_3 := j \cdot \left(\left(t \cdot t_2 + y3 \cdot t_1\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;j \leq -5 \cdot 10^{-12}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -1.52 \cdot 10^{-196}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot t_2\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -7 \cdot 10^{-218}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{-305}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-230}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{-131}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot t_1 + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.45 \cdot 10^{+103}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y0 y5) (* y1 y4)))
        (t_2 (- (* b y4) (* i y5)))
        (t_3 (* j (+ (+ (* t t_2) (* y3 t_1)) (* x (- (* i y1) (* b y0)))))))
   (if (<= j -5e-12)
     t_3
     (if (<= j -1.52e-196)
       (*
        t
        (+
         (+ (* z (- (* c i) (* a b))) (* j t_2))
         (* y2 (- (* a y5) (* c y4)))))
       (if (<= j -7e-218)
         (*
          k
          (+
           (+ (* y2 (- (* y1 y4) (* y0 y5))) (* y (- (* i y5) (* b y4))))
           (* z (- (* b y0) (* i y1)))))
         (if (<= j 4.5e-305)
           (* a (* y5 (- (* t y2) (* y y3))))
           (if (<= j 1.7e-230)
             (*
              y4
              (+
               (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
               (* c (- (* y y3) (* t y2)))))
             (if (<= j 4.2e-131)
               (*
                y3
                (+
                 (* y (- (* c y4) (* a y5)))
                 (+ (* j t_1) (* z (- (* a y1) (* c y0))))))
               (if (<= j 2.45e+103)
                 (*
                  y0
                  (+
                   (+ (* c (- (* x y2) (* z y3))) (* y5 (- (* j y3) (* k y2))))
                   (* b (- (* z k) (* x j)))))
                 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * y5) - (y1 * y4);
	double t_2 = (b * y4) - (i * y5);
	double t_3 = j * (((t * t_2) + (y3 * t_1)) + (x * ((i * y1) - (b * y0))));
	double tmp;
	if (j <= -5e-12) {
		tmp = t_3;
	} else if (j <= -1.52e-196) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_2)) + (y2 * ((a * y5) - (c * y4))));
	} else if (j <= -7e-218) {
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	} else if (j <= 4.5e-305) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (j <= 1.7e-230) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (j <= 4.2e-131) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_1) + (z * ((a * y1) - (c * y0)))));
	} else if (j <= 2.45e+103) {
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y0 * y5) - (y1 * y4)
    t_2 = (b * y4) - (i * y5)
    t_3 = j * (((t * t_2) + (y3 * t_1)) + (x * ((i * y1) - (b * y0))))
    if (j <= (-5d-12)) then
        tmp = t_3
    else if (j <= (-1.52d-196)) then
        tmp = t * (((z * ((c * i) - (a * b))) + (j * t_2)) + (y2 * ((a * y5) - (c * y4))))
    else if (j <= (-7d-218)) then
        tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
    else if (j <= 4.5d-305) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (j <= 1.7d-230) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else if (j <= 4.2d-131) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_1) + (z * ((a * y1) - (c * y0)))))
    else if (j <= 2.45d+103) then
        tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * y5) - (y1 * y4);
	double t_2 = (b * y4) - (i * y5);
	double t_3 = j * (((t * t_2) + (y3 * t_1)) + (x * ((i * y1) - (b * y0))));
	double tmp;
	if (j <= -5e-12) {
		tmp = t_3;
	} else if (j <= -1.52e-196) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_2)) + (y2 * ((a * y5) - (c * y4))));
	} else if (j <= -7e-218) {
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	} else if (j <= 4.5e-305) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (j <= 1.7e-230) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (j <= 4.2e-131) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_1) + (z * ((a * y1) - (c * y0)))));
	} else if (j <= 2.45e+103) {
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y0 * y5) - (y1 * y4)
	t_2 = (b * y4) - (i * y5)
	t_3 = j * (((t * t_2) + (y3 * t_1)) + (x * ((i * y1) - (b * y0))))
	tmp = 0
	if j <= -5e-12:
		tmp = t_3
	elif j <= -1.52e-196:
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_2)) + (y2 * ((a * y5) - (c * y4))))
	elif j <= -7e-218:
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
	elif j <= 4.5e-305:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif j <= 1.7e-230:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	elif j <= 4.2e-131:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_1) + (z * ((a * y1) - (c * y0)))))
	elif j <= 2.45e+103:
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y0 * y5) - Float64(y1 * y4))
	t_2 = Float64(Float64(b * y4) - Float64(i * y5))
	t_3 = Float64(j * Float64(Float64(Float64(t * t_2) + Float64(y3 * t_1)) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (j <= -5e-12)
		tmp = t_3;
	elseif (j <= -1.52e-196)
		tmp = Float64(t * Float64(Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(j * t_2)) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (j <= -7e-218)
		tmp = Float64(k * Float64(Float64(Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))));
	elseif (j <= 4.5e-305)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (j <= 1.7e-230)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (j <= 4.2e-131)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * t_1) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (j <= 2.45e+103)
		tmp = Float64(y0 * Float64(Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2)))) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y0 * y5) - (y1 * y4);
	t_2 = (b * y4) - (i * y5);
	t_3 = j * (((t * t_2) + (y3 * t_1)) + (x * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (j <= -5e-12)
		tmp = t_3;
	elseif (j <= -1.52e-196)
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_2)) + (y2 * ((a * y5) - (c * y4))));
	elseif (j <= -7e-218)
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	elseif (j <= 4.5e-305)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (j <= 1.7e-230)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	elseif (j <= 4.2e-131)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_1) + (z * ((a * y1) - (c * y0)))));
	elseif (j <= 2.45e+103)
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(N[(t * t$95$2), $MachinePrecision] + N[(y3 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5e-12], t$95$3, If[LessEqual[j, -1.52e-196], N[(t * N[(N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -7e-218], N[(k * N[(N[(N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.5e-305], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.7e-230], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.2e-131], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * t$95$1), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.45e+103], N[(y0 * N[(N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -4.9999999999999997e-12 or 2.4499999999999999e103 < j

   1. Initial program 27.0%

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

   2. Taylor expanded in j around inf 63.5%

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

      1. +-commutative 63.5%

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

      2. mul-1-neg 63.5%

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

      3. unsub-neg 63.5%

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

      4. *-commutative 63.5%

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

   4. Simplified 63.5%

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

   if -4.9999999999999997e-12 < j < -1.52e-196

   1. Initial program 41.3%

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

   2. Taylor expanded in t around inf 51.3%

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

   3. Taylor expanded in t around inf 51.0%

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

   if -1.52e-196 < j < -7e-218

   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. Taylor expanded in k around inf 83.3%

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

      1. sub-neg 83.3%

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

      2. +-commutative 83.3%

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

      3. mul-1-neg 83.3%

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

      4. unsub-neg 83.3%

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

      5. *-commutative 83.3%

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

      6. mul-1-neg 83.3%

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

      7. remove-double-neg 83.3%

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

   4. Simplified 83.3%

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

   if -7e-218 < j < 4.5000000000000002e-305

   1. Initial program 35.6%

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

   2. Taylor expanded in y5 around inf 24.0%

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

      1. mul-1-neg 24.0%

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

      2. associate-*r* 29.9%

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

      3. *-commutative 29.9%

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

   4. Simplified 29.9%

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

   5. Taylor expanded in a around inf 54.6%

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

      1. *-commutative 54.6%

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

   7. Simplified 54.6%

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

   if 4.5000000000000002e-305 < j < 1.7e-230

   1. Initial program 49.9%

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

   2. Taylor expanded in y4 around inf 67.5%

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

   if 1.7e-230 < j < 4.19999999999999994e-131

   1. Initial program 40.0%

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

   2. Taylor expanded in y3 around -inf 65.6%

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

   if 4.19999999999999994e-131 < j < 2.4499999999999999e103

   1. Initial program 38.8%

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

   2. Taylor expanded in y0 around inf 60.4%

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

      1. +-commutative 60.4%

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

      2. mul-1-neg 60.4%

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

      3. unsub-neg 60.4%

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

      4. *-commutative 60.4%

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

      5. *-commutative 60.4%

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

      6. *-commutative 60.4%

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

      7. *-commutative 60.4%

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

   4. Simplified 60.4%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5 \cdot 10^{-12}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -1.52 \cdot 10^{-196}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -7 \cdot 10^{-218}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{-305}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-230}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{-131}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.45 \cdot 10^{+103}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]

Alternative 12: 40.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot y5 - y1 \cdot y4\\ t_2 := j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot t_1\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_3 := x \cdot y2 - z \cdot y3\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot t_4\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;j \leq -2.2 \cdot 10^{+17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-87}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq -3.1 \cdot 10^{-174}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -2.7 \cdot 10^{-223}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - \left(a \cdot t_3 - y4 \cdot t_4\right)\right)\\ \mathbf{elif}\;j \leq 7.6 \cdot 10^{-231}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{-131}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot t_1 + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{+102}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot t_3 + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y0 y5) (* y1 y4)))
        (t_2
         (*
          j
          (+
           (+ (* t (- (* b y4) (* i y5))) (* y3 t_1))
           (* x (- (* i y1) (* b y0))))))
        (t_3 (- (* x y2) (* z y3)))
        (t_4 (- (* k y2) (* j y3)))
        (t_5
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 t_4))
           (* c (- (* y y3) (* t y2)))))))
   (if (<= j -2.2e+17)
     t_2
     (if (<= j -3.5e-87)
       t_5
       (if (<= j -3.1e-174)
         (* i (* y5 (- (* y k) (* t j))))
         (if (<= j -2.7e-223)
           (* y1 (- (* i (- (* x j) (* z k))) (- (* a t_3) (* y4 t_4))))
           (if (<= j 7.6e-231)
             t_5
             (if (<= j 2.4e-131)
               (*
                y3
                (+
                 (* y (- (* c y4) (* a y5)))
                 (+ (* j t_1) (* z (- (* a y1) (* c y0))))))
               (if (<= j 7.2e+102)
                 (*
                  y0
                  (+
                   (+ (* c t_3) (* y5 (- (* j y3) (* k y2))))
                   (* b (- (* z k) (* x j)))))
                 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 = (y0 * y5) - (y1 * y4);
	double t_2 = j * (((t * ((b * y4) - (i * y5))) + (y3 * t_1)) + (x * ((i * y1) - (b * y0))));
	double t_3 = (x * y2) - (z * y3);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_4)) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (j <= -2.2e+17) {
		tmp = t_2;
	} else if (j <= -3.5e-87) {
		tmp = t_5;
	} else if (j <= -3.1e-174) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (j <= -2.7e-223) {
		tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * t_3) - (y4 * t_4)));
	} else if (j <= 7.6e-231) {
		tmp = t_5;
	} else if (j <= 2.4e-131) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_1) + (z * ((a * y1) - (c * y0)))));
	} else if (j <= 7.2e+102) {
		tmp = y0 * (((c * t_3) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (y0 * y5) - (y1 * y4)
    t_2 = j * (((t * ((b * y4) - (i * y5))) + (y3 * t_1)) + (x * ((i * y1) - (b * y0))))
    t_3 = (x * y2) - (z * y3)
    t_4 = (k * y2) - (j * y3)
    t_5 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_4)) + (c * ((y * y3) - (t * y2))))
    if (j <= (-2.2d+17)) then
        tmp = t_2
    else if (j <= (-3.5d-87)) then
        tmp = t_5
    else if (j <= (-3.1d-174)) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (j <= (-2.7d-223)) then
        tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * t_3) - (y4 * t_4)))
    else if (j <= 7.6d-231) then
        tmp = t_5
    else if (j <= 2.4d-131) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_1) + (z * ((a * y1) - (c * y0)))))
    else if (j <= 7.2d+102) then
        tmp = y0 * (((c * t_3) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))))
    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 = (y0 * y5) - (y1 * y4);
	double t_2 = j * (((t * ((b * y4) - (i * y5))) + (y3 * t_1)) + (x * ((i * y1) - (b * y0))));
	double t_3 = (x * y2) - (z * y3);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_4)) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (j <= -2.2e+17) {
		tmp = t_2;
	} else if (j <= -3.5e-87) {
		tmp = t_5;
	} else if (j <= -3.1e-174) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (j <= -2.7e-223) {
		tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * t_3) - (y4 * t_4)));
	} else if (j <= 7.6e-231) {
		tmp = t_5;
	} else if (j <= 2.4e-131) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_1) + (z * ((a * y1) - (c * y0)))));
	} else if (j <= 7.2e+102) {
		tmp = y0 * (((c * t_3) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	} 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 = (y0 * y5) - (y1 * y4)
	t_2 = j * (((t * ((b * y4) - (i * y5))) + (y3 * t_1)) + (x * ((i * y1) - (b * y0))))
	t_3 = (x * y2) - (z * y3)
	t_4 = (k * y2) - (j * y3)
	t_5 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_4)) + (c * ((y * y3) - (t * y2))))
	tmp = 0
	if j <= -2.2e+17:
		tmp = t_2
	elif j <= -3.5e-87:
		tmp = t_5
	elif j <= -3.1e-174:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif j <= -2.7e-223:
		tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * t_3) - (y4 * t_4)))
	elif j <= 7.6e-231:
		tmp = t_5
	elif j <= 2.4e-131:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_1) + (z * ((a * y1) - (c * y0)))))
	elif j <= 7.2e+102:
		tmp = y0 * (((c * t_3) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))))
	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(y0 * y5) - Float64(y1 * y4))
	t_2 = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * t_1)) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_3 = Float64(Float64(x * y2) - Float64(z * y3))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * t_4)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	tmp = 0.0
	if (j <= -2.2e+17)
		tmp = t_2;
	elseif (j <= -3.5e-87)
		tmp = t_5;
	elseif (j <= -3.1e-174)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (j <= -2.7e-223)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) - Float64(Float64(a * t_3) - Float64(y4 * t_4))));
	elseif (j <= 7.6e-231)
		tmp = t_5;
	elseif (j <= 2.4e-131)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * t_1) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (j <= 7.2e+102)
		tmp = Float64(y0 * Float64(Float64(Float64(c * t_3) + Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2)))) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))));
	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 = (y0 * y5) - (y1 * y4);
	t_2 = j * (((t * ((b * y4) - (i * y5))) + (y3 * t_1)) + (x * ((i * y1) - (b * y0))));
	t_3 = (x * y2) - (z * y3);
	t_4 = (k * y2) - (j * y3);
	t_5 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_4)) + (c * ((y * y3) - (t * y2))));
	tmp = 0.0;
	if (j <= -2.2e+17)
		tmp = t_2;
	elseif (j <= -3.5e-87)
		tmp = t_5;
	elseif (j <= -3.1e-174)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (j <= -2.7e-223)
		tmp = y1 * ((i * ((x * j) - (z * k))) - ((a * t_3) - (y4 * t_4)));
	elseif (j <= 7.6e-231)
		tmp = t_5;
	elseif (j <= 2.4e-131)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_1) + (z * ((a * y1) - (c * y0)))));
	elseif (j <= 7.2e+102)
		tmp = y0 * (((c * t_3) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	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[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.2e+17], t$95$2, If[LessEqual[j, -3.5e-87], t$95$5, If[LessEqual[j, -3.1e-174], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.7e-223], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t$95$3), $MachinePrecision] - N[(y4 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.6e-231], t$95$5, If[LessEqual[j, 2.4e-131], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * t$95$1), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.2e+102], N[(y0 * N[(N[(N[(c * t$95$3), $MachinePrecision] + N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -2.2e17 or 7.2000000000000003e102 < 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. Taylor expanded in j around inf 64.8%

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

      1. +-commutative 64.8%

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

      2. mul-1-neg 64.8%

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

      3. unsub-neg 64.8%

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

      4. *-commutative 64.8%

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

   4. Simplified 64.8%

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

   if -2.2e17 < j < -3.50000000000000012e-87 or -2.69999999999999988e-223 < j < 7.60000000000000026e-231

   1. Initial program 43.7%

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

   2. Taylor expanded in y4 around inf 58.8%

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

   if -3.50000000000000012e-87 < j < -3.0999999999999999e-174

   1. Initial program 41.5%

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

   2. Taylor expanded in y5 around inf 41.3%

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

      1. mul-1-neg 41.3%

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

      2. associate-*r* 35.5%

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

      3. *-commutative 35.5%

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

   4. Simplified 35.5%

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

   5. Taylor expanded in i around inf 53.8%

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

   if -3.0999999999999999e-174 < j < -2.69999999999999988e-223

   1. Initial program 37.4%

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

   2. Taylor expanded in y1 around -inf 57.3%

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

      1. mul-1-neg 57.3%

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

      2. *-commutative 57.3%

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

      3. distribute-rgt-neg-in 57.3%

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

   4. Simplified 57.3%

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

   if 7.60000000000000026e-231 < j < 2.4e-131

   1. Initial program 40.0%

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

   2. Taylor expanded in y3 around -inf 65.6%

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

   if 2.4e-131 < j < 7.2000000000000003e102

   1. Initial program 38.8%

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

   2. Taylor expanded in y0 around inf 60.4%

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

      1. +-commutative 60.4%

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

      2. mul-1-neg 60.4%

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

      3. unsub-neg 60.4%

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

      4. *-commutative 60.4%

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

      5. *-commutative 60.4%

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

      6. *-commutative 60.4%

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

      7. *-commutative 60.4%

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

   4. Simplified 60.4%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.2 \cdot 10^{+17}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-87}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq -3.1 \cdot 10^{-174}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -2.7 \cdot 10^{-223}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - \left(a \cdot \left(x \cdot y2 - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;j \leq 7.6 \cdot 10^{-231}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{-131}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{+102}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]

Alternative 13: 34.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ t_2 := k \cdot y2 - j \cdot y3\\ t_3 := y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot t_2\right)\\ \mathbf{if}\;k \leq -2.5 \cdot 10^{+245}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -1.35 \cdot 10^{+69}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq -2.8 \cdot 10^{-245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 2.7 \cdot 10^{-257}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 3.95 \cdot 10^{-218}:\\ \;\;\;\;y \cdot \left(i \cdot \left(k \cdot y5\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 1.05 \cdot 10^{-64}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(y2 \cdot y5 - z \cdot b\right)\\ \mathbf{elif}\;k \leq 1.1 \cdot 10^{-22}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 1.15 \cdot 10^{+17}:\\ \;\;\;\;t_2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(i \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 1.26 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (* y0 (+ (* c (- (* x y2) (* z y3))) (* y5 (- (* j y3) (* k y2))))))
        (t_2 (- (* k y2) (* j y3)))
        (t_3 (* y1 (+ (* i (- (* x j) (* z k))) (* y4 t_2)))))
   (if (<= k -2.5e+245)
     (* j (* y3 (- (* y0 y5) (* y1 y4))))
     (if (<= k -1.35e+69)
       t_3
       (if (<= k -2.8e-245)
         t_1
         (if (<= k 2.7e-257)
           (* j (* x (- (* i y1) (* b y0))))
           (if (<= k 3.95e-218)
             (* y (+ (* i (* k y5)) (* y3 (- (* c y4) (* a y5)))))
             (if (<= k 1.05e-64)
               (* (* t a) (- (* y2 y5) (* z b)))
               (if (<= k 1.1e-22)
                 t_3
                 (if (<= k 1.15e+17)
                   (+
                    (* t_2 (- (* y1 y4) (* y0 y5)))
                    (* t (* i (- (* z c) (* j y5)))))
                   (if (<= k 1.26e+135)
                     t_1
                     (* b (* k (- (* z y0) (* y y4)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * ((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2))));
	double t_2 = (k * y2) - (j * y3);
	double t_3 = y1 * ((i * ((x * j) - (z * k))) + (y4 * t_2));
	double tmp;
	if (k <= -2.5e+245) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (k <= -1.35e+69) {
		tmp = t_3;
	} else if (k <= -2.8e-245) {
		tmp = t_1;
	} else if (k <= 2.7e-257) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (k <= 3.95e-218) {
		tmp = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))));
	} else if (k <= 1.05e-64) {
		tmp = (t * a) * ((y2 * y5) - (z * b));
	} else if (k <= 1.1e-22) {
		tmp = t_3;
	} else if (k <= 1.15e+17) {
		tmp = (t_2 * ((y1 * y4) - (y0 * y5))) + (t * (i * ((z * c) - (j * y5))));
	} else if (k <= 1.26e+135) {
		tmp = t_1;
	} else {
		tmp = b * (k * ((z * y0) - (y * y4)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y0 * ((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2))))
    t_2 = (k * y2) - (j * y3)
    t_3 = y1 * ((i * ((x * j) - (z * k))) + (y4 * t_2))
    if (k <= (-2.5d+245)) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (k <= (-1.35d+69)) then
        tmp = t_3
    else if (k <= (-2.8d-245)) then
        tmp = t_1
    else if (k <= 2.7d-257) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (k <= 3.95d-218) then
        tmp = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))))
    else if (k <= 1.05d-64) then
        tmp = (t * a) * ((y2 * y5) - (z * b))
    else if (k <= 1.1d-22) then
        tmp = t_3
    else if (k <= 1.15d+17) then
        tmp = (t_2 * ((y1 * y4) - (y0 * y5))) + (t * (i * ((z * c) - (j * y5))))
    else if (k <= 1.26d+135) then
        tmp = t_1
    else
        tmp = b * (k * ((z * y0) - (y * y4)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * ((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2))));
	double t_2 = (k * y2) - (j * y3);
	double t_3 = y1 * ((i * ((x * j) - (z * k))) + (y4 * t_2));
	double tmp;
	if (k <= -2.5e+245) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (k <= -1.35e+69) {
		tmp = t_3;
	} else if (k <= -2.8e-245) {
		tmp = t_1;
	} else if (k <= 2.7e-257) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (k <= 3.95e-218) {
		tmp = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))));
	} else if (k <= 1.05e-64) {
		tmp = (t * a) * ((y2 * y5) - (z * b));
	} else if (k <= 1.1e-22) {
		tmp = t_3;
	} else if (k <= 1.15e+17) {
		tmp = (t_2 * ((y1 * y4) - (y0 * y5))) + (t * (i * ((z * c) - (j * y5))));
	} else if (k <= 1.26e+135) {
		tmp = t_1;
	} else {
		tmp = b * (k * ((z * y0) - (y * y4)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * ((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2))))
	t_2 = (k * y2) - (j * y3)
	t_3 = y1 * ((i * ((x * j) - (z * k))) + (y4 * t_2))
	tmp = 0
	if k <= -2.5e+245:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif k <= -1.35e+69:
		tmp = t_3
	elif k <= -2.8e-245:
		tmp = t_1
	elif k <= 2.7e-257:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif k <= 3.95e-218:
		tmp = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))))
	elif k <= 1.05e-64:
		tmp = (t * a) * ((y2 * y5) - (z * b))
	elif k <= 1.1e-22:
		tmp = t_3
	elif k <= 1.15e+17:
		tmp = (t_2 * ((y1 * y4) - (y0 * y5))) + (t * (i * ((z * c) - (j * y5))))
	elif k <= 1.26e+135:
		tmp = t_1
	else:
		tmp = b * (k * ((z * y0) - (y * y4)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2)))))
	t_2 = Float64(Float64(k * y2) - Float64(j * y3))
	t_3 = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(y4 * t_2)))
	tmp = 0.0
	if (k <= -2.5e+245)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (k <= -1.35e+69)
		tmp = t_3;
	elseif (k <= -2.8e-245)
		tmp = t_1;
	elseif (k <= 2.7e-257)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (k <= 3.95e-218)
		tmp = Float64(y * Float64(Float64(i * Float64(k * y5)) + Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5)))));
	elseif (k <= 1.05e-64)
		tmp = Float64(Float64(t * a) * Float64(Float64(y2 * y5) - Float64(z * b)));
	elseif (k <= 1.1e-22)
		tmp = t_3;
	elseif (k <= 1.15e+17)
		tmp = Float64(Float64(t_2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(t * Float64(i * Float64(Float64(z * c) - Float64(j * y5)))));
	elseif (k <= 1.26e+135)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y0 * ((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2))));
	t_2 = (k * y2) - (j * y3);
	t_3 = y1 * ((i * ((x * j) - (z * k))) + (y4 * t_2));
	tmp = 0.0;
	if (k <= -2.5e+245)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (k <= -1.35e+69)
		tmp = t_3;
	elseif (k <= -2.8e-245)
		tmp = t_1;
	elseif (k <= 2.7e-257)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (k <= 3.95e-218)
		tmp = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))));
	elseif (k <= 1.05e-64)
		tmp = (t * a) * ((y2 * y5) - (z * b));
	elseif (k <= 1.1e-22)
		tmp = t_3;
	elseif (k <= 1.15e+17)
		tmp = (t_2 * ((y1 * y4) - (y0 * y5))) + (t * (i * ((z * c) - (j * y5))));
	elseif (k <= 1.26e+135)
		tmp = t_1;
	else
		tmp = b * (k * ((z * y0) - (y * y4)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y0 * N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -2.5e+245], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.35e+69], t$95$3, If[LessEqual[k, -2.8e-245], t$95$1, If[LessEqual[k, 2.7e-257], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.95e-218], N[(y * N[(N[(i * N[(k * y5), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.05e-64], N[(N[(t * a), $MachinePrecision] * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.1e-22], t$95$3, If[LessEqual[k, 1.15e+17], N[(N[(t$95$2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(i * N[(N[(z * c), $MachinePrecision] - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.26e+135], t$95$1, N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if k < -2.50000000000000017e245

   1. Initial program 18.8%

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

   2. Taylor expanded in j around inf 44.9%

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

      1. +-commutative 44.9%

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

      2. mul-1-neg 44.9%

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

      3. unsub-neg 44.9%

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

      4. *-commutative 44.9%

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

   4. Simplified 44.9%

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

   5. Taylor expanded in y3 around inf 57.2%

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

   if -2.50000000000000017e245 < k < -1.3499999999999999e69 or 1.05000000000000006e-64 < k < 1.1e-22

   1. Initial program 26.7%

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

   2. Taylor expanded in y1 around -inf 56.0%

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

      1. mul-1-neg 56.0%

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

      2. *-commutative 56.0%

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

      3. distribute-rgt-neg-in 56.0%

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

   4. Simplified 56.0%

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

   5. Taylor expanded in a around 0 62.9%

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

   if -1.3499999999999999e69 < k < -2.8000000000000001e-245 or 1.15e17 < k < 1.2600000000000001e135

   1. Initial program 46.6%

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

   2. Taylor expanded in c around inf 50.8%

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

      1. +-commutative 50.8%

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

      2. mul-1-neg 50.8%

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

      3. unsub-neg 50.8%

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

      4. *-commutative 50.8%

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

      5. *-commutative 50.8%

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

      6. *-commutative 50.8%

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

      7. *-commutative 50.8%

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

   4. Simplified 50.8%

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

   5. Taylor expanded in y0 around inf 52.3%

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

      1. +-commutative 52.3%

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

      2. mul-1-neg 52.3%

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

      3. *-commutative 52.3%

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

      4. *-commutative 52.3%

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

      5. *-commutative 52.3%

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

      6. unsub-neg 52.3%

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

      7. *-commutative 52.3%

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

      8. *-commutative 52.3%

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

      9. *-commutative 52.3%

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

      10. *-commutative 52.3%

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

   7. Simplified 52.3%

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

   if -2.8000000000000001e-245 < k < 2.6999999999999999e-257

   1. Initial program 31.3%

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

   2. Taylor expanded in j around inf 53.0%

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

      1. +-commutative 53.0%

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

      2. mul-1-neg 53.0%

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

      3. unsub-neg 53.0%

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

      4. *-commutative 53.0%

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

   4. Simplified 53.0%

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

   5. Taylor expanded in x around inf 48.6%

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

   if 2.6999999999999999e-257 < k < 3.95e-218

   1. Initial program 49.9%

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

   2. Taylor expanded in y5 around inf 50.6%

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

      1. mul-1-neg 50.6%

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

      2. associate-*r* 60.6%

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

      3. *-commutative 60.6%

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

   4. Simplified 60.6%

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

   5. Taylor expanded in y around -inf 51.4%

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

   if 3.95e-218 < k < 1.05000000000000006e-64

   1. Initial program 28.0%

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

   2. Taylor expanded in t around inf 36.6%

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

   3. Taylor expanded in a around inf 43.1%

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

      1. associate-*r* 43.1%

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

      2. cancel-sign-sub-inv 43.1%

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

      3. metadata-eval 43.1%

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

      4. *-lft-identity 43.1%

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

      5. +-commutative 43.1%

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

      6. mul-1-neg 43.1%

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

      7. unsub-neg 43.1%

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

      8. *-commutative 43.1%

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

   5. Simplified 43.1%

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

   if 1.1e-22 < k < 1.15e17

   1. Initial program 45.3%

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

   2. Taylor expanded in t around inf 63.5%

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

   3. Taylor expanded in i around inf 55.6%

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

      1. +-commutative 55.6%

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

      2. mul-1-neg 55.6%

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

      3. unsub-neg 55.6%

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

      4. *-commutative 55.6%

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

   5. Simplified 55.6%

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

   if 1.2600000000000001e135 < k

   1. Initial program 27.2%

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

   2. Taylor expanded in k around inf 54.8%

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

      1. sub-neg 54.8%

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

      2. +-commutative 54.8%

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

      3. mul-1-neg 54.8%

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

      4. unsub-neg 54.8%

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

      5. *-commutative 54.8%

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

      6. mul-1-neg 54.8%

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

      7. remove-double-neg 54.8%

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

   4. Simplified 54.8%

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

   5. Taylor expanded in b around inf 61.0%

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z - y \cdot y4\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.5 \cdot 10^{+245}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -1.35 \cdot 10^{+69}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq -2.8 \cdot 10^{-245}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 2.7 \cdot 10^{-257}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 3.95 \cdot 10^{-218}:\\ \;\;\;\;y \cdot \left(i \cdot \left(k \cdot y5\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 1.05 \cdot 10^{-64}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(y2 \cdot y5 - z \cdot b\right)\\ \mathbf{elif}\;k \leq 1.1 \cdot 10^{-22}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 1.15 \cdot 10^{+17}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(i \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 1.26 \cdot 10^{+135}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \end{array} \]

Alternative 14: 33.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ t_2 := y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{if}\;k \leq -5.5 \cdot 10^{+245}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -1.58 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq -1.32 \cdot 10^{-245}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 3.1 \cdot 10^{-258}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 3.8 \cdot 10^{-218}:\\ \;\;\;\;y \cdot \left(i \cdot \left(k \cdot y5\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 3.7 \cdot 10^{-65}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(y2 \cdot y5 - z \cdot b\right)\\ \mathbf{elif}\;k \leq 2.7 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 24500000:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;k \leq 8.5 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 2.2 \cdot 10^{+135}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (+ (* i (- (* x j) (* z k))) (* y4 (- (* k y2) (* j y3))))))
        (t_2
         (* y0 (+ (* c (- (* x y2) (* z y3))) (* y5 (- (* j y3) (* k y2)))))))
   (if (<= k -5.5e+245)
     (* j (* y3 (- (* y0 y5) (* y1 y4))))
     (if (<= k -1.58e+69)
       t_1
       (if (<= k -1.32e-245)
         t_2
         (if (<= k 3.1e-258)
           (* j (* x (- (* i y1) (* b y0))))
           (if (<= k 3.8e-218)
             (* y (+ (* i (* k y5)) (* y3 (- (* c y4) (* a y5)))))
             (if (<= k 3.7e-65)
               (* (* t a) (- (* y2 y5) (* z b)))
               (if (<= k 2.7e-22)
                 t_1
                 (if (<= k 24500000.0)
                   (* j (* y5 (- (* y0 y3) (* t i))))
                   (if (<= k 8.5e+16)
                     t_1
                     (if (<= k 2.2e+135)
                       t_2
                       (* b (* k (- (* z y0) (* y y4))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3))));
	double t_2 = y0 * ((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2))));
	double tmp;
	if (k <= -5.5e+245) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (k <= -1.58e+69) {
		tmp = t_1;
	} else if (k <= -1.32e-245) {
		tmp = t_2;
	} else if (k <= 3.1e-258) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (k <= 3.8e-218) {
		tmp = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))));
	} else if (k <= 3.7e-65) {
		tmp = (t * a) * ((y2 * y5) - (z * b));
	} else if (k <= 2.7e-22) {
		tmp = t_1;
	} else if (k <= 24500000.0) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (k <= 8.5e+16) {
		tmp = t_1;
	} else if (k <= 2.2e+135) {
		tmp = t_2;
	} else {
		tmp = b * (k * ((z * y0) - (y * y4)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y1 * ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3))))
    t_2 = y0 * ((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2))))
    if (k <= (-5.5d+245)) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (k <= (-1.58d+69)) then
        tmp = t_1
    else if (k <= (-1.32d-245)) then
        tmp = t_2
    else if (k <= 3.1d-258) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (k <= 3.8d-218) then
        tmp = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))))
    else if (k <= 3.7d-65) then
        tmp = (t * a) * ((y2 * y5) - (z * b))
    else if (k <= 2.7d-22) then
        tmp = t_1
    else if (k <= 24500000.0d0) then
        tmp = j * (y5 * ((y0 * y3) - (t * i)))
    else if (k <= 8.5d+16) then
        tmp = t_1
    else if (k <= 2.2d+135) then
        tmp = t_2
    else
        tmp = b * (k * ((z * y0) - (y * y4)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3))));
	double t_2 = y0 * ((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2))));
	double tmp;
	if (k <= -5.5e+245) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (k <= -1.58e+69) {
		tmp = t_1;
	} else if (k <= -1.32e-245) {
		tmp = t_2;
	} else if (k <= 3.1e-258) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (k <= 3.8e-218) {
		tmp = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))));
	} else if (k <= 3.7e-65) {
		tmp = (t * a) * ((y2 * y5) - (z * b));
	} else if (k <= 2.7e-22) {
		tmp = t_1;
	} else if (k <= 24500000.0) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (k <= 8.5e+16) {
		tmp = t_1;
	} else if (k <= 2.2e+135) {
		tmp = t_2;
	} else {
		tmp = b * (k * ((z * y0) - (y * y4)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y1 * ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3))))
	t_2 = y0 * ((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2))))
	tmp = 0
	if k <= -5.5e+245:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif k <= -1.58e+69:
		tmp = t_1
	elif k <= -1.32e-245:
		tmp = t_2
	elif k <= 3.1e-258:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif k <= 3.8e-218:
		tmp = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))))
	elif k <= 3.7e-65:
		tmp = (t * a) * ((y2 * y5) - (z * b))
	elif k <= 2.7e-22:
		tmp = t_1
	elif k <= 24500000.0:
		tmp = j * (y5 * ((y0 * y3) - (t * i)))
	elif k <= 8.5e+16:
		tmp = t_1
	elif k <= 2.2e+135:
		tmp = t_2
	else:
		tmp = b * (k * ((z * y0) - (y * y4)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3)))))
	t_2 = Float64(y0 * Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2)))))
	tmp = 0.0
	if (k <= -5.5e+245)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (k <= -1.58e+69)
		tmp = t_1;
	elseif (k <= -1.32e-245)
		tmp = t_2;
	elseif (k <= 3.1e-258)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (k <= 3.8e-218)
		tmp = Float64(y * Float64(Float64(i * Float64(k * y5)) + Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5)))));
	elseif (k <= 3.7e-65)
		tmp = Float64(Float64(t * a) * Float64(Float64(y2 * y5) - Float64(z * b)));
	elseif (k <= 2.7e-22)
		tmp = t_1;
	elseif (k <= 24500000.0)
		tmp = Float64(j * Float64(y5 * Float64(Float64(y0 * y3) - Float64(t * i))));
	elseif (k <= 8.5e+16)
		tmp = t_1;
	elseif (k <= 2.2e+135)
		tmp = t_2;
	else
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y1 * ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3))));
	t_2 = y0 * ((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2))));
	tmp = 0.0;
	if (k <= -5.5e+245)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (k <= -1.58e+69)
		tmp = t_1;
	elseif (k <= -1.32e-245)
		tmp = t_2;
	elseif (k <= 3.1e-258)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (k <= 3.8e-218)
		tmp = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))));
	elseif (k <= 3.7e-65)
		tmp = (t * a) * ((y2 * y5) - (z * b));
	elseif (k <= 2.7e-22)
		tmp = t_1;
	elseif (k <= 24500000.0)
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	elseif (k <= 8.5e+16)
		tmp = t_1;
	elseif (k <= 2.2e+135)
		tmp = t_2;
	else
		tmp = b * (k * ((z * y0) - (y * y4)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y0 * N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -5.5e+245], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.58e+69], t$95$1, If[LessEqual[k, -1.32e-245], t$95$2, If[LessEqual[k, 3.1e-258], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.8e-218], N[(y * N[(N[(i * N[(k * y5), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.7e-65], N[(N[(t * a), $MachinePrecision] * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.7e-22], t$95$1, If[LessEqual[k, 24500000.0], N[(j * N[(y5 * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 8.5e+16], t$95$1, If[LessEqual[k, 2.2e+135], t$95$2, N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if k < -5.4999999999999997e245

   1. Initial program 18.8%

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

   2. Taylor expanded in j around inf 44.9%

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

      1. +-commutative 44.9%

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

      2. mul-1-neg 44.9%

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

      3. unsub-neg 44.9%

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

      4. *-commutative 44.9%

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

   4. Simplified 44.9%

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

   5. Taylor expanded in y3 around inf 57.2%

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

   if -5.4999999999999997e245 < k < -1.58e69 or 3.7e-65 < k < 2.7000000000000002e-22 or 2.45e7 < k < 8.5e16

   1. Initial program 28.6%

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

   2. Taylor expanded in y1 around -inf 57.6%

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

      1. mul-1-neg 57.6%

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

      2. *-commutative 57.6%

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

      3. distribute-rgt-neg-in 57.6%

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

   4. Simplified 57.6%

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

   5. Taylor expanded in a around 0 63.9%

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

   if -1.58e69 < k < -1.32e-245 or 8.5e16 < k < 2.1999999999999999e135

   1. Initial program 46.6%

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

   2. Taylor expanded in c around inf 50.8%

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

      1. +-commutative 50.8%

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

      2. mul-1-neg 50.8%

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

      3. unsub-neg 50.8%

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

      4. *-commutative 50.8%

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

      5. *-commutative 50.8%

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

      6. *-commutative 50.8%

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

      7. *-commutative 50.8%

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

   4. Simplified 50.8%

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

   5. Taylor expanded in y0 around inf 52.3%

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

      1. +-commutative 52.3%

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

      2. mul-1-neg 52.3%

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

      3. *-commutative 52.3%

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

      4. *-commutative 52.3%

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

      5. *-commutative 52.3%

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

      6. unsub-neg 52.3%

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

      7. *-commutative 52.3%

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

      8. *-commutative 52.3%

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

      9. *-commutative 52.3%

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

      10. *-commutative 52.3%

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

   7. Simplified 52.3%

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

   if -1.32e-245 < k < 3.09999999999999999e-258

   1. Initial program 31.3%

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

   2. Taylor expanded in j around inf 53.0%

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

      1. +-commutative 53.0%

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

      2. mul-1-neg 53.0%

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

      3. unsub-neg 53.0%

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

      4. *-commutative 53.0%

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

   4. Simplified 53.0%

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

   5. Taylor expanded in x around inf 48.6%

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

   if 3.09999999999999999e-258 < k < 3.7999999999999999e-218

   1. Initial program 49.9%

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

   2. Taylor expanded in y5 around inf 50.6%

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

      1. mul-1-neg 50.6%

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

      2. associate-*r* 60.6%

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

      3. *-commutative 60.6%

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

   4. Simplified 60.6%

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

   5. Taylor expanded in y around -inf 51.4%

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

   if 3.7999999999999999e-218 < k < 3.7e-65

   1. Initial program 28.0%

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

   2. Taylor expanded in t around inf 36.6%

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

   3. Taylor expanded in a around inf 43.1%

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

      1. associate-*r* 43.1%

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

      2. cancel-sign-sub-inv 43.1%

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

      3. metadata-eval 43.1%

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

      4. *-lft-identity 43.1%

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

      5. +-commutative 43.1%

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

      6. mul-1-neg 43.1%

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

      7. unsub-neg 43.1%

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

      8. *-commutative 43.1%

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

   5. Simplified 43.1%

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

   if 2.7000000000000002e-22 < k < 2.45e7

   1. Initial program 42.6%

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

   2. Taylor expanded in j around inf 71.3%

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

      1. +-commutative 71.3%

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

      2. mul-1-neg 71.3%

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

      3. unsub-neg 71.3%

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

      4. *-commutative 71.3%

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

   4. Simplified 71.3%

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

   5. Taylor expanded in y5 around -inf 72.1%

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

      1. associate-*r* 72.1%

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

      2. neg-mul-1 72.1%

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

      3. *-commutative 72.1%

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

   7. Simplified 72.1%

      \[\leadsto \color{blue}{\left(-j\right) \cdot \left(y5 \cdot \left(t \cdot i - y0 \cdot y3\right)\right)} \]

   if 2.1999999999999999e135 < k

   1. Initial program 27.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in k around inf 54.8%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 54.8%

         \[\leadsto k \cdot \color{blue}{\left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. +-commutative 54.8%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      3. mul-1-neg 54.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      4. unsub-neg 54.8%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-commutative 54.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. mul-1-neg 54.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + \left(-\color{blue}{\left(-z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      7. remove-double-neg 54.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + \color{blue}{z \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Simplified 54.8%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf 61.0%

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z - y \cdot y4\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -5.5 \cdot 10^{+245}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -1.58 \cdot 10^{+69}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq -1.32 \cdot 10^{-245}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 3.1 \cdot 10^{-258}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 3.8 \cdot 10^{-218}:\\ \;\;\;\;y \cdot \left(i \cdot \left(k \cdot y5\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 3.7 \cdot 10^{-65}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(y2 \cdot y5 - z \cdot b\right)\\ \mathbf{elif}\;k \leq 2.7 \cdot 10^{-22}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 24500000:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;k \leq 8.5 \cdot 10^{+16}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 2.2 \cdot 10^{+135}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \end{array} \]

Alternative 15: 31.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{if}\;k \leq -5.2 \cdot 10^{+214}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -1.15 \cdot 10^{+160}:\\ \;\;\;\;y \cdot \left(i \cdot \left(k \cdot y5\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq -1 \cdot 10^{+70}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;k \leq -2.3 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 8.8 \cdot 10^{-257}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 4 \cdot 10^{-193}:\\ \;\;\;\;\left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5\right)\\ \mathbf{elif}\;k \leq 700000000000:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;k \leq 7 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (* y0 (+ (* c (- (* x y2) (* z y3))) (* y5 (- (* j y3) (* k y2)))))))
   (if (<= k -5.2e+214)
     (* j (* y3 (- (* y0 y5) (* y1 y4))))
     (if (<= k -1.15e+160)
       (* y (+ (* i (* k y5)) (* y3 (- (* c y4) (* a y5)))))
       (if (<= k -1e+70)
         (* c (* x (- (* y0 y2) (* y i))))
         (if (<= k -2.3e-247)
           t_1
           (if (<= k 8.8e-257)
             (* j (* x (- (* i y1) (* b y0))))
             (if (<= k 4e-193)
               (* (- (* t y2) (* y y3)) (* a y5))
               (if (<= k 700000000000.0)
                 (* j (* y5 (- (* y0 y3) (* t i))))
                 (if (<= k 7e+136)
                   t_1
                   (* b (* k (- (* z y0) (* y y4))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * ((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2))));
	double tmp;
	if (k <= -5.2e+214) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (k <= -1.15e+160) {
		tmp = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))));
	} else if (k <= -1e+70) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (k <= -2.3e-247) {
		tmp = t_1;
	} else if (k <= 8.8e-257) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (k <= 4e-193) {
		tmp = ((t * y2) - (y * y3)) * (a * y5);
	} else if (k <= 700000000000.0) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (k <= 7e+136) {
		tmp = t_1;
	} else {
		tmp = b * (k * ((z * y0) - (y * y4)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y0 * ((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2))))
    if (k <= (-5.2d+214)) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (k <= (-1.15d+160)) then
        tmp = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))))
    else if (k <= (-1d+70)) then
        tmp = c * (x * ((y0 * y2) - (y * i)))
    else if (k <= (-2.3d-247)) then
        tmp = t_1
    else if (k <= 8.8d-257) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (k <= 4d-193) then
        tmp = ((t * y2) - (y * y3)) * (a * y5)
    else if (k <= 700000000000.0d0) then
        tmp = j * (y5 * ((y0 * y3) - (t * i)))
    else if (k <= 7d+136) then
        tmp = t_1
    else
        tmp = b * (k * ((z * y0) - (y * y4)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * ((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2))));
	double tmp;
	if (k <= -5.2e+214) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (k <= -1.15e+160) {
		tmp = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))));
	} else if (k <= -1e+70) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (k <= -2.3e-247) {
		tmp = t_1;
	} else if (k <= 8.8e-257) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (k <= 4e-193) {
		tmp = ((t * y2) - (y * y3)) * (a * y5);
	} else if (k <= 700000000000.0) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (k <= 7e+136) {
		tmp = t_1;
	} else {
		tmp = b * (k * ((z * y0) - (y * y4)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * ((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2))))
	tmp = 0
	if k <= -5.2e+214:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif k <= -1.15e+160:
		tmp = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))))
	elif k <= -1e+70:
		tmp = c * (x * ((y0 * y2) - (y * i)))
	elif k <= -2.3e-247:
		tmp = t_1
	elif k <= 8.8e-257:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif k <= 4e-193:
		tmp = ((t * y2) - (y * y3)) * (a * y5)
	elif k <= 700000000000.0:
		tmp = j * (y5 * ((y0 * y3) - (t * i)))
	elif k <= 7e+136:
		tmp = t_1
	else:
		tmp = b * (k * ((z * y0) - (y * y4)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2)))))
	tmp = 0.0
	if (k <= -5.2e+214)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (k <= -1.15e+160)
		tmp = Float64(y * Float64(Float64(i * Float64(k * y5)) + Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5)))));
	elseif (k <= -1e+70)
		tmp = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))));
	elseif (k <= -2.3e-247)
		tmp = t_1;
	elseif (k <= 8.8e-257)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (k <= 4e-193)
		tmp = Float64(Float64(Float64(t * y2) - Float64(y * y3)) * Float64(a * y5));
	elseif (k <= 700000000000.0)
		tmp = Float64(j * Float64(y5 * Float64(Float64(y0 * y3) - Float64(t * i))));
	elseif (k <= 7e+136)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y0 * ((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2))));
	tmp = 0.0;
	if (k <= -5.2e+214)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (k <= -1.15e+160)
		tmp = y * ((i * (k * y5)) + (y3 * ((c * y4) - (a * y5))));
	elseif (k <= -1e+70)
		tmp = c * (x * ((y0 * y2) - (y * i)));
	elseif (k <= -2.3e-247)
		tmp = t_1;
	elseif (k <= 8.8e-257)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (k <= 4e-193)
		tmp = ((t * y2) - (y * y3)) * (a * y5);
	elseif (k <= 700000000000.0)
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	elseif (k <= 7e+136)
		tmp = t_1;
	else
		tmp = b * (k * ((z * y0) - (y * y4)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y0 * N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -5.2e+214], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.15e+160], N[(y * N[(N[(i * N[(k * y5), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1e+70], N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2.3e-247], t$95$1, If[LessEqual[k, 8.8e-257], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4e-193], N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * N[(a * y5), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 700000000000.0], N[(j * N[(y5 * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 7e+136], t$95$1, N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if k < -5.19999999999999986e214

   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. Taylor expanded in j around inf 42.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 42.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 42.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 42.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 42.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 42.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y3 around inf 55.1%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if -5.19999999999999986e214 < k < -1.14999999999999994e160

   1. Initial program 13.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 40.0%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 40.0%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 40.0%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 40.0%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 40.0%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y around -inf 73.7%

      \[\leadsto \color{blue}{y \cdot \left(i \cdot \left(k \cdot y5\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   if -1.14999999999999994e160 < k < -1.00000000000000007e70

   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. Taylor expanded in c around inf 34.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 34.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 34.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 34.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 34.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 34.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 34.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 34.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 34.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in x around inf 51.5%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2 - i \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 51.5%

         \[\leadsto c \cdot \left(x \cdot \left(\color{blue}{y2 \cdot y0} - i \cdot y\right)\right) \]

   7. Simplified 51.5%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0 - i \cdot y\right)\right)} \]

   if -1.00000000000000007e70 < k < -2.3e-247 or 7e11 < k < 7.00000000000000002e136

   1. Initial program 46.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 52.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 52.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 52.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 52.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 52.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 52.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 52.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 52.0%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 52.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 51.1%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 51.1%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 51.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]

      3. *-commutative 51.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot y5}\right)\right) \]

      4. *-commutative 51.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(\color{blue}{y2 \cdot k} - j \cdot y3\right) \cdot y5\right)\right) \]

      5. *-commutative 51.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(y2 \cdot k - \color{blue}{y3 \cdot j}\right) \cdot y5\right)\right) \]

      6. unsub-neg 51.1%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right)} \]

      7. *-commutative 51.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right) \]

      8. *-commutative 51.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(\color{blue}{k \cdot y2} - y3 \cdot j\right) \cdot y5\right) \]

      9. *-commutative 51.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) \cdot y5\right) \]

      10. *-commutative 51.1%

          \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \color{blue}{y5 \cdot \left(k \cdot y2 - j \cdot y3\right)}\right) \]

   7. Simplified 51.1%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   if -2.3e-247 < k < 8.7999999999999995e-257

   1. Initial program 31.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 53.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 53.0%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 53.0%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 53.0%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 53.0%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 53.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in x around inf 48.6%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   if 8.7999999999999995e-257 < k < 4.0000000000000002e-193

   1. Initial program 41.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 35.6%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 35.6%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 41.5%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 41.5%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 41.5%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 53.6%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 53.6%

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 53.6%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in a around 0 53.6%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 53.6%

         \[\leadsto \color{blue}{\left(a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

      2. *-commutative 53.6%

         \[\leadsto \left(a \cdot y5\right) \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right) \]

      3. *-commutative 53.6%

         \[\leadsto \left(a \cdot y5\right) \cdot \left(\color{blue}{y2 \cdot t} - y3 \cdot y\right) \]

      4. *-commutative 53.6%

         \[\leadsto \color{blue}{\left(y2 \cdot t - y3 \cdot y\right) \cdot \left(a \cdot y5\right)} \]

      5. *-commutative 53.6%

         \[\leadsto \left(y2 \cdot t - y3 \cdot y\right) \cdot \color{blue}{\left(y5 \cdot a\right)} \]

   10. Simplified 53.6%

       \[\leadsto \color{blue}{\left(y2 \cdot t - y3 \cdot y\right) \cdot \left(y5 \cdot a\right)} \]

   if 4.0000000000000002e-193 < k < 7e11

   1. Initial program 35.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 46.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 46.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 46.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 46.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 46.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 46.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y5 around -inf 38.9%

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(y5 \cdot \left(i \cdot t - y0 \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 38.9%

         \[\leadsto \color{blue}{\left(-1 \cdot j\right) \cdot \left(y5 \cdot \left(i \cdot t - y0 \cdot y3\right)\right)} \]

      2. neg-mul-1 38.9%

         \[\leadsto \color{blue}{\left(-j\right)} \cdot \left(y5 \cdot \left(i \cdot t - y0 \cdot y3\right)\right) \]

      3. *-commutative 38.9%

         \[\leadsto \left(-j\right) \cdot \left(y5 \cdot \left(\color{blue}{t \cdot i} - y0 \cdot y3\right)\right) \]

   7. Simplified 38.9%

      \[\leadsto \color{blue}{\left(-j\right) \cdot \left(y5 \cdot \left(t \cdot i - y0 \cdot y3\right)\right)} \]

   if 7.00000000000000002e136 < k

   1. Initial program 27.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in k around inf 54.8%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 54.8%

         \[\leadsto k \cdot \color{blue}{\left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. +-commutative 54.8%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      3. mul-1-neg 54.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      4. unsub-neg 54.8%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-commutative 54.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. mul-1-neg 54.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + \left(-\color{blue}{\left(-z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      7. remove-double-neg 54.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + \color{blue}{z \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Simplified 54.8%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf 61.0%

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z - y \cdot y4\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -5.2 \cdot 10^{+214}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -1.15 \cdot 10^{+160}:\\ \;\;\;\;y \cdot \left(i \cdot \left(k \cdot y5\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq -1 \cdot 10^{+70}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;k \leq -2.3 \cdot 10^{-247}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 8.8 \cdot 10^{-257}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 4 \cdot 10^{-193}:\\ \;\;\;\;\left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5\right)\\ \mathbf{elif}\;k \leq 700000000000:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;k \leq 7 \cdot 10^{+136}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \end{array} \]

Alternative 16: 30.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ t_2 := i \cdot y1 - b \cdot y0\\ t_3 := j \cdot \left(x \cdot t_2\right)\\ t_4 := \left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{if}\;y5 \leq -4.6 \cdot 10^{+222}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq -1.9 \cdot 10^{+137}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -2.75 \cdot 10^{+115}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(y2 \cdot y5 - z \cdot b\right)\\ \mathbf{elif}\;y5 \leq -2.2 \cdot 10^{+85}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y5 \leq -1.7 \cdot 10^{+27}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -1 \cdot 10^{-102}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -3 \cdot 10^{-248}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y5 \leq -1.15 \cdot 10^{-286}:\\ \;\;\;\;\left(x \cdot j\right) \cdot t_2\\ \mathbf{elif}\;y5 \leq 1.15 \cdot 10^{-204}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y5 \leq 3 \cdot 10^{-81}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 0.0077:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y5 \leq 9.8 \cdot 10^{+53}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* y5 (- (* j y3) (* k y2)))))
        (t_2 (- (* i y1) (* b y0)))
        (t_3 (* j (* x t_2)))
        (t_4 (* (* y c) (- (* y3 y4) (* x i)))))
   (if (<= y5 -4.6e+222)
     t_1
     (if (<= y5 -1.9e+137)
       (* i (* y5 (- (* y k) (* t j))))
       (if (<= y5 -2.75e+115)
         (* (* t a) (- (* y2 y5) (* z b)))
         (if (<= y5 -2.2e+85)
           t_3
           (if (<= y5 -1.7e+27)
             (* j (* y3 (- (* y0 y5) (* y1 y4))))
             (if (<= y5 -1e-102)
               (* y1 (* y4 (* k y2)))
               (if (<= y5 -3e-248)
                 t_4
                 (if (<= y5 -1.15e-286)
                   (* (* x j) t_2)
                   (if (<= y5 1.15e-204)
                     t_4
                     (if (<= y5 3e-81)
                       (* c (* t (- (* z i) (* y2 y4))))
                       (if (<= y5 0.0077)
                         t_3
                         (if (<= y5 9.8e+53)
                           (* (* t b) (- (* j y4) (* z a)))
                           t_1))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (y5 * ((j * y3) - (k * y2)));
	double t_2 = (i * y1) - (b * y0);
	double t_3 = j * (x * t_2);
	double t_4 = (y * c) * ((y3 * y4) - (x * i));
	double tmp;
	if (y5 <= -4.6e+222) {
		tmp = t_1;
	} else if (y5 <= -1.9e+137) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y5 <= -2.75e+115) {
		tmp = (t * a) * ((y2 * y5) - (z * b));
	} else if (y5 <= -2.2e+85) {
		tmp = t_3;
	} else if (y5 <= -1.7e+27) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (y5 <= -1e-102) {
		tmp = y1 * (y4 * (k * y2));
	} else if (y5 <= -3e-248) {
		tmp = t_4;
	} else if (y5 <= -1.15e-286) {
		tmp = (x * j) * t_2;
	} else if (y5 <= 1.15e-204) {
		tmp = t_4;
	} else if (y5 <= 3e-81) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (y5 <= 0.0077) {
		tmp = t_3;
	} else if (y5 <= 9.8e+53) {
		tmp = (t * b) * ((j * y4) - (z * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = y0 * (y5 * ((j * y3) - (k * y2)))
    t_2 = (i * y1) - (b * y0)
    t_3 = j * (x * t_2)
    t_4 = (y * c) * ((y3 * y4) - (x * i))
    if (y5 <= (-4.6d+222)) then
        tmp = t_1
    else if (y5 <= (-1.9d+137)) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (y5 <= (-2.75d+115)) then
        tmp = (t * a) * ((y2 * y5) - (z * b))
    else if (y5 <= (-2.2d+85)) then
        tmp = t_3
    else if (y5 <= (-1.7d+27)) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (y5 <= (-1d-102)) then
        tmp = y1 * (y4 * (k * y2))
    else if (y5 <= (-3d-248)) then
        tmp = t_4
    else if (y5 <= (-1.15d-286)) then
        tmp = (x * j) * t_2
    else if (y5 <= 1.15d-204) then
        tmp = t_4
    else if (y5 <= 3d-81) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (y5 <= 0.0077d0) then
        tmp = t_3
    else if (y5 <= 9.8d+53) then
        tmp = (t * b) * ((j * y4) - (z * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (y5 * ((j * y3) - (k * y2)));
	double t_2 = (i * y1) - (b * y0);
	double t_3 = j * (x * t_2);
	double t_4 = (y * c) * ((y3 * y4) - (x * i));
	double tmp;
	if (y5 <= -4.6e+222) {
		tmp = t_1;
	} else if (y5 <= -1.9e+137) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y5 <= -2.75e+115) {
		tmp = (t * a) * ((y2 * y5) - (z * b));
	} else if (y5 <= -2.2e+85) {
		tmp = t_3;
	} else if (y5 <= -1.7e+27) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (y5 <= -1e-102) {
		tmp = y1 * (y4 * (k * y2));
	} else if (y5 <= -3e-248) {
		tmp = t_4;
	} else if (y5 <= -1.15e-286) {
		tmp = (x * j) * t_2;
	} else if (y5 <= 1.15e-204) {
		tmp = t_4;
	} else if (y5 <= 3e-81) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (y5 <= 0.0077) {
		tmp = t_3;
	} else if (y5 <= 9.8e+53) {
		tmp = (t * b) * ((j * y4) - (z * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * (y5 * ((j * y3) - (k * y2)))
	t_2 = (i * y1) - (b * y0)
	t_3 = j * (x * t_2)
	t_4 = (y * c) * ((y3 * y4) - (x * i))
	tmp = 0
	if y5 <= -4.6e+222:
		tmp = t_1
	elif y5 <= -1.9e+137:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif y5 <= -2.75e+115:
		tmp = (t * a) * ((y2 * y5) - (z * b))
	elif y5 <= -2.2e+85:
		tmp = t_3
	elif y5 <= -1.7e+27:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif y5 <= -1e-102:
		tmp = y1 * (y4 * (k * y2))
	elif y5 <= -3e-248:
		tmp = t_4
	elif y5 <= -1.15e-286:
		tmp = (x * j) * t_2
	elif y5 <= 1.15e-204:
		tmp = t_4
	elif y5 <= 3e-81:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif y5 <= 0.0077:
		tmp = t_3
	elif y5 <= 9.8e+53:
		tmp = (t * b) * ((j * y4) - (z * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))))
	t_2 = Float64(Float64(i * y1) - Float64(b * y0))
	t_3 = Float64(j * Float64(x * t_2))
	t_4 = Float64(Float64(y * c) * Float64(Float64(y3 * y4) - Float64(x * i)))
	tmp = 0.0
	if (y5 <= -4.6e+222)
		tmp = t_1;
	elseif (y5 <= -1.9e+137)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (y5 <= -2.75e+115)
		tmp = Float64(Float64(t * a) * Float64(Float64(y2 * y5) - Float64(z * b)));
	elseif (y5 <= -2.2e+85)
		tmp = t_3;
	elseif (y5 <= -1.7e+27)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (y5 <= -1e-102)
		tmp = Float64(y1 * Float64(y4 * Float64(k * y2)));
	elseif (y5 <= -3e-248)
		tmp = t_4;
	elseif (y5 <= -1.15e-286)
		tmp = Float64(Float64(x * j) * t_2);
	elseif (y5 <= 1.15e-204)
		tmp = t_4;
	elseif (y5 <= 3e-81)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (y5 <= 0.0077)
		tmp = t_3;
	elseif (y5 <= 9.8e+53)
		tmp = Float64(Float64(t * b) * Float64(Float64(j * y4) - Float64(z * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y0 * (y5 * ((j * y3) - (k * y2)));
	t_2 = (i * y1) - (b * y0);
	t_3 = j * (x * t_2);
	t_4 = (y * c) * ((y3 * y4) - (x * i));
	tmp = 0.0;
	if (y5 <= -4.6e+222)
		tmp = t_1;
	elseif (y5 <= -1.9e+137)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (y5 <= -2.75e+115)
		tmp = (t * a) * ((y2 * y5) - (z * b));
	elseif (y5 <= -2.2e+85)
		tmp = t_3;
	elseif (y5 <= -1.7e+27)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (y5 <= -1e-102)
		tmp = y1 * (y4 * (k * y2));
	elseif (y5 <= -3e-248)
		tmp = t_4;
	elseif (y5 <= -1.15e-286)
		tmp = (x * j) * t_2;
	elseif (y5 <= 1.15e-204)
		tmp = t_4;
	elseif (y5 <= 3e-81)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (y5 <= 0.0077)
		tmp = t_3;
	elseif (y5 <= 9.8e+53)
		tmp = (t * b) * ((j * y4) - (z * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(x * t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y * c), $MachinePrecision] * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -4.6e+222], t$95$1, If[LessEqual[y5, -1.9e+137], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2.75e+115], N[(N[(t * a), $MachinePrecision] * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2.2e+85], t$95$3, If[LessEqual[y5, -1.7e+27], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1e-102], N[(y1 * N[(y4 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -3e-248], t$95$4, If[LessEqual[y5, -1.15e-286], N[(N[(x * j), $MachinePrecision] * t$95$2), $MachinePrecision], If[LessEqual[y5, 1.15e-204], t$95$4, If[LessEqual[y5, 3e-81], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 0.0077], t$95$3, If[LessEqual[y5, 9.8e+53], N[(N[(t * b), $MachinePrecision] * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y5 < -4.60000000000000021e222 or 9.80000000000000036e53 < y5

   1. Initial program 34.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 34.5%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 34.5%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 42.0%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 42.0%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 42.0%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 63.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 63.3%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

      2. neg-mul-1 63.3%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   7. Simplified 63.3%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   if -4.60000000000000021e222 < y5 < -1.89999999999999981e137

   1. Initial program 21.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 26.9%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 26.9%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 26.9%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 26.9%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 26.9%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in i around inf 63.7%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} \]

   if -1.89999999999999981e137 < y5 < -2.75e115

   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. Taylor expanded in t around inf 0.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in a around inf 83.5%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) - -1 \cdot \left(y2 \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 83.5%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \left(-1 \cdot \left(b \cdot z\right) - -1 \cdot \left(y2 \cdot y5\right)\right)} \]

      2. cancel-sign-sub-inv 83.5%

         \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right) + \left(--1\right) \cdot \left(y2 \cdot y5\right)\right)} \]

      3. metadata-eval 83.5%

         \[\leadsto \left(a \cdot t\right) \cdot \left(-1 \cdot \left(b \cdot z\right) + \color{blue}{1} \cdot \left(y2 \cdot y5\right)\right) \]

      4. *-lft-identity 83.5%

         \[\leadsto \left(a \cdot t\right) \cdot \left(-1 \cdot \left(b \cdot z\right) + \color{blue}{y2 \cdot y5}\right) \]

      5. +-commutative 83.5%

         \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)} \]

      6. mul-1-neg 83.5%

         \[\leadsto \left(a \cdot t\right) \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right) \]

      7. unsub-neg 83.5%

         \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)} \]

      8. *-commutative 83.5%

         \[\leadsto \left(a \cdot t\right) \cdot \left(\color{blue}{y5 \cdot y2} - b \cdot z\right) \]

   5. Simplified 83.5%

      \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \left(y5 \cdot y2 - b \cdot z\right)} \]

   if -2.75e115 < y5 < -2.2000000000000002e85 or 2.9999999999999999e-81 < y5 < 0.0077000000000000002

   1. Initial program 42.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 53.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 53.9%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 53.9%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 53.9%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 53.9%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 53.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in x around inf 64.9%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   if -2.2000000000000002e85 < y5 < -1.7e27

   1. Initial program 11.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 45.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 45.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 45.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 45.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 45.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 45.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y3 around inf 57.1%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if -1.7e27 < y5 < -9.99999999999999933e-103

   1. Initial program 24.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 47.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 47.9%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 47.9%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 47.9%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 47.9%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in y4 around -inf 47.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   6. Taylor expanded in k around inf 52.5%

      \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y2\right)}\right) \]

   if -9.99999999999999933e-103 < y5 < -3.00000000000000014e-248 or -1.1500000000000001e-286 < y5 < 1.15e-204

   1. Initial program 39.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 34.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 34.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 34.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 34.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 34.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 34.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 34.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 34.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 34.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y around -inf 47.7%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 46.0%

         \[\leadsto \color{blue}{\left(c \cdot y\right) \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)} \]

      2. +-commutative 46.0%

         \[\leadsto \left(c \cdot y\right) \cdot \color{blue}{\left(y3 \cdot y4 + -1 \cdot \left(i \cdot x\right)\right)} \]

      3. mul-1-neg 46.0%

         \[\leadsto \left(c \cdot y\right) \cdot \left(y3 \cdot y4 + \color{blue}{\left(-i \cdot x\right)}\right) \]

      4. unsub-neg 46.0%

         \[\leadsto \left(c \cdot y\right) \cdot \color{blue}{\left(y3 \cdot y4 - i \cdot x\right)} \]

      5. *-commutative 46.0%

         \[\leadsto \left(c \cdot y\right) \cdot \left(y3 \cdot y4 - \color{blue}{x \cdot i}\right) \]

   7. Simplified 46.0%

      \[\leadsto \color{blue}{\left(c \cdot y\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)} \]

   if -3.00000000000000014e-248 < y5 < -1.1500000000000001e-286

   1. Initial program 32.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 55.5%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 55.5%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 55.5%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 55.5%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 55.5%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 55.5%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in x around inf 48.4%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 55.7%

         \[\leadsto \color{blue}{\left(j \cdot x\right) \cdot \left(i \cdot y1 - b \cdot y0\right)} \]

   7. Simplified 55.7%

      \[\leadsto \color{blue}{\left(j \cdot x\right) \cdot \left(i \cdot y1 - b \cdot y0\right)} \]

   if 1.15e-204 < y5 < 2.9999999999999999e-81

   1. Initial program 46.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in t around inf 46.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in c around inf 43.1%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   if 0.0077000000000000002 < y5 < 9.80000000000000036e53

   1. Initial program 49.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in t around inf 42.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in b around inf 43.2%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 43.2%

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      2. *-commutative 43.2%

         \[\leadsto \color{blue}{\left(t \cdot b\right)} \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right) \]

      3. +-commutative 43.2%

         \[\leadsto \left(t \cdot b\right) \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)} \]

      4. mul-1-neg 43.2%

         \[\leadsto \left(t \cdot b\right) \cdot \left(j \cdot y4 + \color{blue}{\left(-a \cdot z\right)}\right) \]

      5. unsub-neg 43.2%

         \[\leadsto \left(t \cdot b\right) \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)} \]

      6. *-commutative 43.2%

         \[\leadsto \left(t \cdot b\right) \cdot \left(j \cdot y4 - \color{blue}{z \cdot a}\right) \]

   5. Simplified 43.2%

      \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -4.6 \cdot 10^{+222}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -1.9 \cdot 10^{+137}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -2.75 \cdot 10^{+115}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(y2 \cdot y5 - z \cdot b\right)\\ \mathbf{elif}\;y5 \leq -2.2 \cdot 10^{+85}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq -1.7 \cdot 10^{+27}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -1 \cdot 10^{-102}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -3 \cdot 10^{-248}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{elif}\;y5 \leq -1.15 \cdot 10^{-286}:\\ \;\;\;\;\left(x \cdot j\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\\ \mathbf{elif}\;y5 \leq 1.15 \cdot 10^{-204}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{elif}\;y5 \leq 3 \cdot 10^{-81}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 0.0077:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 9.8 \cdot 10^{+53}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \end{array} \]

Alternative 17: 28.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ t_2 := b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ t_3 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;j \leq -4 \cdot 10^{+214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -9.8 \cdot 10^{+147}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -2 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-37}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -5.8 \cdot 10^{-169}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{-299}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 4.9 \cdot 10^{-118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{-38}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;j \leq 10^{+71}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{+213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{+271}:\\ \;\;\;\;\left(j \cdot y0\right) \cdot \left(y3 \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* j (- (* t y4) (* x y0)))))
        (t_2 (* b (* k (- (* z y0) (* y y4)))))
        (t_3 (* a (* y5 (- (* t y2) (* y y3))))))
   (if (<= j -4e+214)
     t_1
     (if (<= j -9.8e+147)
       (* j (* y0 (* y3 y5)))
       (if (<= j -2e+91)
         t_1
         (if (<= j -5.5e-37)
           t_3
           (if (<= j -5.8e-169)
             t_2
             (if (<= j 8.2e-299)
               t_3
               (if (<= j 4.9e-118)
                 t_2
                 (if (<= j 7.5e-38)
                   (* c (* x (- (* y0 y2) (* y i))))
                   (if (<= j 1e+71)
                     (* y0 (* k (* y2 (- y5))))
                     (if (<= j 6e+213)
                       t_1
                       (if (<= j 2.7e+271)
                         (* (* j y0) (* y3 y5))
                         (* k (* y1 (* y2 y4))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (j * ((t * y4) - (x * y0)));
	double t_2 = b * (k * ((z * y0) - (y * y4)));
	double t_3 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (j <= -4e+214) {
		tmp = t_1;
	} else if (j <= -9.8e+147) {
		tmp = j * (y0 * (y3 * y5));
	} else if (j <= -2e+91) {
		tmp = t_1;
	} else if (j <= -5.5e-37) {
		tmp = t_3;
	} else if (j <= -5.8e-169) {
		tmp = t_2;
	} else if (j <= 8.2e-299) {
		tmp = t_3;
	} else if (j <= 4.9e-118) {
		tmp = t_2;
	} else if (j <= 7.5e-38) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (j <= 1e+71) {
		tmp = y0 * (k * (y2 * -y5));
	} else if (j <= 6e+213) {
		tmp = t_1;
	} else if (j <= 2.7e+271) {
		tmp = (j * y0) * (y3 * y5);
	} else {
		tmp = k * (y1 * (y2 * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * (j * ((t * y4) - (x * y0)))
    t_2 = b * (k * ((z * y0) - (y * y4)))
    t_3 = a * (y5 * ((t * y2) - (y * y3)))
    if (j <= (-4d+214)) then
        tmp = t_1
    else if (j <= (-9.8d+147)) then
        tmp = j * (y0 * (y3 * y5))
    else if (j <= (-2d+91)) then
        tmp = t_1
    else if (j <= (-5.5d-37)) then
        tmp = t_3
    else if (j <= (-5.8d-169)) then
        tmp = t_2
    else if (j <= 8.2d-299) then
        tmp = t_3
    else if (j <= 4.9d-118) then
        tmp = t_2
    else if (j <= 7.5d-38) then
        tmp = c * (x * ((y0 * y2) - (y * i)))
    else if (j <= 1d+71) then
        tmp = y0 * (k * (y2 * -y5))
    else if (j <= 6d+213) then
        tmp = t_1
    else if (j <= 2.7d+271) then
        tmp = (j * y0) * (y3 * y5)
    else
        tmp = k * (y1 * (y2 * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (j * ((t * y4) - (x * y0)));
	double t_2 = b * (k * ((z * y0) - (y * y4)));
	double t_3 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (j <= -4e+214) {
		tmp = t_1;
	} else if (j <= -9.8e+147) {
		tmp = j * (y0 * (y3 * y5));
	} else if (j <= -2e+91) {
		tmp = t_1;
	} else if (j <= -5.5e-37) {
		tmp = t_3;
	} else if (j <= -5.8e-169) {
		tmp = t_2;
	} else if (j <= 8.2e-299) {
		tmp = t_3;
	} else if (j <= 4.9e-118) {
		tmp = t_2;
	} else if (j <= 7.5e-38) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (j <= 1e+71) {
		tmp = y0 * (k * (y2 * -y5));
	} else if (j <= 6e+213) {
		tmp = t_1;
	} else if (j <= 2.7e+271) {
		tmp = (j * y0) * (y3 * y5);
	} else {
		tmp = k * (y1 * (y2 * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (j * ((t * y4) - (x * y0)))
	t_2 = b * (k * ((z * y0) - (y * y4)))
	t_3 = a * (y5 * ((t * y2) - (y * y3)))
	tmp = 0
	if j <= -4e+214:
		tmp = t_1
	elif j <= -9.8e+147:
		tmp = j * (y0 * (y3 * y5))
	elif j <= -2e+91:
		tmp = t_1
	elif j <= -5.5e-37:
		tmp = t_3
	elif j <= -5.8e-169:
		tmp = t_2
	elif j <= 8.2e-299:
		tmp = t_3
	elif j <= 4.9e-118:
		tmp = t_2
	elif j <= 7.5e-38:
		tmp = c * (x * ((y0 * y2) - (y * i)))
	elif j <= 1e+71:
		tmp = y0 * (k * (y2 * -y5))
	elif j <= 6e+213:
		tmp = t_1
	elif j <= 2.7e+271:
		tmp = (j * y0) * (y3 * y5)
	else:
		tmp = k * (y1 * (y2 * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))))
	t_2 = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))))
	t_3 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	tmp = 0.0
	if (j <= -4e+214)
		tmp = t_1;
	elseif (j <= -9.8e+147)
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	elseif (j <= -2e+91)
		tmp = t_1;
	elseif (j <= -5.5e-37)
		tmp = t_3;
	elseif (j <= -5.8e-169)
		tmp = t_2;
	elseif (j <= 8.2e-299)
		tmp = t_3;
	elseif (j <= 4.9e-118)
		tmp = t_2;
	elseif (j <= 7.5e-38)
		tmp = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))));
	elseif (j <= 1e+71)
		tmp = Float64(y0 * Float64(k * Float64(y2 * Float64(-y5))));
	elseif (j <= 6e+213)
		tmp = t_1;
	elseif (j <= 2.7e+271)
		tmp = Float64(Float64(j * y0) * Float64(y3 * y5));
	else
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (j * ((t * y4) - (x * y0)));
	t_2 = b * (k * ((z * y0) - (y * y4)));
	t_3 = a * (y5 * ((t * y2) - (y * y3)));
	tmp = 0.0;
	if (j <= -4e+214)
		tmp = t_1;
	elseif (j <= -9.8e+147)
		tmp = j * (y0 * (y3 * y5));
	elseif (j <= -2e+91)
		tmp = t_1;
	elseif (j <= -5.5e-37)
		tmp = t_3;
	elseif (j <= -5.8e-169)
		tmp = t_2;
	elseif (j <= 8.2e-299)
		tmp = t_3;
	elseif (j <= 4.9e-118)
		tmp = t_2;
	elseif (j <= 7.5e-38)
		tmp = c * (x * ((y0 * y2) - (y * i)));
	elseif (j <= 1e+71)
		tmp = y0 * (k * (y2 * -y5));
	elseif (j <= 6e+213)
		tmp = t_1;
	elseif (j <= 2.7e+271)
		tmp = (j * y0) * (y3 * y5);
	else
		tmp = k * (y1 * (y2 * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4e+214], t$95$1, If[LessEqual[j, -9.8e+147], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2e+91], t$95$1, If[LessEqual[j, -5.5e-37], t$95$3, If[LessEqual[j, -5.8e-169], t$95$2, If[LessEqual[j, 8.2e-299], t$95$3, If[LessEqual[j, 4.9e-118], t$95$2, If[LessEqual[j, 7.5e-38], N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1e+71], N[(y0 * N[(k * N[(y2 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6e+213], t$95$1, If[LessEqual[j, 2.7e+271], N[(N[(j * y0), $MachinePrecision] * N[(y3 * y5), $MachinePrecision]), $MachinePrecision], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if j < -3.9999999999999998e214 or -9.7999999999999996e147 < j < -2.00000000000000016e91 or 1e71 < j < 6.0000000000000002e213

   1. Initial program 35.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 70.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 70.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 70.8%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 70.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 70.8%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 70.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in b around inf 54.6%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -3.9999999999999998e214 < j < -9.7999999999999996e147

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 36.0%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 36.0%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 43.2%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 43.2%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 43.2%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 57.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 57.7%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

      2. neg-mul-1 57.7%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   7. Simplified 57.7%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in k around 0 58.3%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]

   if -2.00000000000000016e91 < j < -5.4999999999999998e-37 or -5.80000000000000038e-169 < j < 8.2000000000000002e-299

   1. Initial program 31.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 38.5%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 38.5%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 41.9%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 41.9%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 41.9%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 44.4%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 44.4%

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 44.4%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   if -5.4999999999999998e-37 < j < -5.80000000000000038e-169 or 8.2000000000000002e-299 < j < 4.8999999999999998e-118

   1. Initial program 45.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in k around inf 42.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 42.1%

         \[\leadsto k \cdot \color{blue}{\left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. +-commutative 42.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      3. mul-1-neg 42.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      4. unsub-neg 42.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-commutative 42.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. mul-1-neg 42.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + \left(-\color{blue}{\left(-z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      7. remove-double-neg 42.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + \color{blue}{z \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Simplified 42.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf 40.4%

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z - y \cdot y4\right)\right)} \]

   if 4.8999999999999998e-118 < j < 7.5e-38

   1. Initial program 41.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 59.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 59.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 59.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 59.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 59.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 59.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 59.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 59.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 59.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in x around inf 55.6%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2 - i \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 55.6%

         \[\leadsto c \cdot \left(x \cdot \left(\color{blue}{y2 \cdot y0} - i \cdot y\right)\right) \]

   7. Simplified 55.6%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0 - i \cdot y\right)\right)} \]

   if 7.5e-38 < j < 1e71

   1. Initial program 35.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 30.6%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 30.6%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 35.4%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 35.4%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 35.4%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 50.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 50.7%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

      2. neg-mul-1 50.7%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   7. Simplified 50.7%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in k around inf 46.3%

      \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y5\right)\right)} \]

   if 6.0000000000000002e213 < j < 2.69999999999999989e271

   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. Taylor expanded in y5 around inf 45.5%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 45.5%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 45.5%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 45.5%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 45.5%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 72.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 72.8%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

      2. neg-mul-1 72.8%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   7. Simplified 72.8%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in k around 0 73.3%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 82.0%

         \[\leadsto \color{blue}{\left(j \cdot y0\right) \cdot \left(y3 \cdot y5\right)} \]

   10. Simplified 82.0%

       \[\leadsto \color{blue}{\left(j \cdot y0\right) \cdot \left(y3 \cdot y5\right)} \]

   if 2.69999999999999989e271 < j

   1. Initial program 0.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 55.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 55.2%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 55.2%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 55.2%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 55.2%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in y4 around -inf 45.8%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   6. Taylor expanded in k around inf 56.2%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4 \cdot 10^{+214}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -9.8 \cdot 10^{+147}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -2 \cdot 10^{+91}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-37}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq -5.8 \cdot 10^{-169}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{-299}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 4.9 \cdot 10^{-118}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{-38}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;j \leq 10^{+71}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{+213}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{+271}:\\ \;\;\;\;\left(j \cdot y0\right) \cdot \left(y3 \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \]

Alternative 18: 28.2% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ t_2 := b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ t_3 := b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{if}\;j \leq -1.5 \cdot 10^{+214}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -3.3 \cdot 10^{+148}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -8 \cdot 10^{+90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -5.8 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -3.15 \cdot 10^{-167}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-119}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-36}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{+79}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{+209}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+270}:\\ \;\;\;\;\left(j \cdot y0\right) \cdot \left(y3 \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y5 (- (* t y2) (* y y3)))))
        (t_2 (* b (* j (- (* t y4) (* x y0)))))
        (t_3 (* b (* k (- (* z y0) (* y y4))))))
   (if (<= j -1.5e+214)
     (* j (* x (- (* i y1) (* b y0))))
     (if (<= j -3.3e+148)
       (* j (* y0 (* y3 y5)))
       (if (<= j -8e+90)
         t_2
         (if (<= j -5.8e-37)
           t_1
           (if (<= j -3.15e-167)
             t_3
             (if (<= j 1.2e-299)
               t_1
               (if (<= j 1.7e-119)
                 t_3
                 (if (<= j 3.8e-36)
                   (* c (* x (- (* y0 y2) (* y i))))
                   (if (<= j 2.6e+79)
                     (* y0 (* k (* y2 (- y5))))
                     (if (<= j 8.2e+209)
                       t_2
                       (if (<= j 9.5e+270)
                         (* (* j y0) (* y3 y5))
                         (* k (* y1 (* y2 y4))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double t_2 = b * (j * ((t * y4) - (x * y0)));
	double t_3 = b * (k * ((z * y0) - (y * y4)));
	double tmp;
	if (j <= -1.5e+214) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (j <= -3.3e+148) {
		tmp = j * (y0 * (y3 * y5));
	} else if (j <= -8e+90) {
		tmp = t_2;
	} else if (j <= -5.8e-37) {
		tmp = t_1;
	} else if (j <= -3.15e-167) {
		tmp = t_3;
	} else if (j <= 1.2e-299) {
		tmp = t_1;
	} else if (j <= 1.7e-119) {
		tmp = t_3;
	} else if (j <= 3.8e-36) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (j <= 2.6e+79) {
		tmp = y0 * (k * (y2 * -y5));
	} else if (j <= 8.2e+209) {
		tmp = t_2;
	} else if (j <= 9.5e+270) {
		tmp = (j * y0) * (y3 * y5);
	} else {
		tmp = k * (y1 * (y2 * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (y5 * ((t * y2) - (y * y3)))
    t_2 = b * (j * ((t * y4) - (x * y0)))
    t_3 = b * (k * ((z * y0) - (y * y4)))
    if (j <= (-1.5d+214)) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (j <= (-3.3d+148)) then
        tmp = j * (y0 * (y3 * y5))
    else if (j <= (-8d+90)) then
        tmp = t_2
    else if (j <= (-5.8d-37)) then
        tmp = t_1
    else if (j <= (-3.15d-167)) then
        tmp = t_3
    else if (j <= 1.2d-299) then
        tmp = t_1
    else if (j <= 1.7d-119) then
        tmp = t_3
    else if (j <= 3.8d-36) then
        tmp = c * (x * ((y0 * y2) - (y * i)))
    else if (j <= 2.6d+79) then
        tmp = y0 * (k * (y2 * -y5))
    else if (j <= 8.2d+209) then
        tmp = t_2
    else if (j <= 9.5d+270) then
        tmp = (j * y0) * (y3 * y5)
    else
        tmp = k * (y1 * (y2 * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double t_2 = b * (j * ((t * y4) - (x * y0)));
	double t_3 = b * (k * ((z * y0) - (y * y4)));
	double tmp;
	if (j <= -1.5e+214) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (j <= -3.3e+148) {
		tmp = j * (y0 * (y3 * y5));
	} else if (j <= -8e+90) {
		tmp = t_2;
	} else if (j <= -5.8e-37) {
		tmp = t_1;
	} else if (j <= -3.15e-167) {
		tmp = t_3;
	} else if (j <= 1.2e-299) {
		tmp = t_1;
	} else if (j <= 1.7e-119) {
		tmp = t_3;
	} else if (j <= 3.8e-36) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (j <= 2.6e+79) {
		tmp = y0 * (k * (y2 * -y5));
	} else if (j <= 8.2e+209) {
		tmp = t_2;
	} else if (j <= 9.5e+270) {
		tmp = (j * y0) * (y3 * y5);
	} else {
		tmp = k * (y1 * (y2 * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y5 * ((t * y2) - (y * y3)))
	t_2 = b * (j * ((t * y4) - (x * y0)))
	t_3 = b * (k * ((z * y0) - (y * y4)))
	tmp = 0
	if j <= -1.5e+214:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif j <= -3.3e+148:
		tmp = j * (y0 * (y3 * y5))
	elif j <= -8e+90:
		tmp = t_2
	elif j <= -5.8e-37:
		tmp = t_1
	elif j <= -3.15e-167:
		tmp = t_3
	elif j <= 1.2e-299:
		tmp = t_1
	elif j <= 1.7e-119:
		tmp = t_3
	elif j <= 3.8e-36:
		tmp = c * (x * ((y0 * y2) - (y * i)))
	elif j <= 2.6e+79:
		tmp = y0 * (k * (y2 * -y5))
	elif j <= 8.2e+209:
		tmp = t_2
	elif j <= 9.5e+270:
		tmp = (j * y0) * (y3 * y5)
	else:
		tmp = k * (y1 * (y2 * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	t_2 = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))))
	t_3 = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))))
	tmp = 0.0
	if (j <= -1.5e+214)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (j <= -3.3e+148)
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	elseif (j <= -8e+90)
		tmp = t_2;
	elseif (j <= -5.8e-37)
		tmp = t_1;
	elseif (j <= -3.15e-167)
		tmp = t_3;
	elseif (j <= 1.2e-299)
		tmp = t_1;
	elseif (j <= 1.7e-119)
		tmp = t_3;
	elseif (j <= 3.8e-36)
		tmp = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))));
	elseif (j <= 2.6e+79)
		tmp = Float64(y0 * Float64(k * Float64(y2 * Float64(-y5))));
	elseif (j <= 8.2e+209)
		tmp = t_2;
	elseif (j <= 9.5e+270)
		tmp = Float64(Float64(j * y0) * Float64(y3 * y5));
	else
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y5 * ((t * y2) - (y * y3)));
	t_2 = b * (j * ((t * y4) - (x * y0)));
	t_3 = b * (k * ((z * y0) - (y * y4)));
	tmp = 0.0;
	if (j <= -1.5e+214)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (j <= -3.3e+148)
		tmp = j * (y0 * (y3 * y5));
	elseif (j <= -8e+90)
		tmp = t_2;
	elseif (j <= -5.8e-37)
		tmp = t_1;
	elseif (j <= -3.15e-167)
		tmp = t_3;
	elseif (j <= 1.2e-299)
		tmp = t_1;
	elseif (j <= 1.7e-119)
		tmp = t_3;
	elseif (j <= 3.8e-36)
		tmp = c * (x * ((y0 * y2) - (y * i)));
	elseif (j <= 2.6e+79)
		tmp = y0 * (k * (y2 * -y5));
	elseif (j <= 8.2e+209)
		tmp = t_2;
	elseif (j <= 9.5e+270)
		tmp = (j * y0) * (y3 * y5);
	else
		tmp = k * (y1 * (y2 * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.5e+214], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.3e+148], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -8e+90], t$95$2, If[LessEqual[j, -5.8e-37], t$95$1, If[LessEqual[j, -3.15e-167], t$95$3, If[LessEqual[j, 1.2e-299], t$95$1, If[LessEqual[j, 1.7e-119], t$95$3, If[LessEqual[j, 3.8e-36], N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.6e+79], N[(y0 * N[(k * N[(y2 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.2e+209], t$95$2, If[LessEqual[j, 9.5e+270], N[(N[(j * y0), $MachinePrecision] * N[(y3 * y5), $MachinePrecision]), $MachinePrecision], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if j < -1.5000000000000001e214

   1. Initial program 31.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 89.4%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 89.4%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 89.4%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 89.4%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 89.4%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 89.4%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in x around inf 53.5%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   if -1.5000000000000001e214 < j < -3.3000000000000001e148

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 36.0%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 36.0%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 43.2%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 43.2%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 43.2%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 57.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 57.7%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

      2. neg-mul-1 57.7%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   7. Simplified 57.7%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in k around 0 58.3%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]

   if -3.3000000000000001e148 < j < -7.99999999999999973e90 or 2.60000000000000015e79 < j < 8.20000000000000031e209

   1. Initial program 37.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 60.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 60.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 60.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 60.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 60.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 60.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in b around inf 55.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -7.99999999999999973e90 < j < -5.80000000000000009e-37 or -3.1500000000000001e-167 < j < 1.2000000000000001e-299

   1. Initial program 31.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 38.5%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 38.5%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 41.9%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 41.9%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 41.9%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 44.4%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 44.4%

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 44.4%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   if -5.80000000000000009e-37 < j < -3.1500000000000001e-167 or 1.2000000000000001e-299 < j < 1.70000000000000012e-119

   1. Initial program 45.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in k around inf 42.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 42.1%

         \[\leadsto k \cdot \color{blue}{\left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. +-commutative 42.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      3. mul-1-neg 42.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      4. unsub-neg 42.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-commutative 42.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. mul-1-neg 42.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + \left(-\color{blue}{\left(-z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      7. remove-double-neg 42.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + \color{blue}{z \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Simplified 42.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf 40.4%

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z - y \cdot y4\right)\right)} \]

   if 1.70000000000000012e-119 < j < 3.79999999999999971e-36

   1. Initial program 41.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 59.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 59.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 59.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 59.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 59.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 59.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 59.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 59.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 59.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in x around inf 55.6%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2 - i \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 55.6%

         \[\leadsto c \cdot \left(x \cdot \left(\color{blue}{y2 \cdot y0} - i \cdot y\right)\right) \]

   7. Simplified 55.6%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0 - i \cdot y\right)\right)} \]

   if 3.79999999999999971e-36 < j < 2.60000000000000015e79

   1. Initial program 35.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 30.6%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 30.6%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 35.4%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 35.4%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 35.4%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 50.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 50.7%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

      2. neg-mul-1 50.7%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   7. Simplified 50.7%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in k around inf 46.3%

      \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y5\right)\right)} \]

   if 8.20000000000000031e209 < j < 9.4999999999999993e270

   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. Taylor expanded in y5 around inf 45.5%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 45.5%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 45.5%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 45.5%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 45.5%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 72.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 72.8%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

      2. neg-mul-1 72.8%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   7. Simplified 72.8%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in k around 0 73.3%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 82.0%

         \[\leadsto \color{blue}{\left(j \cdot y0\right) \cdot \left(y3 \cdot y5\right)} \]

   10. Simplified 82.0%

       \[\leadsto \color{blue}{\left(j \cdot y0\right) \cdot \left(y3 \cdot y5\right)} \]

   if 9.4999999999999993e270 < j

   1. Initial program 0.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 55.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 55.2%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 55.2%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 55.2%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 55.2%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in y4 around -inf 45.8%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   6. Taylor expanded in k around inf 56.2%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.5 \cdot 10^{+214}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -3.3 \cdot 10^{+148}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -8 \cdot 10^{+90}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -5.8 \cdot 10^{-37}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq -3.15 \cdot 10^{-167}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{-299}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-119}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-36}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{+79}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{+209}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+270}:\\ \;\;\;\;\left(j \cdot y0\right) \cdot \left(y3 \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \]

Alternative 19: 30.6% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot y1 - b \cdot y0\\ t_2 := j \cdot \left(x \cdot t_1\right)\\ t_3 := \left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{if}\;y5 \leq -3.55 \cdot 10^{+127}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;y5 \leq -2.8 \cdot 10^{+89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y5 \leq -7.2 \cdot 10^{+28}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -8.2 \cdot 10^{-104}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -3 \cdot 10^{-248}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y5 \leq -1.45 \cdot 10^{-287}:\\ \;\;\;\;\left(x \cdot j\right) \cdot t_1\\ \mathbf{elif}\;y5 \leq 7.4 \cdot 10^{-205}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y5 \leq 1.72 \cdot 10^{-81}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 5.6:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y5 \leq 2.1 \cdot 10^{+54}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* i y1) (* b y0)))
        (t_2 (* j (* x t_1)))
        (t_3 (* (* y c) (- (* y3 y4) (* x i)))))
   (if (<= y5 -3.55e+127)
     (* j (* y5 (- (* y0 y3) (* t i))))
     (if (<= y5 -2.8e+89)
       t_2
       (if (<= y5 -7.2e+28)
         (* j (* y3 (- (* y0 y5) (* y1 y4))))
         (if (<= y5 -8.2e-104)
           (* y1 (* y4 (* k y2)))
           (if (<= y5 -3e-248)
             t_3
             (if (<= y5 -1.45e-287)
               (* (* x j) t_1)
               (if (<= y5 7.4e-205)
                 t_3
                 (if (<= y5 1.72e-81)
                   (* c (* t (- (* z i) (* y2 y4))))
                   (if (<= y5 5.6)
                     t_2
                     (if (<= y5 2.1e+54)
                       (* (* t b) (- (* j y4) (* z a)))
                       (* y0 (* y5 (- (* j y3) (* k y2))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (i * y1) - (b * y0);
	double t_2 = j * (x * t_1);
	double t_3 = (y * c) * ((y3 * y4) - (x * i));
	double tmp;
	if (y5 <= -3.55e+127) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (y5 <= -2.8e+89) {
		tmp = t_2;
	} else if (y5 <= -7.2e+28) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (y5 <= -8.2e-104) {
		tmp = y1 * (y4 * (k * y2));
	} else if (y5 <= -3e-248) {
		tmp = t_3;
	} else if (y5 <= -1.45e-287) {
		tmp = (x * j) * t_1;
	} else if (y5 <= 7.4e-205) {
		tmp = t_3;
	} else if (y5 <= 1.72e-81) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (y5 <= 5.6) {
		tmp = t_2;
	} else if (y5 <= 2.1e+54) {
		tmp = (t * b) * ((j * y4) - (z * a));
	} else {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (i * y1) - (b * y0)
    t_2 = j * (x * t_1)
    t_3 = (y * c) * ((y3 * y4) - (x * i))
    if (y5 <= (-3.55d+127)) then
        tmp = j * (y5 * ((y0 * y3) - (t * i)))
    else if (y5 <= (-2.8d+89)) then
        tmp = t_2
    else if (y5 <= (-7.2d+28)) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (y5 <= (-8.2d-104)) then
        tmp = y1 * (y4 * (k * y2))
    else if (y5 <= (-3d-248)) then
        tmp = t_3
    else if (y5 <= (-1.45d-287)) then
        tmp = (x * j) * t_1
    else if (y5 <= 7.4d-205) then
        tmp = t_3
    else if (y5 <= 1.72d-81) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (y5 <= 5.6d0) then
        tmp = t_2
    else if (y5 <= 2.1d+54) then
        tmp = (t * b) * ((j * y4) - (z * a))
    else
        tmp = y0 * (y5 * ((j * y3) - (k * y2)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (i * y1) - (b * y0);
	double t_2 = j * (x * t_1);
	double t_3 = (y * c) * ((y3 * y4) - (x * i));
	double tmp;
	if (y5 <= -3.55e+127) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (y5 <= -2.8e+89) {
		tmp = t_2;
	} else if (y5 <= -7.2e+28) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (y5 <= -8.2e-104) {
		tmp = y1 * (y4 * (k * y2));
	} else if (y5 <= -3e-248) {
		tmp = t_3;
	} else if (y5 <= -1.45e-287) {
		tmp = (x * j) * t_1;
	} else if (y5 <= 7.4e-205) {
		tmp = t_3;
	} else if (y5 <= 1.72e-81) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (y5 <= 5.6) {
		tmp = t_2;
	} else if (y5 <= 2.1e+54) {
		tmp = (t * b) * ((j * y4) - (z * a));
	} else {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (i * y1) - (b * y0)
	t_2 = j * (x * t_1)
	t_3 = (y * c) * ((y3 * y4) - (x * i))
	tmp = 0
	if y5 <= -3.55e+127:
		tmp = j * (y5 * ((y0 * y3) - (t * i)))
	elif y5 <= -2.8e+89:
		tmp = t_2
	elif y5 <= -7.2e+28:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif y5 <= -8.2e-104:
		tmp = y1 * (y4 * (k * y2))
	elif y5 <= -3e-248:
		tmp = t_3
	elif y5 <= -1.45e-287:
		tmp = (x * j) * t_1
	elif y5 <= 7.4e-205:
		tmp = t_3
	elif y5 <= 1.72e-81:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif y5 <= 5.6:
		tmp = t_2
	elif y5 <= 2.1e+54:
		tmp = (t * b) * ((j * y4) - (z * a))
	else:
		tmp = y0 * (y5 * ((j * y3) - (k * y2)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(i * y1) - Float64(b * y0))
	t_2 = Float64(j * Float64(x * t_1))
	t_3 = Float64(Float64(y * c) * Float64(Float64(y3 * y4) - Float64(x * i)))
	tmp = 0.0
	if (y5 <= -3.55e+127)
		tmp = Float64(j * Float64(y5 * Float64(Float64(y0 * y3) - Float64(t * i))));
	elseif (y5 <= -2.8e+89)
		tmp = t_2;
	elseif (y5 <= -7.2e+28)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (y5 <= -8.2e-104)
		tmp = Float64(y1 * Float64(y4 * Float64(k * y2)));
	elseif (y5 <= -3e-248)
		tmp = t_3;
	elseif (y5 <= -1.45e-287)
		tmp = Float64(Float64(x * j) * t_1);
	elseif (y5 <= 7.4e-205)
		tmp = t_3;
	elseif (y5 <= 1.72e-81)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (y5 <= 5.6)
		tmp = t_2;
	elseif (y5 <= 2.1e+54)
		tmp = Float64(Float64(t * b) * Float64(Float64(j * y4) - Float64(z * a)));
	else
		tmp = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (i * y1) - (b * y0);
	t_2 = j * (x * t_1);
	t_3 = (y * c) * ((y3 * y4) - (x * i));
	tmp = 0.0;
	if (y5 <= -3.55e+127)
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	elseif (y5 <= -2.8e+89)
		tmp = t_2;
	elseif (y5 <= -7.2e+28)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (y5 <= -8.2e-104)
		tmp = y1 * (y4 * (k * y2));
	elseif (y5 <= -3e-248)
		tmp = t_3;
	elseif (y5 <= -1.45e-287)
		tmp = (x * j) * t_1;
	elseif (y5 <= 7.4e-205)
		tmp = t_3;
	elseif (y5 <= 1.72e-81)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (y5 <= 5.6)
		tmp = t_2;
	elseif (y5 <= 2.1e+54)
		tmp = (t * b) * ((j * y4) - (z * a));
	else
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * c), $MachinePrecision] * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -3.55e+127], N[(j * N[(y5 * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2.8e+89], t$95$2, If[LessEqual[y5, -7.2e+28], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -8.2e-104], N[(y1 * N[(y4 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -3e-248], t$95$3, If[LessEqual[y5, -1.45e-287], N[(N[(x * j), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[y5, 7.4e-205], t$95$3, If[LessEqual[y5, 1.72e-81], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 5.6], t$95$2, If[LessEqual[y5, 2.1e+54], N[(N[(t * b), $MachinePrecision] * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y5 < -3.5499999999999998e127

   1. Initial program 22.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 50.4%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 50.4%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 50.4%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 50.4%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 50.4%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 50.4%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y5 around -inf 50.6%

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(y5 \cdot \left(i \cdot t - y0 \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 50.6%

         \[\leadsto \color{blue}{\left(-1 \cdot j\right) \cdot \left(y5 \cdot \left(i \cdot t - y0 \cdot y3\right)\right)} \]

      2. neg-mul-1 50.6%

         \[\leadsto \color{blue}{\left(-j\right)} \cdot \left(y5 \cdot \left(i \cdot t - y0 \cdot y3\right)\right) \]

      3. *-commutative 50.6%

         \[\leadsto \left(-j\right) \cdot \left(y5 \cdot \left(\color{blue}{t \cdot i} - y0 \cdot y3\right)\right) \]

   7. Simplified 50.6%

      \[\leadsto \color{blue}{\left(-j\right) \cdot \left(y5 \cdot \left(t \cdot i - y0 \cdot y3\right)\right)} \]

   if -3.5499999999999998e127 < y5 < -2.7999999999999998e89 or 1.72000000000000007e-81 < y5 < 5.5999999999999996

   1. Initial program 41.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 52.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 52.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 52.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 52.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 52.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 52.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in x around inf 62.6%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   if -2.7999999999999998e89 < y5 < -7.1999999999999999e28

   1. Initial program 11.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 45.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 45.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 45.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 45.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 45.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 45.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y3 around inf 57.1%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if -7.1999999999999999e28 < y5 < -8.19999999999999968e-104

   1. Initial program 24.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 47.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 47.9%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 47.9%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 47.9%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 47.9%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in y4 around -inf 47.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   6. Taylor expanded in k around inf 52.5%

      \[\leadsto y1 \cdot \left(y4 \cdot \color{blue}{\left(k \cdot y2\right)}\right) \]

   if -8.19999999999999968e-104 < y5 < -3.00000000000000014e-248 or -1.4499999999999999e-287 < y5 < 7.4000000000000002e-205

   1. Initial program 39.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 34.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 34.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 34.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 34.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 34.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 34.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 34.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 34.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 34.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y around -inf 47.7%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 46.0%

         \[\leadsto \color{blue}{\left(c \cdot y\right) \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)} \]

      2. +-commutative 46.0%

         \[\leadsto \left(c \cdot y\right) \cdot \color{blue}{\left(y3 \cdot y4 + -1 \cdot \left(i \cdot x\right)\right)} \]

      3. mul-1-neg 46.0%

         \[\leadsto \left(c \cdot y\right) \cdot \left(y3 \cdot y4 + \color{blue}{\left(-i \cdot x\right)}\right) \]

      4. unsub-neg 46.0%

         \[\leadsto \left(c \cdot y\right) \cdot \color{blue}{\left(y3 \cdot y4 - i \cdot x\right)} \]

      5. *-commutative 46.0%

         \[\leadsto \left(c \cdot y\right) \cdot \left(y3 \cdot y4 - \color{blue}{x \cdot i}\right) \]

   7. Simplified 46.0%

      \[\leadsto \color{blue}{\left(c \cdot y\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)} \]

   if -3.00000000000000014e-248 < y5 < -1.4499999999999999e-287

   1. Initial program 32.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 55.5%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 55.5%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 55.5%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 55.5%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 55.5%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 55.5%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in x around inf 48.4%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 55.7%

         \[\leadsto \color{blue}{\left(j \cdot x\right) \cdot \left(i \cdot y1 - b \cdot y0\right)} \]

   7. Simplified 55.7%

      \[\leadsto \color{blue}{\left(j \cdot x\right) \cdot \left(i \cdot y1 - b \cdot y0\right)} \]

   if 7.4000000000000002e-205 < y5 < 1.72000000000000007e-81

   1. Initial program 46.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in t around inf 46.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in c around inf 43.1%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   if 5.5999999999999996 < y5 < 2.09999999999999986e54

   1. Initial program 49.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in t around inf 42.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in b around inf 43.2%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 43.2%

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      2. *-commutative 43.2%

         \[\leadsto \color{blue}{\left(t \cdot b\right)} \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right) \]

      3. +-commutative 43.2%

         \[\leadsto \left(t \cdot b\right) \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)} \]

      4. mul-1-neg 43.2%

         \[\leadsto \left(t \cdot b\right) \cdot \left(j \cdot y4 + \color{blue}{\left(-a \cdot z\right)}\right) \]

      5. unsub-neg 43.2%

         \[\leadsto \left(t \cdot b\right) \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)} \]

      6. *-commutative 43.2%

         \[\leadsto \left(t \cdot b\right) \cdot \left(j \cdot y4 - \color{blue}{z \cdot a}\right) \]

   5. Simplified 43.2%

      \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)} \]

   if 2.09999999999999986e54 < y5

   1. Initial program 35.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 37.0%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 37.0%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 44.4%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 44.4%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 44.4%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 61.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 61.8%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

      2. neg-mul-1 61.8%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   7. Simplified 61.8%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -3.55 \cdot 10^{+127}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;y5 \leq -2.8 \cdot 10^{+89}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq -7.2 \cdot 10^{+28}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -8.2 \cdot 10^{-104}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -3 \cdot 10^{-248}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{elif}\;y5 \leq -1.45 \cdot 10^{-287}:\\ \;\;\;\;\left(x \cdot j\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\\ \mathbf{elif}\;y5 \leq 7.4 \cdot 10^{-205}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{elif}\;y5 \leq 1.72 \cdot 10^{-81}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 5.6:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 2.1 \cdot 10^{+54}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \end{array} \]

Alternative 20: 30.7% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+82}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+53}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-48}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-123}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-284}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-156}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-94}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+126}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* y c) (- (* y3 y4) (* x i)))))
   (if (<= y -6e+194)
     t_1
     (if (<= y -2e+82)
       (* j (* y3 (- (* y0 y5) (* y1 y4))))
       (if (<= y -6.2e+53)
         (* c (* z (- (* t i) (* y0 y3))))
         (if (<= y -4.8e-48)
           (* y1 (* y4 (- (* k y2) (* j y3))))
           (if (<= y -2.7e-123)
             (* k (* y0 (- (* z b) (* y2 y5))))
             (if (<= y 6e-284)
               (* j (* x (- (* i y1) (* b y0))))
               (if (<= y 4.7e-156)
                 (* y0 (* y5 (- (* j y3) (* k y2))))
                 (if (<= y 7.5e-94)
                   (* t (* z (- (* c i) (* a b))))
                   (if (<= y 1.55e+126)
                     (* j (* y5 (- (* y0 y3) (* t i))))
                     t_1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * c) * ((y3 * y4) - (x * i));
	double tmp;
	if (y <= -6e+194) {
		tmp = t_1;
	} else if (y <= -2e+82) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (y <= -6.2e+53) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else if (y <= -4.8e-48) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (y <= -2.7e-123) {
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	} else if (y <= 6e-284) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y <= 4.7e-156) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (y <= 7.5e-94) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (y <= 1.55e+126) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} 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 = (y * c) * ((y3 * y4) - (x * i))
    if (y <= (-6d+194)) then
        tmp = t_1
    else if (y <= (-2d+82)) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (y <= (-6.2d+53)) then
        tmp = c * (z * ((t * i) - (y0 * y3)))
    else if (y <= (-4.8d-48)) then
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    else if (y <= (-2.7d-123)) then
        tmp = k * (y0 * ((z * b) - (y2 * y5)))
    else if (y <= 6d-284) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (y <= 4.7d-156) then
        tmp = y0 * (y5 * ((j * y3) - (k * y2)))
    else if (y <= 7.5d-94) then
        tmp = t * (z * ((c * i) - (a * b)))
    else if (y <= 1.55d+126) then
        tmp = j * (y5 * ((y0 * y3) - (t * i)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * c) * ((y3 * y4) - (x * i));
	double tmp;
	if (y <= -6e+194) {
		tmp = t_1;
	} else if (y <= -2e+82) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (y <= -6.2e+53) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else if (y <= -4.8e-48) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (y <= -2.7e-123) {
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	} else if (y <= 6e-284) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y <= 4.7e-156) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (y <= 7.5e-94) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (y <= 1.55e+126) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y * c) * ((y3 * y4) - (x * i))
	tmp = 0
	if y <= -6e+194:
		tmp = t_1
	elif y <= -2e+82:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif y <= -6.2e+53:
		tmp = c * (z * ((t * i) - (y0 * y3)))
	elif y <= -4.8e-48:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	elif y <= -2.7e-123:
		tmp = k * (y0 * ((z * b) - (y2 * y5)))
	elif y <= 6e-284:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif y <= 4.7e-156:
		tmp = y0 * (y5 * ((j * y3) - (k * y2)))
	elif y <= 7.5e-94:
		tmp = t * (z * ((c * i) - (a * b)))
	elif y <= 1.55e+126:
		tmp = j * (y5 * ((y0 * y3) - (t * i)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * c) * Float64(Float64(y3 * y4) - Float64(x * i)))
	tmp = 0.0
	if (y <= -6e+194)
		tmp = t_1;
	elseif (y <= -2e+82)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (y <= -6.2e+53)
		tmp = Float64(c * Float64(z * Float64(Float64(t * i) - Float64(y0 * y3))));
	elseif (y <= -4.8e-48)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (y <= -2.7e-123)
		tmp = Float64(k * Float64(y0 * Float64(Float64(z * b) - Float64(y2 * y5))));
	elseif (y <= 6e-284)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (y <= 4.7e-156)
		tmp = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))));
	elseif (y <= 7.5e-94)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	elseif (y <= 1.55e+126)
		tmp = Float64(j * Float64(y5 * Float64(Float64(y0 * y3) - Float64(t * i))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y * c) * ((y3 * y4) - (x * i));
	tmp = 0.0;
	if (y <= -6e+194)
		tmp = t_1;
	elseif (y <= -2e+82)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (y <= -6.2e+53)
		tmp = c * (z * ((t * i) - (y0 * y3)));
	elseif (y <= -4.8e-48)
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	elseif (y <= -2.7e-123)
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	elseif (y <= 6e-284)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (y <= 4.7e-156)
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	elseif (y <= 7.5e-94)
		tmp = t * (z * ((c * i) - (a * b)));
	elseif (y <= 1.55e+126)
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y * c), $MachinePrecision] * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e+194], t$95$1, If[LessEqual[y, -2e+82], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.2e+53], N[(c * N[(z * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.8e-48], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.7e-123], N[(k * N[(y0 * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e-284], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.7e-156], N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e-94], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e+126], N[(j * N[(y5 * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y < -6.0000000000000006e194 or 1.55e126 < y

   1. Initial program 31.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 43.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 43.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 43.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 43.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 43.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 43.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 43.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 43.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 43.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y around -inf 72.1%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 62.7%

         \[\leadsto \color{blue}{\left(c \cdot y\right) \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)} \]

      2. +-commutative 62.7%

         \[\leadsto \left(c \cdot y\right) \cdot \color{blue}{\left(y3 \cdot y4 + -1 \cdot \left(i \cdot x\right)\right)} \]

      3. mul-1-neg 62.7%

         \[\leadsto \left(c \cdot y\right) \cdot \left(y3 \cdot y4 + \color{blue}{\left(-i \cdot x\right)}\right) \]

      4. unsub-neg 62.7%

         \[\leadsto \left(c \cdot y\right) \cdot \color{blue}{\left(y3 \cdot y4 - i \cdot x\right)} \]

      5. *-commutative 62.7%

         \[\leadsto \left(c \cdot y\right) \cdot \left(y3 \cdot y4 - \color{blue}{x \cdot i}\right) \]

   7. Simplified 62.7%

      \[\leadsto \color{blue}{\left(c \cdot y\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)} \]

   if -6.0000000000000006e194 < y < -1.9999999999999999e82

   1. Initial program 25.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 58.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 58.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 58.8%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 58.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 58.8%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 58.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y3 around inf 59.1%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if -1.9999999999999999e82 < y < -6.20000000000000038e53

   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. Taylor expanded in c around inf 25.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 25.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 25.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 25.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 25.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 25.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 25.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 25.8%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 25.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in z around inf 75.3%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) - -1 \cdot \left(i \cdot t\right)\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 75.3%

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot y3 - i \cdot t\right)\right)}\right) \]

      2. *-commutative 75.3%

         \[\leadsto c \cdot \left(z \cdot \left(-1 \cdot \left(\color{blue}{y3 \cdot y0} - i \cdot t\right)\right)\right) \]

   7. Simplified 75.3%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-1 \cdot \left(y3 \cdot y0 - i \cdot t\right)\right)\right)} \]

   if -6.20000000000000038e53 < y < -4.8e-48

   1. Initial program 39.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 36.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 36.3%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 36.3%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 36.3%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 36.3%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in y4 around -inf 40.4%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   if -4.8e-48 < y < -2.7000000000000001e-123

   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. Taylor expanded in k around inf 57.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 57.2%

         \[\leadsto k \cdot \color{blue}{\left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. +-commutative 57.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      3. mul-1-neg 57.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      4. unsub-neg 57.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-commutative 57.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. mul-1-neg 57.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + \left(-\color{blue}{\left(-z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      7. remove-double-neg 57.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + \color{blue}{z \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Simplified 57.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in y0 around inf 56.4%

      \[\leadsto \color{blue}{k \cdot \left(y0 \cdot \left(-1 \cdot \left(y2 \cdot y5\right) + b \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 56.4%

         \[\leadsto k \cdot \left(y0 \cdot \color{blue}{\left(b \cdot z + -1 \cdot \left(y2 \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 56.4%

         \[\leadsto k \cdot \left(y0 \cdot \left(b \cdot z + \color{blue}{\left(-y2 \cdot y5\right)}\right)\right) \]

      3. sub-neg 56.4%

         \[\leadsto k \cdot \left(y0 \cdot \color{blue}{\left(b \cdot z - y2 \cdot y5\right)}\right) \]

      4. *-commutative 56.4%

         \[\leadsto k \cdot \left(y0 \cdot \left(b \cdot z - \color{blue}{y5 \cdot y2}\right)\right) \]

   7. Simplified 56.4%

      \[\leadsto \color{blue}{k \cdot \left(y0 \cdot \left(b \cdot z - y5 \cdot y2\right)\right)} \]

   if -2.7000000000000001e-123 < y < 5.9999999999999999e-284

   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. Taylor expanded in j around inf 40.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 40.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 40.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 40.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 40.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 40.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in x around inf 40.6%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   if 5.9999999999999999e-284 < y < 4.70000000000000046e-156

   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. Taylor expanded in y5 around inf 42.7%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 42.7%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 46.1%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 46.1%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 46.1%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 49.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 49.5%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

      2. neg-mul-1 49.5%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   7. Simplified 49.5%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   if 4.70000000000000046e-156 < y < 7.5000000000000003e-94

   1. Initial program 29.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in t around inf 35.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in z around inf 48.3%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 48.3%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. neg-mul-1 48.3%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) \]

      3. *-commutative 48.3%

         \[\leadsto \left(-t\right) \cdot \left(z \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right)\right) \]

      4. *-commutative 48.3%

         \[\leadsto \left(-t\right) \cdot \left(z \cdot \left(b \cdot a - \color{blue}{i \cdot c}\right)\right) \]

   5. Simplified 48.3%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(z \cdot \left(b \cdot a - i \cdot c\right)\right)} \]

   if 7.5000000000000003e-94 < y < 1.55e126

   1. Initial program 38.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 39.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 39.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 39.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 39.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 39.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 39.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y5 around -inf 42.3%

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(y5 \cdot \left(i \cdot t - y0 \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 42.3%

         \[\leadsto \color{blue}{\left(-1 \cdot j\right) \cdot \left(y5 \cdot \left(i \cdot t - y0 \cdot y3\right)\right)} \]

      2. neg-mul-1 42.3%

         \[\leadsto \color{blue}{\left(-j\right)} \cdot \left(y5 \cdot \left(i \cdot t - y0 \cdot y3\right)\right) \]

      3. *-commutative 42.3%

         \[\leadsto \left(-j\right) \cdot \left(y5 \cdot \left(\color{blue}{t \cdot i} - y0 \cdot y3\right)\right) \]

   7. Simplified 42.3%

      \[\leadsto \color{blue}{\left(-j\right) \cdot \left(y5 \cdot \left(t \cdot i - y0 \cdot y3\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+194}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+82}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+53}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-48}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-123}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-284}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-156}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-94}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+126}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \end{array} \]

Alternative 21: 29.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ t_2 := b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ t_3 := b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{if}\;j \leq -3 \cdot 10^{+214}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{+94}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq -2.1 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{-165}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 1.32 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.85 \cdot 10^{-39}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+79}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 3.9 \cdot 10^{+211}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{+271}:\\ \;\;\;\;\left(j \cdot y0\right) \cdot \left(y3 \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y5 (- (* t y2) (* y y3)))))
        (t_2 (* b (* j (- (* t y4) (* x y0)))))
        (t_3 (* b (* k (- (* z y0) (* y y4))))))
   (if (<= j -3e+214)
     t_2
     (if (<= j -8.5e+94)
       (* y0 (* y5 (* j y3)))
       (if (<= j -2.1e-37)
         t_1
         (if (<= j -1.8e-165)
           t_3
           (if (<= j 1.32e-298)
             t_1
             (if (<= j 2.85e-39)
               t_3
               (if (<= j 9.5e+79)
                 (* y0 (* k (* y2 (- y5))))
                 (if (<= j 3.9e+211)
                   t_2
                   (if (<= j 2.7e+271)
                     (* (* j y0) (* y3 y5))
                     (* k (* y1 (* y2 y4))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double t_2 = b * (j * ((t * y4) - (x * y0)));
	double t_3 = b * (k * ((z * y0) - (y * y4)));
	double tmp;
	if (j <= -3e+214) {
		tmp = t_2;
	} else if (j <= -8.5e+94) {
		tmp = y0 * (y5 * (j * y3));
	} else if (j <= -2.1e-37) {
		tmp = t_1;
	} else if (j <= -1.8e-165) {
		tmp = t_3;
	} else if (j <= 1.32e-298) {
		tmp = t_1;
	} else if (j <= 2.85e-39) {
		tmp = t_3;
	} else if (j <= 9.5e+79) {
		tmp = y0 * (k * (y2 * -y5));
	} else if (j <= 3.9e+211) {
		tmp = t_2;
	} else if (j <= 2.7e+271) {
		tmp = (j * y0) * (y3 * y5);
	} else {
		tmp = k * (y1 * (y2 * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (y5 * ((t * y2) - (y * y3)))
    t_2 = b * (j * ((t * y4) - (x * y0)))
    t_3 = b * (k * ((z * y0) - (y * y4)))
    if (j <= (-3d+214)) then
        tmp = t_2
    else if (j <= (-8.5d+94)) then
        tmp = y0 * (y5 * (j * y3))
    else if (j <= (-2.1d-37)) then
        tmp = t_1
    else if (j <= (-1.8d-165)) then
        tmp = t_3
    else if (j <= 1.32d-298) then
        tmp = t_1
    else if (j <= 2.85d-39) then
        tmp = t_3
    else if (j <= 9.5d+79) then
        tmp = y0 * (k * (y2 * -y5))
    else if (j <= 3.9d+211) then
        tmp = t_2
    else if (j <= 2.7d+271) then
        tmp = (j * y0) * (y3 * y5)
    else
        tmp = k * (y1 * (y2 * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double t_2 = b * (j * ((t * y4) - (x * y0)));
	double t_3 = b * (k * ((z * y0) - (y * y4)));
	double tmp;
	if (j <= -3e+214) {
		tmp = t_2;
	} else if (j <= -8.5e+94) {
		tmp = y0 * (y5 * (j * y3));
	} else if (j <= -2.1e-37) {
		tmp = t_1;
	} else if (j <= -1.8e-165) {
		tmp = t_3;
	} else if (j <= 1.32e-298) {
		tmp = t_1;
	} else if (j <= 2.85e-39) {
		tmp = t_3;
	} else if (j <= 9.5e+79) {
		tmp = y0 * (k * (y2 * -y5));
	} else if (j <= 3.9e+211) {
		tmp = t_2;
	} else if (j <= 2.7e+271) {
		tmp = (j * y0) * (y3 * y5);
	} else {
		tmp = k * (y1 * (y2 * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y5 * ((t * y2) - (y * y3)))
	t_2 = b * (j * ((t * y4) - (x * y0)))
	t_3 = b * (k * ((z * y0) - (y * y4)))
	tmp = 0
	if j <= -3e+214:
		tmp = t_2
	elif j <= -8.5e+94:
		tmp = y0 * (y5 * (j * y3))
	elif j <= -2.1e-37:
		tmp = t_1
	elif j <= -1.8e-165:
		tmp = t_3
	elif j <= 1.32e-298:
		tmp = t_1
	elif j <= 2.85e-39:
		tmp = t_3
	elif j <= 9.5e+79:
		tmp = y0 * (k * (y2 * -y5))
	elif j <= 3.9e+211:
		tmp = t_2
	elif j <= 2.7e+271:
		tmp = (j * y0) * (y3 * y5)
	else:
		tmp = k * (y1 * (y2 * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	t_2 = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))))
	t_3 = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))))
	tmp = 0.0
	if (j <= -3e+214)
		tmp = t_2;
	elseif (j <= -8.5e+94)
		tmp = Float64(y0 * Float64(y5 * Float64(j * y3)));
	elseif (j <= -2.1e-37)
		tmp = t_1;
	elseif (j <= -1.8e-165)
		tmp = t_3;
	elseif (j <= 1.32e-298)
		tmp = t_1;
	elseif (j <= 2.85e-39)
		tmp = t_3;
	elseif (j <= 9.5e+79)
		tmp = Float64(y0 * Float64(k * Float64(y2 * Float64(-y5))));
	elseif (j <= 3.9e+211)
		tmp = t_2;
	elseif (j <= 2.7e+271)
		tmp = Float64(Float64(j * y0) * Float64(y3 * y5));
	else
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y5 * ((t * y2) - (y * y3)));
	t_2 = b * (j * ((t * y4) - (x * y0)));
	t_3 = b * (k * ((z * y0) - (y * y4)));
	tmp = 0.0;
	if (j <= -3e+214)
		tmp = t_2;
	elseif (j <= -8.5e+94)
		tmp = y0 * (y5 * (j * y3));
	elseif (j <= -2.1e-37)
		tmp = t_1;
	elseif (j <= -1.8e-165)
		tmp = t_3;
	elseif (j <= 1.32e-298)
		tmp = t_1;
	elseif (j <= 2.85e-39)
		tmp = t_3;
	elseif (j <= 9.5e+79)
		tmp = y0 * (k * (y2 * -y5));
	elseif (j <= 3.9e+211)
		tmp = t_2;
	elseif (j <= 2.7e+271)
		tmp = (j * y0) * (y3 * y5);
	else
		tmp = k * (y1 * (y2 * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3e+214], t$95$2, If[LessEqual[j, -8.5e+94], N[(y0 * N[(y5 * N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.1e-37], t$95$1, If[LessEqual[j, -1.8e-165], t$95$3, If[LessEqual[j, 1.32e-298], t$95$1, If[LessEqual[j, 2.85e-39], t$95$3, If[LessEqual[j, 9.5e+79], N[(y0 * N[(k * N[(y2 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.9e+211], t$95$2, If[LessEqual[j, 2.7e+271], N[(N[(j * y0), $MachinePrecision] * N[(y3 * y5), $MachinePrecision]), $MachinePrecision], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -3.0000000000000001e214 or 9.49999999999999994e79 < j < 3.90000000000000023e211

   1. Initial program 35.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 71.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 71.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 71.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 71.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 71.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 71.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in b around inf 53.2%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -3.0000000000000001e214 < j < -8.50000000000000054e94

   1. Initial program 32.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 48.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 48.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 48.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 48.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 48.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 48.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 48.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 48.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 48.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 48.3%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 48.3%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 48.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]

      3. *-commutative 48.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot y5}\right)\right) \]

      4. *-commutative 48.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(\color{blue}{y2 \cdot k} - j \cdot y3\right) \cdot y5\right)\right) \]

      5. *-commutative 48.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(y2 \cdot k - \color{blue}{y3 \cdot j}\right) \cdot y5\right)\right) \]

      6. unsub-neg 48.3%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right)} \]

      7. *-commutative 48.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right) \]

      8. *-commutative 48.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(\color{blue}{k \cdot y2} - y3 \cdot j\right) \cdot y5\right) \]

      9. *-commutative 48.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) \cdot y5\right) \]

      10. *-commutative 48.3%

          \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \color{blue}{y5 \cdot \left(k \cdot y2 - j \cdot y3\right)}\right) \]

   7. Simplified 48.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in j around inf 45.3%

      \[\leadsto y0 \cdot \color{blue}{\left(j \cdot \left(y3 \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 53.0%

         \[\leadsto y0 \cdot \color{blue}{\left(\left(j \cdot y3\right) \cdot y5\right)} \]

      2. *-commutative 53.0%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(y3 \cdot j\right)} \cdot y5\right) \]

   10. Simplified 53.0%

       \[\leadsto y0 \cdot \color{blue}{\left(\left(y3 \cdot j\right) \cdot y5\right)} \]

   if -8.50000000000000054e94 < j < -2.1000000000000001e-37 or -1.79999999999999992e-165 < j < 1.3200000000000001e-298

   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. Taylor expanded in y5 around inf 38.0%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 38.0%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 41.4%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 41.4%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 41.4%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 43.7%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 43.7%

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 43.7%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   if -2.1000000000000001e-37 < j < -1.79999999999999992e-165 or 1.3200000000000001e-298 < j < 2.8499999999999998e-39

   1. Initial program 45.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in k around inf 40.3%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 40.3%

         \[\leadsto k \cdot \color{blue}{\left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. +-commutative 40.3%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      3. mul-1-neg 40.3%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      4. unsub-neg 40.3%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-commutative 40.3%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. mul-1-neg 40.3%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + \left(-\color{blue}{\left(-z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      7. remove-double-neg 40.3%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + \color{blue}{z \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Simplified 40.3%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf 39.0%

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z - y \cdot y4\right)\right)} \]

   if 2.8499999999999998e-39 < j < 9.49999999999999994e79

   1. Initial program 33.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 29.1%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 29.1%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 33.7%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 33.7%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 33.7%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 48.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 48.4%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

      2. neg-mul-1 48.4%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   7. Simplified 48.4%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in k around inf 44.1%

      \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y5\right)\right)} \]

   if 3.90000000000000023e211 < j < 2.69999999999999989e271

   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. Taylor expanded in y5 around inf 45.5%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 45.5%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 45.5%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 45.5%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 45.5%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 72.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 72.8%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

      2. neg-mul-1 72.8%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   7. Simplified 72.8%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in k around 0 73.3%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 82.0%

         \[\leadsto \color{blue}{\left(j \cdot y0\right) \cdot \left(y3 \cdot y5\right)} \]

   10. Simplified 82.0%

       \[\leadsto \color{blue}{\left(j \cdot y0\right) \cdot \left(y3 \cdot y5\right)} \]

   if 2.69999999999999989e271 < j

   1. Initial program 0.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 55.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 55.2%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 55.2%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 55.2%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 55.2%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in y4 around -inf 45.8%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   6. Taylor expanded in k around inf 56.2%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3 \cdot 10^{+214}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{+94}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq -2.1 \cdot 10^{-37}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{-165}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 1.32 \cdot 10^{-298}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 2.85 \cdot 10^{-39}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+79}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 3.9 \cdot 10^{+211}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{+271}:\\ \;\;\;\;\left(j \cdot y0\right) \cdot \left(y3 \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \]

Alternative 22: 28.9% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ t_2 := b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{if}\;j \leq -1.1 \cdot 10^{+148}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -1.3 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.1 \cdot 10^{-167}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-297}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 1.02 \cdot 10^{-119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-35}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{+69}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{+210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.45 \cdot 10^{+271}:\\ \;\;\;\;\left(j \cdot y0\right) \cdot \left(y3 \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* j (- (* t y4) (* x y0)))))
        (t_2 (* b (* k (- (* z y0) (* y y4))))))
   (if (<= j -1.1e+148)
     (* j (* y3 (- (* y0 y5) (* y1 y4))))
     (if (<= j -1.3e-37)
       t_1
       (if (<= j -2.1e-167)
         t_2
         (if (<= j 3.6e-297)
           (* a (* y5 (- (* t y2) (* y y3))))
           (if (<= j 1.02e-119)
             t_2
             (if (<= j 2.6e-35)
               (* c (* x (- (* y0 y2) (* y i))))
               (if (<= j 5e+69)
                 (* y0 (* k (* y2 (- y5))))
                 (if (<= j 1.1e+210)
                   t_1
                   (if (<= j 2.45e+271)
                     (* (* j y0) (* y3 y5))
                     (* k (* y1 (* y2 y4))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (j * ((t * y4) - (x * y0)));
	double t_2 = b * (k * ((z * y0) - (y * y4)));
	double tmp;
	if (j <= -1.1e+148) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (j <= -1.3e-37) {
		tmp = t_1;
	} else if (j <= -2.1e-167) {
		tmp = t_2;
	} else if (j <= 3.6e-297) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (j <= 1.02e-119) {
		tmp = t_2;
	} else if (j <= 2.6e-35) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (j <= 5e+69) {
		tmp = y0 * (k * (y2 * -y5));
	} else if (j <= 1.1e+210) {
		tmp = t_1;
	} else if (j <= 2.45e+271) {
		tmp = (j * y0) * (y3 * y5);
	} else {
		tmp = k * (y1 * (y2 * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (j * ((t * y4) - (x * y0)))
    t_2 = b * (k * ((z * y0) - (y * y4)))
    if (j <= (-1.1d+148)) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (j <= (-1.3d-37)) then
        tmp = t_1
    else if (j <= (-2.1d-167)) then
        tmp = t_2
    else if (j <= 3.6d-297) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (j <= 1.02d-119) then
        tmp = t_2
    else if (j <= 2.6d-35) then
        tmp = c * (x * ((y0 * y2) - (y * i)))
    else if (j <= 5d+69) then
        tmp = y0 * (k * (y2 * -y5))
    else if (j <= 1.1d+210) then
        tmp = t_1
    else if (j <= 2.45d+271) then
        tmp = (j * y0) * (y3 * y5)
    else
        tmp = k * (y1 * (y2 * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (j * ((t * y4) - (x * y0)));
	double t_2 = b * (k * ((z * y0) - (y * y4)));
	double tmp;
	if (j <= -1.1e+148) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (j <= -1.3e-37) {
		tmp = t_1;
	} else if (j <= -2.1e-167) {
		tmp = t_2;
	} else if (j <= 3.6e-297) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (j <= 1.02e-119) {
		tmp = t_2;
	} else if (j <= 2.6e-35) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (j <= 5e+69) {
		tmp = y0 * (k * (y2 * -y5));
	} else if (j <= 1.1e+210) {
		tmp = t_1;
	} else if (j <= 2.45e+271) {
		tmp = (j * y0) * (y3 * y5);
	} else {
		tmp = k * (y1 * (y2 * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (j * ((t * y4) - (x * y0)))
	t_2 = b * (k * ((z * y0) - (y * y4)))
	tmp = 0
	if j <= -1.1e+148:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif j <= -1.3e-37:
		tmp = t_1
	elif j <= -2.1e-167:
		tmp = t_2
	elif j <= 3.6e-297:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif j <= 1.02e-119:
		tmp = t_2
	elif j <= 2.6e-35:
		tmp = c * (x * ((y0 * y2) - (y * i)))
	elif j <= 5e+69:
		tmp = y0 * (k * (y2 * -y5))
	elif j <= 1.1e+210:
		tmp = t_1
	elif j <= 2.45e+271:
		tmp = (j * y0) * (y3 * y5)
	else:
		tmp = k * (y1 * (y2 * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))))
	t_2 = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))))
	tmp = 0.0
	if (j <= -1.1e+148)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (j <= -1.3e-37)
		tmp = t_1;
	elseif (j <= -2.1e-167)
		tmp = t_2;
	elseif (j <= 3.6e-297)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (j <= 1.02e-119)
		tmp = t_2;
	elseif (j <= 2.6e-35)
		tmp = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))));
	elseif (j <= 5e+69)
		tmp = Float64(y0 * Float64(k * Float64(y2 * Float64(-y5))));
	elseif (j <= 1.1e+210)
		tmp = t_1;
	elseif (j <= 2.45e+271)
		tmp = Float64(Float64(j * y0) * Float64(y3 * y5));
	else
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (j * ((t * y4) - (x * y0)));
	t_2 = b * (k * ((z * y0) - (y * y4)));
	tmp = 0.0;
	if (j <= -1.1e+148)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (j <= -1.3e-37)
		tmp = t_1;
	elseif (j <= -2.1e-167)
		tmp = t_2;
	elseif (j <= 3.6e-297)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (j <= 1.02e-119)
		tmp = t_2;
	elseif (j <= 2.6e-35)
		tmp = c * (x * ((y0 * y2) - (y * i)));
	elseif (j <= 5e+69)
		tmp = y0 * (k * (y2 * -y5));
	elseif (j <= 1.1e+210)
		tmp = t_1;
	elseif (j <= 2.45e+271)
		tmp = (j * y0) * (y3 * y5);
	else
		tmp = k * (y1 * (y2 * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.1e+148], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.3e-37], t$95$1, If[LessEqual[j, -2.1e-167], t$95$2, If[LessEqual[j, 3.6e-297], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.02e-119], t$95$2, If[LessEqual[j, 2.6e-35], N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5e+69], N[(y0 * N[(k * N[(y2 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.1e+210], t$95$1, If[LessEqual[j, 2.45e+271], N[(N[(j * y0), $MachinePrecision] * N[(y3 * y5), $MachinePrecision]), $MachinePrecision], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if j < -1.0999999999999999e148

   1. Initial program 30.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 82.4%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 82.4%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 82.4%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 82.4%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 82.4%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 82.4%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y3 around inf 49.7%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if -1.0999999999999999e148 < j < -1.2999999999999999e-37 or 5.00000000000000036e69 < j < 1.09999999999999993e210

   1. Initial program 31.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 49.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 49.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 49.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 49.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 49.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 49.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in b around inf 44.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -1.2999999999999999e-37 < j < -2.10000000000000017e-167 or 3.59999999999999994e-297 < j < 1.02e-119

   1. Initial program 45.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in k around inf 42.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 42.1%

         \[\leadsto k \cdot \color{blue}{\left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. +-commutative 42.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      3. mul-1-neg 42.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      4. unsub-neg 42.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-commutative 42.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. mul-1-neg 42.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + \left(-\color{blue}{\left(-z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      7. remove-double-neg 42.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + \color{blue}{z \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Simplified 42.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf 40.4%

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z - y \cdot y4\right)\right)} \]

   if -2.10000000000000017e-167 < j < 3.59999999999999994e-297

   1. Initial program 36.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 39.8%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 39.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 42.8%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 42.8%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 42.8%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 46.7%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 46.7%

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 46.7%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   if 1.02e-119 < j < 2.60000000000000005e-35

   1. Initial program 41.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 59.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 59.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 59.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 59.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 59.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 59.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 59.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 59.6%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 59.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in x around inf 55.6%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2 - i \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 55.6%

         \[\leadsto c \cdot \left(x \cdot \left(\color{blue}{y2 \cdot y0} - i \cdot y\right)\right) \]

   7. Simplified 55.6%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0 - i \cdot y\right)\right)} \]

   if 2.60000000000000005e-35 < j < 5.00000000000000036e69

   1. Initial program 35.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 30.6%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 30.6%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 35.4%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 35.4%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 35.4%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 50.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 50.7%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

      2. neg-mul-1 50.7%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   7. Simplified 50.7%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in k around inf 46.3%

      \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y5\right)\right)} \]

   if 1.09999999999999993e210 < j < 2.45e271

   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. Taylor expanded in y5 around inf 45.5%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 45.5%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 45.5%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 45.5%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 45.5%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 72.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 72.8%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

      2. neg-mul-1 72.8%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   7. Simplified 72.8%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in k around 0 73.3%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 82.0%

         \[\leadsto \color{blue}{\left(j \cdot y0\right) \cdot \left(y3 \cdot y5\right)} \]

   10. Simplified 82.0%

       \[\leadsto \color{blue}{\left(j \cdot y0\right) \cdot \left(y3 \cdot y5\right)} \]

   if 2.45e271 < j

   1. Initial program 0.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 55.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 55.2%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 55.2%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 55.2%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 55.2%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in y4 around -inf 45.8%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   6. Taylor expanded in k around inf 56.2%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.1 \cdot 10^{+148}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -1.3 \cdot 10^{-37}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -2.1 \cdot 10^{-167}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-297}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 1.02 \cdot 10^{-119}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-35}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{+69}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{+210}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 2.45 \cdot 10^{+271}:\\ \;\;\;\;\left(j \cdot y0\right) \cdot \left(y3 \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \]

Alternative 23: 31.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ t_2 := k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+83}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-47}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-211}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+142}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* y c) (- (* y3 y4) (* x i))))
        (t_2 (* k (* y0 (- (* z b) (* y2 y5))))))
   (if (<= y -2e+194)
     t_1
     (if (<= y -8.5e+83)
       (* j (* y3 (- (* y0 y5) (* y1 y4))))
       (if (<= y -2.8e+62)
         t_1
         (if (<= y -3.5e-7)
           (* b (* k (- (* z y0) (* y y4))))
           (if (<= y -1.55e-47)
             (* a (* y5 (- (* t y2) (* y y3))))
             (if (<= y -2.3e-123)
               t_2
               (if (<= y -3e-211)
                 (* j (* x (- (* i y1) (* b y0))))
                 (if (<= y 2.05e+142) t_2 t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * c) * ((y3 * y4) - (x * i));
	double t_2 = k * (y0 * ((z * b) - (y2 * y5)));
	double tmp;
	if (y <= -2e+194) {
		tmp = t_1;
	} else if (y <= -8.5e+83) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (y <= -2.8e+62) {
		tmp = t_1;
	} else if (y <= -3.5e-7) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (y <= -1.55e-47) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y <= -2.3e-123) {
		tmp = t_2;
	} else if (y <= -3e-211) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y <= 2.05e+142) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * c) * ((y3 * y4) - (x * i))
    t_2 = k * (y0 * ((z * b) - (y2 * y5)))
    if (y <= (-2d+194)) then
        tmp = t_1
    else if (y <= (-8.5d+83)) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (y <= (-2.8d+62)) then
        tmp = t_1
    else if (y <= (-3.5d-7)) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (y <= (-1.55d-47)) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (y <= (-2.3d-123)) then
        tmp = t_2
    else if (y <= (-3d-211)) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (y <= 2.05d+142) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * c) * ((y3 * y4) - (x * i));
	double t_2 = k * (y0 * ((z * b) - (y2 * y5)));
	double tmp;
	if (y <= -2e+194) {
		tmp = t_1;
	} else if (y <= -8.5e+83) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (y <= -2.8e+62) {
		tmp = t_1;
	} else if (y <= -3.5e-7) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (y <= -1.55e-47) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y <= -2.3e-123) {
		tmp = t_2;
	} else if (y <= -3e-211) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y <= 2.05e+142) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y * c) * ((y3 * y4) - (x * i))
	t_2 = k * (y0 * ((z * b) - (y2 * y5)))
	tmp = 0
	if y <= -2e+194:
		tmp = t_1
	elif y <= -8.5e+83:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif y <= -2.8e+62:
		tmp = t_1
	elif y <= -3.5e-7:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif y <= -1.55e-47:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif y <= -2.3e-123:
		tmp = t_2
	elif y <= -3e-211:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif y <= 2.05e+142:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * c) * Float64(Float64(y3 * y4) - Float64(x * i)))
	t_2 = Float64(k * Float64(y0 * Float64(Float64(z * b) - Float64(y2 * y5))))
	tmp = 0.0
	if (y <= -2e+194)
		tmp = t_1;
	elseif (y <= -8.5e+83)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (y <= -2.8e+62)
		tmp = t_1;
	elseif (y <= -3.5e-7)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (y <= -1.55e-47)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (y <= -2.3e-123)
		tmp = t_2;
	elseif (y <= -3e-211)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (y <= 2.05e+142)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y * c) * ((y3 * y4) - (x * i));
	t_2 = k * (y0 * ((z * b) - (y2 * y5)));
	tmp = 0.0;
	if (y <= -2e+194)
		tmp = t_1;
	elseif (y <= -8.5e+83)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (y <= -2.8e+62)
		tmp = t_1;
	elseif (y <= -3.5e-7)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (y <= -1.55e-47)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (y <= -2.3e-123)
		tmp = t_2;
	elseif (y <= -3e-211)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (y <= 2.05e+142)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y * c), $MachinePrecision] * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(y0 * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+194], t$95$1, If[LessEqual[y, -8.5e+83], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.8e+62], t$95$1, If[LessEqual[y, -3.5e-7], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.55e-47], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.3e-123], t$95$2, If[LessEqual[y, -3e-211], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e+142], t$95$2, t$95$1]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.99999999999999989e194 or -8.4999999999999995e83 < y < -2.80000000000000014e62 or 2.04999999999999991e142 < y

   1. Initial program 30.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 42.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 42.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 42.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 42.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 42.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 42.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 42.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 42.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 42.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y around -inf 71.5%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 63.8%

         \[\leadsto \color{blue}{\left(c \cdot y\right) \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)} \]

      2. +-commutative 63.8%

         \[\leadsto \left(c \cdot y\right) \cdot \color{blue}{\left(y3 \cdot y4 + -1 \cdot \left(i \cdot x\right)\right)} \]

      3. mul-1-neg 63.8%

         \[\leadsto \left(c \cdot y\right) \cdot \left(y3 \cdot y4 + \color{blue}{\left(-i \cdot x\right)}\right) \]

      4. unsub-neg 63.8%

         \[\leadsto \left(c \cdot y\right) \cdot \color{blue}{\left(y3 \cdot y4 - i \cdot x\right)} \]

      5. *-commutative 63.8%

         \[\leadsto \left(c \cdot y\right) \cdot \left(y3 \cdot y4 - \color{blue}{x \cdot i}\right) \]

   7. Simplified 63.8%

      \[\leadsto \color{blue}{\left(c \cdot y\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)} \]

   if -1.99999999999999989e194 < y < -8.4999999999999995e83

   1. Initial program 25.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 58.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 58.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 58.8%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 58.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 58.8%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 58.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y3 around inf 59.1%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if -2.80000000000000014e62 < y < -3.49999999999999984e-7

   1. Initial program 41.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in k around inf 53.3%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 53.3%

         \[\leadsto k \cdot \color{blue}{\left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. +-commutative 53.3%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      3. mul-1-neg 53.3%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      4. unsub-neg 53.3%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-commutative 53.3%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. mul-1-neg 53.3%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + \left(-\color{blue}{\left(-z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      7. remove-double-neg 53.3%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + \color{blue}{z \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Simplified 53.3%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf 53.6%

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z - y \cdot y4\right)\right)} \]

   if -3.49999999999999984e-7 < y < -1.5499999999999999e-47

   1. Initial program 23.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 44.9%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 44.9%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 44.9%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 44.9%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 44.9%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 55.7%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 55.7%

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 55.7%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   if -1.5499999999999999e-47 < y < -2.29999999999999987e-123 or -3.00000000000000005e-211 < y < 2.04999999999999991e142

   1. Initial program 38.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in k around inf 37.6%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 37.6%

         \[\leadsto k \cdot \color{blue}{\left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. +-commutative 37.6%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      3. mul-1-neg 37.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      4. unsub-neg 37.6%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-commutative 37.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. mul-1-neg 37.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + \left(-\color{blue}{\left(-z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      7. remove-double-neg 37.6%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + \color{blue}{z \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Simplified 37.6%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in y0 around inf 39.4%

      \[\leadsto \color{blue}{k \cdot \left(y0 \cdot \left(-1 \cdot \left(y2 \cdot y5\right) + b \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 39.4%

         \[\leadsto k \cdot \left(y0 \cdot \color{blue}{\left(b \cdot z + -1 \cdot \left(y2 \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 39.4%

         \[\leadsto k \cdot \left(y0 \cdot \left(b \cdot z + \color{blue}{\left(-y2 \cdot y5\right)}\right)\right) \]

      3. sub-neg 39.4%

         \[\leadsto k \cdot \left(y0 \cdot \color{blue}{\left(b \cdot z - y2 \cdot y5\right)}\right) \]

      4. *-commutative 39.4%

         \[\leadsto k \cdot \left(y0 \cdot \left(b \cdot z - \color{blue}{y5 \cdot y2}\right)\right) \]

   7. Simplified 39.4%

      \[\leadsto \color{blue}{k \cdot \left(y0 \cdot \left(b \cdot z - y5 \cdot y2\right)\right)} \]

   if -2.29999999999999987e-123 < y < -3.00000000000000005e-211

   1. Initial program 39.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 50.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 50.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 50.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 50.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 50.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 50.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in x around inf 51.0%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+194}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+83}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+62}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-47}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-123}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-211}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+142}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \end{array} \]

Alternative 24: 29.1% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{if}\;b \leq -7.4 \cdot 10^{+64}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-70}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-188}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-290}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{-98}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{+138}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+220}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y5 (- (* y0 y3) (* t i))))))
   (if (<= b -7.4e+64)
     (* j (* x (- (* i y1) (* b y0))))
     (if (<= b -9e-70)
       (* c (* t (- (* z i) (* y2 y4))))
       (if (<= b -8e-188)
         (* (* y c) (- (* y3 y4) (* x i)))
         (if (<= b 3.5e-290)
           t_1
           (if (<= b 5.4e-98)
             (* c (* y4 (- (* y y3) (* t y2))))
             (if (<= b 2.3e-57)
               t_1
               (if (<= b 5.4e+138)
                 (* c (* x (- (* y0 y2) (* y i))))
                 (if (<= b 8.5e+220)
                   (* j (* y3 (- (* y0 y5) (* y1 y4))))
                   (* (* t b) (- (* j y4) (* z 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 t_1 = j * (y5 * ((y0 * y3) - (t * i)));
	double tmp;
	if (b <= -7.4e+64) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (b <= -9e-70) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (b <= -8e-188) {
		tmp = (y * c) * ((y3 * y4) - (x * i));
	} else if (b <= 3.5e-290) {
		tmp = t_1;
	} else if (b <= 5.4e-98) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (b <= 2.3e-57) {
		tmp = t_1;
	} else if (b <= 5.4e+138) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (b <= 8.5e+220) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else {
		tmp = (t * b) * ((j * y4) - (z * 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) :: t_1
    real(8) :: tmp
    t_1 = j * (y5 * ((y0 * y3) - (t * i)))
    if (b <= (-7.4d+64)) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (b <= (-9d-70)) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (b <= (-8d-188)) then
        tmp = (y * c) * ((y3 * y4) - (x * i))
    else if (b <= 3.5d-290) then
        tmp = t_1
    else if (b <= 5.4d-98) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (b <= 2.3d-57) then
        tmp = t_1
    else if (b <= 5.4d+138) then
        tmp = c * (x * ((y0 * y2) - (y * i)))
    else if (b <= 8.5d+220) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else
        tmp = (t * b) * ((j * y4) - (z * 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 t_1 = j * (y5 * ((y0 * y3) - (t * i)));
	double tmp;
	if (b <= -7.4e+64) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (b <= -9e-70) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (b <= -8e-188) {
		tmp = (y * c) * ((y3 * y4) - (x * i));
	} else if (b <= 3.5e-290) {
		tmp = t_1;
	} else if (b <= 5.4e-98) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (b <= 2.3e-57) {
		tmp = t_1;
	} else if (b <= 5.4e+138) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (b <= 8.5e+220) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else {
		tmp = (t * b) * ((j * y4) - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (y5 * ((y0 * y3) - (t * i)))
	tmp = 0
	if b <= -7.4e+64:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif b <= -9e-70:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif b <= -8e-188:
		tmp = (y * c) * ((y3 * y4) - (x * i))
	elif b <= 3.5e-290:
		tmp = t_1
	elif b <= 5.4e-98:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif b <= 2.3e-57:
		tmp = t_1
	elif b <= 5.4e+138:
		tmp = c * (x * ((y0 * y2) - (y * i)))
	elif b <= 8.5e+220:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	else:
		tmp = (t * b) * ((j * y4) - (z * a))
	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(y5 * Float64(Float64(y0 * y3) - Float64(t * i))))
	tmp = 0.0
	if (b <= -7.4e+64)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (b <= -9e-70)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (b <= -8e-188)
		tmp = Float64(Float64(y * c) * Float64(Float64(y3 * y4) - Float64(x * i)));
	elseif (b <= 3.5e-290)
		tmp = t_1;
	elseif (b <= 5.4e-98)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (b <= 2.3e-57)
		tmp = t_1;
	elseif (b <= 5.4e+138)
		tmp = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))));
	elseif (b <= 8.5e+220)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	else
		tmp = Float64(Float64(t * b) * Float64(Float64(j * y4) - Float64(z * 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)
	t_1 = j * (y5 * ((y0 * y3) - (t * i)));
	tmp = 0.0;
	if (b <= -7.4e+64)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (b <= -9e-70)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (b <= -8e-188)
		tmp = (y * c) * ((y3 * y4) - (x * i));
	elseif (b <= 3.5e-290)
		tmp = t_1;
	elseif (b <= 5.4e-98)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (b <= 2.3e-57)
		tmp = t_1;
	elseif (b <= 5.4e+138)
		tmp = c * (x * ((y0 * y2) - (y * i)));
	elseif (b <= 8.5e+220)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	else
		tmp = (t * b) * ((j * y4) - (z * a));
	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[(y5 * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.4e+64], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -9e-70], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8e-188], N[(N[(y * c), $MachinePrecision] * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.5e-290], t$95$1, If[LessEqual[b, 5.4e-98], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e-57], t$95$1, If[LessEqual[b, 5.4e+138], N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e+220], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * b), $MachinePrecision] * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if b < -7.39999999999999966e64

   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. Taylor expanded in j around inf 46.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 46.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 46.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 46.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 46.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 46.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in x around inf 46.4%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   if -7.39999999999999966e64 < b < -9.00000000000000044e-70

   1. Initial program 37.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in t around inf 43.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in c around inf 38.1%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   if -9.00000000000000044e-70 < b < -7.9999999999999996e-188

   1. Initial program 43.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 47.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 47.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 47.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 47.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 47.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 47.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 47.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 47.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 47.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y around -inf 51.4%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 51.4%

         \[\leadsto \color{blue}{\left(c \cdot y\right) \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)} \]

      2. +-commutative 51.4%

         \[\leadsto \left(c \cdot y\right) \cdot \color{blue}{\left(y3 \cdot y4 + -1 \cdot \left(i \cdot x\right)\right)} \]

      3. mul-1-neg 51.4%

         \[\leadsto \left(c \cdot y\right) \cdot \left(y3 \cdot y4 + \color{blue}{\left(-i \cdot x\right)}\right) \]

      4. unsub-neg 51.4%

         \[\leadsto \left(c \cdot y\right) \cdot \color{blue}{\left(y3 \cdot y4 - i \cdot x\right)} \]

      5. *-commutative 51.4%

         \[\leadsto \left(c \cdot y\right) \cdot \left(y3 \cdot y4 - \color{blue}{x \cdot i}\right) \]

   7. Simplified 51.4%

      \[\leadsto \color{blue}{\left(c \cdot y\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)} \]

   if -7.9999999999999996e-188 < b < 3.49999999999999981e-290 or 5.3999999999999997e-98 < b < 2.3e-57

   1. Initial program 40.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 63.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 63.0%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 63.0%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 63.0%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 63.0%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 63.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y5 around -inf 63.0%

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(y5 \cdot \left(i \cdot t - y0 \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 63.0%

         \[\leadsto \color{blue}{\left(-1 \cdot j\right) \cdot \left(y5 \cdot \left(i \cdot t - y0 \cdot y3\right)\right)} \]

      2. neg-mul-1 63.0%

         \[\leadsto \color{blue}{\left(-j\right)} \cdot \left(y5 \cdot \left(i \cdot t - y0 \cdot y3\right)\right) \]

      3. *-commutative 63.0%

         \[\leadsto \left(-j\right) \cdot \left(y5 \cdot \left(\color{blue}{t \cdot i} - y0 \cdot y3\right)\right) \]

   7. Simplified 63.0%

      \[\leadsto \color{blue}{\left(-j\right) \cdot \left(y5 \cdot \left(t \cdot i - y0 \cdot y3\right)\right)} \]

   if 3.49999999999999981e-290 < b < 5.3999999999999997e-98

   1. Initial program 43.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 40.7%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 40.7%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 45.5%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 45.5%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 45.5%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in c around inf 50.1%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 50.1%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. neg-mul-1 50.1%

         \[\leadsto \color{blue}{\left(-c\right)} \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. *-commutative 50.1%

         \[\leadsto \left(-c\right) \cdot \left(y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 50.1%

      \[\leadsto \color{blue}{\left(-c\right) \cdot \left(y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   if 2.3e-57 < b < 5.40000000000000018e138

   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. Taylor expanded in c around inf 44.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 44.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 44.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 44.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 44.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 44.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 44.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 44.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 44.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in x around inf 44.8%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2 - i \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 44.8%

         \[\leadsto c \cdot \left(x \cdot \left(\color{blue}{y2 \cdot y0} - i \cdot y\right)\right) \]

   7. Simplified 44.8%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0 - i \cdot y\right)\right)} \]

   if 5.40000000000000018e138 < b < 8.4999999999999996e220

   1. Initial program 22.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 52.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 52.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 52.8%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 52.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 52.8%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 52.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y3 around inf 53.0%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if 8.4999999999999996e220 < b

   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. Taylor expanded in t around inf 38.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in b around inf 61.4%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 66.8%

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      2. *-commutative 66.8%

         \[\leadsto \color{blue}{\left(t \cdot b\right)} \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right) \]

      3. +-commutative 66.8%

         \[\leadsto \left(t \cdot b\right) \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)} \]

      4. mul-1-neg 66.8%

         \[\leadsto \left(t \cdot b\right) \cdot \left(j \cdot y4 + \color{blue}{\left(-a \cdot z\right)}\right) \]

      5. unsub-neg 66.8%

         \[\leadsto \left(t \cdot b\right) \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)} \]

      6. *-commutative 66.8%

         \[\leadsto \left(t \cdot b\right) \cdot \left(j \cdot y4 - \color{blue}{z \cdot a}\right) \]

   5. Simplified 66.8%

      \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.4 \cdot 10^{+64}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-70}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-188}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-290}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{-98}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-57}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{+138}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+220}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)\\ \end{array} \]

Alternative 25: 27.0% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{if}\;j \leq -1.5 \cdot 10^{+214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -6.4 \cdot 10^{+94}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{-290}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 1.46 \cdot 10^{-229}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 2.02 \cdot 10^{-100}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{+74}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 10^{+214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{+271}:\\ \;\;\;\;\left(j \cdot y0\right) \cdot \left(y3 \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* j (- (* t y4) (* x y0))))))
   (if (<= j -1.5e+214)
     t_1
     (if (<= j -6.4e+94)
       (* y0 (* y5 (* j y3)))
       (if (<= j 1.4e-290)
         (* a (* y5 (- (* t y2) (* y y3))))
         (if (<= j 1.46e-229)
           (* y1 (* k (* y2 y4)))
           (if (<= j 2.02e-100)
             (* y0 (* c (* z (- y3))))
             (if (<= j 3.5e+74)
               (* y0 (* k (* y2 (- y5))))
               (if (<= j 1e+214)
                 t_1
                 (if (<= j 2.7e+271)
                   (* (* j y0) (* y3 y5))
                   (* k (* y1 (* y2 y4)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (j * ((t * y4) - (x * y0)));
	double tmp;
	if (j <= -1.5e+214) {
		tmp = t_1;
	} else if (j <= -6.4e+94) {
		tmp = y0 * (y5 * (j * y3));
	} else if (j <= 1.4e-290) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (j <= 1.46e-229) {
		tmp = y1 * (k * (y2 * y4));
	} else if (j <= 2.02e-100) {
		tmp = y0 * (c * (z * -y3));
	} else if (j <= 3.5e+74) {
		tmp = y0 * (k * (y2 * -y5));
	} else if (j <= 1e+214) {
		tmp = t_1;
	} else if (j <= 2.7e+271) {
		tmp = (j * y0) * (y3 * y5);
	} else {
		tmp = k * (y1 * (y2 * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (j * ((t * y4) - (x * y0)))
    if (j <= (-1.5d+214)) then
        tmp = t_1
    else if (j <= (-6.4d+94)) then
        tmp = y0 * (y5 * (j * y3))
    else if (j <= 1.4d-290) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (j <= 1.46d-229) then
        tmp = y1 * (k * (y2 * y4))
    else if (j <= 2.02d-100) then
        tmp = y0 * (c * (z * -y3))
    else if (j <= 3.5d+74) then
        tmp = y0 * (k * (y2 * -y5))
    else if (j <= 1d+214) then
        tmp = t_1
    else if (j <= 2.7d+271) then
        tmp = (j * y0) * (y3 * y5)
    else
        tmp = k * (y1 * (y2 * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (j * ((t * y4) - (x * y0)));
	double tmp;
	if (j <= -1.5e+214) {
		tmp = t_1;
	} else if (j <= -6.4e+94) {
		tmp = y0 * (y5 * (j * y3));
	} else if (j <= 1.4e-290) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (j <= 1.46e-229) {
		tmp = y1 * (k * (y2 * y4));
	} else if (j <= 2.02e-100) {
		tmp = y0 * (c * (z * -y3));
	} else if (j <= 3.5e+74) {
		tmp = y0 * (k * (y2 * -y5));
	} else if (j <= 1e+214) {
		tmp = t_1;
	} else if (j <= 2.7e+271) {
		tmp = (j * y0) * (y3 * y5);
	} else {
		tmp = k * (y1 * (y2 * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (j * ((t * y4) - (x * y0)))
	tmp = 0
	if j <= -1.5e+214:
		tmp = t_1
	elif j <= -6.4e+94:
		tmp = y0 * (y5 * (j * y3))
	elif j <= 1.4e-290:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif j <= 1.46e-229:
		tmp = y1 * (k * (y2 * y4))
	elif j <= 2.02e-100:
		tmp = y0 * (c * (z * -y3))
	elif j <= 3.5e+74:
		tmp = y0 * (k * (y2 * -y5))
	elif j <= 1e+214:
		tmp = t_1
	elif j <= 2.7e+271:
		tmp = (j * y0) * (y3 * y5)
	else:
		tmp = k * (y1 * (y2 * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))))
	tmp = 0.0
	if (j <= -1.5e+214)
		tmp = t_1;
	elseif (j <= -6.4e+94)
		tmp = Float64(y0 * Float64(y5 * Float64(j * y3)));
	elseif (j <= 1.4e-290)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (j <= 1.46e-229)
		tmp = Float64(y1 * Float64(k * Float64(y2 * y4)));
	elseif (j <= 2.02e-100)
		tmp = Float64(y0 * Float64(c * Float64(z * Float64(-y3))));
	elseif (j <= 3.5e+74)
		tmp = Float64(y0 * Float64(k * Float64(y2 * Float64(-y5))));
	elseif (j <= 1e+214)
		tmp = t_1;
	elseif (j <= 2.7e+271)
		tmp = Float64(Float64(j * y0) * Float64(y3 * y5));
	else
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (j * ((t * y4) - (x * y0)));
	tmp = 0.0;
	if (j <= -1.5e+214)
		tmp = t_1;
	elseif (j <= -6.4e+94)
		tmp = y0 * (y5 * (j * y3));
	elseif (j <= 1.4e-290)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (j <= 1.46e-229)
		tmp = y1 * (k * (y2 * y4));
	elseif (j <= 2.02e-100)
		tmp = y0 * (c * (z * -y3));
	elseif (j <= 3.5e+74)
		tmp = y0 * (k * (y2 * -y5));
	elseif (j <= 1e+214)
		tmp = t_1;
	elseif (j <= 2.7e+271)
		tmp = (j * y0) * (y3 * y5);
	else
		tmp = k * (y1 * (y2 * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.5e+214], t$95$1, If[LessEqual[j, -6.4e+94], N[(y0 * N[(y5 * N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.4e-290], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.46e-229], N[(y1 * N[(k * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.02e-100], N[(y0 * N[(c * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.5e+74], N[(y0 * N[(k * N[(y2 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1e+214], t$95$1, If[LessEqual[j, 2.7e+271], N[(N[(j * y0), $MachinePrecision] * N[(y3 * y5), $MachinePrecision]), $MachinePrecision], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if j < -1.5000000000000001e214 or 3.50000000000000014e74 < j < 9.9999999999999995e213

   1. Initial program 35.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 71.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 71.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 71.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 71.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 71.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 71.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in b around inf 53.2%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -1.5000000000000001e214 < j < -6.40000000000000028e94

   1. Initial program 32.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 48.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 48.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 48.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 48.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 48.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 48.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 48.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 48.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 48.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 48.3%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 48.3%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 48.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]

      3. *-commutative 48.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot y5}\right)\right) \]

      4. *-commutative 48.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(\color{blue}{y2 \cdot k} - j \cdot y3\right) \cdot y5\right)\right) \]

      5. *-commutative 48.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(y2 \cdot k - \color{blue}{y3 \cdot j}\right) \cdot y5\right)\right) \]

      6. unsub-neg 48.3%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right)} \]

      7. *-commutative 48.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right) \]

      8. *-commutative 48.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(\color{blue}{k \cdot y2} - y3 \cdot j\right) \cdot y5\right) \]

      9. *-commutative 48.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) \cdot y5\right) \]

      10. *-commutative 48.3%

          \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \color{blue}{y5 \cdot \left(k \cdot y2 - j \cdot y3\right)}\right) \]

   7. Simplified 48.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in j around inf 45.3%

      \[\leadsto y0 \cdot \color{blue}{\left(j \cdot \left(y3 \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 53.0%

         \[\leadsto y0 \cdot \color{blue}{\left(\left(j \cdot y3\right) \cdot y5\right)} \]

      2. *-commutative 53.0%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(y3 \cdot j\right)} \cdot y5\right) \]

   10. Simplified 53.0%

       \[\leadsto y0 \cdot \color{blue}{\left(\left(y3 \cdot j\right) \cdot y5\right)} \]

   if -6.40000000000000028e94 < j < 1.39999999999999998e-290

   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. Taylor expanded in y5 around inf 36.5%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 36.5%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 37.7%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 37.7%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 37.7%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 35.9%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 35.9%

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 35.9%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   if 1.39999999999999998e-290 < j < 1.46e-229

   1. Initial program 49.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 34.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 34.0%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 34.0%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 34.0%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 34.0%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in y4 around -inf 29.9%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   6. Taylor expanded in k around inf 35.3%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y4\right)\right)} \]

   if 1.46e-229 < j < 2.02000000000000005e-100

   1. Initial program 38.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 18.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 18.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 18.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 18.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 18.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 18.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 18.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 18.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 18.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 42.4%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 42.4%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 42.4%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]

      3. *-commutative 42.4%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot y5}\right)\right) \]

      4. *-commutative 42.4%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(\color{blue}{y2 \cdot k} - j \cdot y3\right) \cdot y5\right)\right) \]

      5. *-commutative 42.4%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(y2 \cdot k - \color{blue}{y3 \cdot j}\right) \cdot y5\right)\right) \]

      6. unsub-neg 42.4%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right)} \]

      7. *-commutative 42.4%

         \[\leadsto y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right) \]

      8. *-commutative 42.4%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(\color{blue}{k \cdot y2} - y3 \cdot j\right) \cdot y5\right) \]

      9. *-commutative 42.4%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) \cdot y5\right) \]

      10. *-commutative 42.4%

          \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \color{blue}{y5 \cdot \left(k \cdot y2 - j \cdot y3\right)}\right) \]

   7. Simplified 42.4%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in z around inf 32.5%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 32.5%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]

      2. *-commutative 32.5%

         \[\leadsto \left(-1 \cdot c\right) \cdot \color{blue}{\left(\left(y3 \cdot z\right) \cdot y0\right)} \]

      3. associate-*r* 35.8%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot c\right) \cdot \left(y3 \cdot z\right)\right) \cdot y0} \]

      4. associate-*r* 35.8%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot \left(y3 \cdot z\right)\right)\right)} \cdot y0 \]

      5. mul-1-neg 35.8%

         \[\leadsto \color{blue}{\left(-c \cdot \left(y3 \cdot z\right)\right)} \cdot y0 \]

      6. distribute-rgt-neg-in 35.8%

         \[\leadsto \color{blue}{\left(c \cdot \left(-y3 \cdot z\right)\right)} \cdot y0 \]

      7. distribute-rgt-neg-in 35.8%

         \[\leadsto \left(c \cdot \color{blue}{\left(y3 \cdot \left(-z\right)\right)}\right) \cdot y0 \]

   10. Simplified 35.8%

       \[\leadsto \color{blue}{\left(c \cdot \left(y3 \cdot \left(-z\right)\right)\right) \cdot y0} \]

   if 2.02000000000000005e-100 < j < 3.50000000000000014e74

   1. Initial program 39.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 28.8%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 28.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 31.5%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 31.5%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 31.5%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 37.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 37.1%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

      2. neg-mul-1 37.1%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   7. Simplified 37.1%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in k around inf 37.2%

      \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y5\right)\right)} \]

   if 9.9999999999999995e213 < j < 2.69999999999999989e271

   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. Taylor expanded in y5 around inf 45.5%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 45.5%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 45.5%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 45.5%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 45.5%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 72.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 72.8%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

      2. neg-mul-1 72.8%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   7. Simplified 72.8%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in k around 0 73.3%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 82.0%

         \[\leadsto \color{blue}{\left(j \cdot y0\right) \cdot \left(y3 \cdot y5\right)} \]

   10. Simplified 82.0%

       \[\leadsto \color{blue}{\left(j \cdot y0\right) \cdot \left(y3 \cdot y5\right)} \]

   if 2.69999999999999989e271 < j

   1. Initial program 0.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 55.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 55.2%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 55.2%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 55.2%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 55.2%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in y4 around -inf 45.8%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   6. Taylor expanded in k around inf 56.2%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.5 \cdot 10^{+214}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -6.4 \cdot 10^{+94}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{-290}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 1.46 \cdot 10^{-229}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 2.02 \cdot 10^{-100}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{+74}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 10^{+214}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{+271}:\\ \;\;\;\;\left(j \cdot y0\right) \cdot \left(y3 \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \]

Alternative 26: 29.3% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ t_2 := k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{if}\;y \leq -8.8 \cdot 10^{+209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-47}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-210}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+173}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+210}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* x (- (* y0 y2) (* y i)))))
        (t_2 (* k (* y0 (- (* z b) (* y2 y5))))))
   (if (<= y -8.8e+209)
     t_1
     (if (<= y -1.8e-47)
       (* j (* y3 (- (* y0 y5) (* y1 y4))))
       (if (<= y -2.8e-123)
         t_2
         (if (<= y -1.02e-210)
           (* j (* x (- (* i y1) (* b y0))))
           (if (<= y 2.2e+143)
             t_2
             (if (<= y 3.8e+173)
               (* a (* y5 (- (* t y2) (* y y3))))
               (if (<= y 8.8e+210) (* k (* y1 (* y2 y4))) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (x * ((y0 * y2) - (y * i)));
	double t_2 = k * (y0 * ((z * b) - (y2 * y5)));
	double tmp;
	if (y <= -8.8e+209) {
		tmp = t_1;
	} else if (y <= -1.8e-47) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (y <= -2.8e-123) {
		tmp = t_2;
	} else if (y <= -1.02e-210) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y <= 2.2e+143) {
		tmp = t_2;
	} else if (y <= 3.8e+173) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y <= 8.8e+210) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (x * ((y0 * y2) - (y * i)))
    t_2 = k * (y0 * ((z * b) - (y2 * y5)))
    if (y <= (-8.8d+209)) then
        tmp = t_1
    else if (y <= (-1.8d-47)) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (y <= (-2.8d-123)) then
        tmp = t_2
    else if (y <= (-1.02d-210)) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (y <= 2.2d+143) then
        tmp = t_2
    else if (y <= 3.8d+173) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (y <= 8.8d+210) then
        tmp = k * (y1 * (y2 * y4))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (x * ((y0 * y2) - (y * i)));
	double t_2 = k * (y0 * ((z * b) - (y2 * y5)));
	double tmp;
	if (y <= -8.8e+209) {
		tmp = t_1;
	} else if (y <= -1.8e-47) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (y <= -2.8e-123) {
		tmp = t_2;
	} else if (y <= -1.02e-210) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y <= 2.2e+143) {
		tmp = t_2;
	} else if (y <= 3.8e+173) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y <= 8.8e+210) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (x * ((y0 * y2) - (y * i)))
	t_2 = k * (y0 * ((z * b) - (y2 * y5)))
	tmp = 0
	if y <= -8.8e+209:
		tmp = t_1
	elif y <= -1.8e-47:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif y <= -2.8e-123:
		tmp = t_2
	elif y <= -1.02e-210:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif y <= 2.2e+143:
		tmp = t_2
	elif y <= 3.8e+173:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif y <= 8.8e+210:
		tmp = k * (y1 * (y2 * y4))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))))
	t_2 = Float64(k * Float64(y0 * Float64(Float64(z * b) - Float64(y2 * y5))))
	tmp = 0.0
	if (y <= -8.8e+209)
		tmp = t_1;
	elseif (y <= -1.8e-47)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (y <= -2.8e-123)
		tmp = t_2;
	elseif (y <= -1.02e-210)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (y <= 2.2e+143)
		tmp = t_2;
	elseif (y <= 3.8e+173)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (y <= 8.8e+210)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (x * ((y0 * y2) - (y * i)));
	t_2 = k * (y0 * ((z * b) - (y2 * y5)));
	tmp = 0.0;
	if (y <= -8.8e+209)
		tmp = t_1;
	elseif (y <= -1.8e-47)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (y <= -2.8e-123)
		tmp = t_2;
	elseif (y <= -1.02e-210)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (y <= 2.2e+143)
		tmp = t_2;
	elseif (y <= 3.8e+173)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (y <= 8.8e+210)
		tmp = k * (y1 * (y2 * y4));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(y0 * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.8e+209], t$95$1, If[LessEqual[y, -1.8e-47], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.8e-123], t$95$2, If[LessEqual[y, -1.02e-210], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+143], t$95$2, If[LessEqual[y, 3.8e+173], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.8e+210], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -8.7999999999999995e209 or 8.79999999999999948e210 < y

   1. Initial program 31.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 44.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 44.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 44.9%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 44.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 44.9%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 44.9%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 44.9%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 44.9%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 44.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in x around inf 55.8%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2 - i \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 55.8%

         \[\leadsto c \cdot \left(x \cdot \left(\color{blue}{y2 \cdot y0} - i \cdot y\right)\right) \]

   7. Simplified 55.8%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0 - i \cdot y\right)\right)} \]

   if -8.7999999999999995e209 < y < -1.79999999999999995e-47

   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. Taylor expanded in j around inf 47.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 47.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 47.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 47.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 47.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 47.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y3 around inf 41.1%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if -1.79999999999999995e-47 < y < -2.7999999999999999e-123 or -1.02000000000000002e-210 < y < 2.20000000000000014e143

   1. Initial program 38.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in k around inf 38.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 38.1%

         \[\leadsto k \cdot \color{blue}{\left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. +-commutative 38.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      3. mul-1-neg 38.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      4. unsub-neg 38.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-commutative 38.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. mul-1-neg 38.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + \left(-\color{blue}{\left(-z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      7. remove-double-neg 38.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + \color{blue}{z \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Simplified 38.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in y0 around inf 39.1%

      \[\leadsto \color{blue}{k \cdot \left(y0 \cdot \left(-1 \cdot \left(y2 \cdot y5\right) + b \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 39.1%

         \[\leadsto k \cdot \left(y0 \cdot \color{blue}{\left(b \cdot z + -1 \cdot \left(y2 \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 39.1%

         \[\leadsto k \cdot \left(y0 \cdot \left(b \cdot z + \color{blue}{\left(-y2 \cdot y5\right)}\right)\right) \]

      3. sub-neg 39.1%

         \[\leadsto k \cdot \left(y0 \cdot \color{blue}{\left(b \cdot z - y2 \cdot y5\right)}\right) \]

      4. *-commutative 39.1%

         \[\leadsto k \cdot \left(y0 \cdot \left(b \cdot z - \color{blue}{y5 \cdot y2}\right)\right) \]

   7. Simplified 39.1%

      \[\leadsto \color{blue}{k \cdot \left(y0 \cdot \left(b \cdot z - y5 \cdot y2\right)\right)} \]

   if -2.7999999999999999e-123 < y < -1.02000000000000002e-210

   1. Initial program 39.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 50.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 50.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 50.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 50.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 50.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 50.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in x around inf 51.0%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   if 2.20000000000000014e143 < y < 3.80000000000000011e173

   1. Initial program 12.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 12.5%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 12.5%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 25.0%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 25.0%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 25.0%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 87.7%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 87.7%

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 87.7%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   if 3.80000000000000011e173 < y < 8.79999999999999948e210

   1. Initial program 14.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 14.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 14.7%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 14.7%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 14.7%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 14.7%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in y4 around -inf 28.9%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   6. Taylor expanded in k around inf 57.5%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+209}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-47}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-123}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-210}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+143}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+173}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+210}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \end{array} \]

Alternative 27: 29.5% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ t_2 := k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+208}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-48}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -1.22 \cdot 10^{-122}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-211}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+176}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+196}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(y2 \cdot y5 - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* x (- (* y0 y2) (* y i)))))
        (t_2 (* k (* y0 (- (* z b) (* y2 y5))))))
   (if (<= y -4.5e+208)
     t_1
     (if (<= y -5.4e-48)
       (* j (* y3 (- (* y0 y5) (* y1 y4))))
       (if (<= y -1.22e-122)
         t_2
         (if (<= y -7e-211)
           (* j (* x (- (* i y1) (* b y0))))
           (if (<= y 1.2e+144)
             t_2
             (if (<= y 2.6e+176)
               (* a (* y5 (- (* t y2) (* y y3))))
               (if (<= y 8.5e+196)
                 (* (* t a) (- (* y2 y5) (* z 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 = c * (x * ((y0 * y2) - (y * i)));
	double t_2 = k * (y0 * ((z * b) - (y2 * y5)));
	double tmp;
	if (y <= -4.5e+208) {
		tmp = t_1;
	} else if (y <= -5.4e-48) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (y <= -1.22e-122) {
		tmp = t_2;
	} else if (y <= -7e-211) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y <= 1.2e+144) {
		tmp = t_2;
	} else if (y <= 2.6e+176) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y <= 8.5e+196) {
		tmp = (t * a) * ((y2 * y5) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (x * ((y0 * y2) - (y * i)))
    t_2 = k * (y0 * ((z * b) - (y2 * y5)))
    if (y <= (-4.5d+208)) then
        tmp = t_1
    else if (y <= (-5.4d-48)) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (y <= (-1.22d-122)) then
        tmp = t_2
    else if (y <= (-7d-211)) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (y <= 1.2d+144) then
        tmp = t_2
    else if (y <= 2.6d+176) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (y <= 8.5d+196) then
        tmp = (t * a) * ((y2 * y5) - (z * 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 = c * (x * ((y0 * y2) - (y * i)));
	double t_2 = k * (y0 * ((z * b) - (y2 * y5)));
	double tmp;
	if (y <= -4.5e+208) {
		tmp = t_1;
	} else if (y <= -5.4e-48) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (y <= -1.22e-122) {
		tmp = t_2;
	} else if (y <= -7e-211) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y <= 1.2e+144) {
		tmp = t_2;
	} else if (y <= 2.6e+176) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y <= 8.5e+196) {
		tmp = (t * a) * ((y2 * y5) - (z * 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 = c * (x * ((y0 * y2) - (y * i)))
	t_2 = k * (y0 * ((z * b) - (y2 * y5)))
	tmp = 0
	if y <= -4.5e+208:
		tmp = t_1
	elif y <= -5.4e-48:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif y <= -1.22e-122:
		tmp = t_2
	elif y <= -7e-211:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif y <= 1.2e+144:
		tmp = t_2
	elif y <= 2.6e+176:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif y <= 8.5e+196:
		tmp = (t * a) * ((y2 * y5) - (z * 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(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))))
	t_2 = Float64(k * Float64(y0 * Float64(Float64(z * b) - Float64(y2 * y5))))
	tmp = 0.0
	if (y <= -4.5e+208)
		tmp = t_1;
	elseif (y <= -5.4e-48)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (y <= -1.22e-122)
		tmp = t_2;
	elseif (y <= -7e-211)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (y <= 1.2e+144)
		tmp = t_2;
	elseif (y <= 2.6e+176)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (y <= 8.5e+196)
		tmp = Float64(Float64(t * a) * Float64(Float64(y2 * y5) - Float64(z * 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 = c * (x * ((y0 * y2) - (y * i)));
	t_2 = k * (y0 * ((z * b) - (y2 * y5)));
	tmp = 0.0;
	if (y <= -4.5e+208)
		tmp = t_1;
	elseif (y <= -5.4e-48)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (y <= -1.22e-122)
		tmp = t_2;
	elseif (y <= -7e-211)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (y <= 1.2e+144)
		tmp = t_2;
	elseif (y <= 2.6e+176)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (y <= 8.5e+196)
		tmp = (t * a) * ((y2 * y5) - (z * 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[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(y0 * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e+208], t$95$1, If[LessEqual[y, -5.4e-48], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.22e-122], t$95$2, If[LessEqual[y, -7e-211], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+144], t$95$2, If[LessEqual[y, 2.6e+176], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e+196], N[(N[(t * a), $MachinePrecision] * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -4.50000000000000015e208 or 8.50000000000000041e196 < y

   1. Initial program 31.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 44.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 44.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 44.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 44.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 44.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 44.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 44.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 44.1%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 44.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in x around inf 54.2%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2 - i \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 54.2%

         \[\leadsto c \cdot \left(x \cdot \left(\color{blue}{y2 \cdot y0} - i \cdot y\right)\right) \]

   7. Simplified 54.2%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0 - i \cdot y\right)\right)} \]

   if -4.50000000000000015e208 < y < -5.40000000000000023e-48

   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. Taylor expanded in j around inf 47.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 47.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 47.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 47.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 47.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 47.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y3 around inf 41.1%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if -5.40000000000000023e-48 < y < -1.22000000000000003e-122 or -7e-211 < y < 1.2e144

   1. Initial program 38.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in k around inf 38.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 38.1%

         \[\leadsto k \cdot \color{blue}{\left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. +-commutative 38.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      3. mul-1-neg 38.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      4. unsub-neg 38.1%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-commutative 38.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. mul-1-neg 38.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + \left(-\color{blue}{\left(-z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      7. remove-double-neg 38.1%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + \color{blue}{z \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Simplified 38.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in y0 around inf 39.1%

      \[\leadsto \color{blue}{k \cdot \left(y0 \cdot \left(-1 \cdot \left(y2 \cdot y5\right) + b \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 39.1%

         \[\leadsto k \cdot \left(y0 \cdot \color{blue}{\left(b \cdot z + -1 \cdot \left(y2 \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 39.1%

         \[\leadsto k \cdot \left(y0 \cdot \left(b \cdot z + \color{blue}{\left(-y2 \cdot y5\right)}\right)\right) \]

      3. sub-neg 39.1%

         \[\leadsto k \cdot \left(y0 \cdot \color{blue}{\left(b \cdot z - y2 \cdot y5\right)}\right) \]

      4. *-commutative 39.1%

         \[\leadsto k \cdot \left(y0 \cdot \left(b \cdot z - \color{blue}{y5 \cdot y2}\right)\right) \]

   7. Simplified 39.1%

      \[\leadsto \color{blue}{k \cdot \left(y0 \cdot \left(b \cdot z - y5 \cdot y2\right)\right)} \]

   if -1.22000000000000003e-122 < y < -7e-211

   1. Initial program 39.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 50.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 50.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 50.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 50.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 50.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 50.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in x around inf 51.0%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   if 1.2e144 < y < 2.59999999999999991e176

   1. Initial program 12.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 12.5%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 12.5%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 25.0%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 25.0%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 25.0%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 87.7%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 87.7%

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 87.7%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   if 2.59999999999999991e176 < y < 8.50000000000000041e196

   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. Taylor expanded in t around inf 25.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in a around inf 52.3%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) - -1 \cdot \left(y2 \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 76.1%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \left(-1 \cdot \left(b \cdot z\right) - -1 \cdot \left(y2 \cdot y5\right)\right)} \]

      2. cancel-sign-sub-inv 76.1%

         \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right) + \left(--1\right) \cdot \left(y2 \cdot y5\right)\right)} \]

      3. metadata-eval 76.1%

         \[\leadsto \left(a \cdot t\right) \cdot \left(-1 \cdot \left(b \cdot z\right) + \color{blue}{1} \cdot \left(y2 \cdot y5\right)\right) \]

      4. *-lft-identity 76.1%

         \[\leadsto \left(a \cdot t\right) \cdot \left(-1 \cdot \left(b \cdot z\right) + \color{blue}{y2 \cdot y5}\right) \]

      5. +-commutative 76.1%

         \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)} \]

      6. mul-1-neg 76.1%

         \[\leadsto \left(a \cdot t\right) \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right) \]

      7. unsub-neg 76.1%

         \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)} \]

      8. *-commutative 76.1%

         \[\leadsto \left(a \cdot t\right) \cdot \left(\color{blue}{y5 \cdot y2} - b \cdot z\right) \]

   5. Simplified 76.1%

      \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \left(y5 \cdot y2 - b \cdot z\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+208}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-48}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -1.22 \cdot 10^{-122}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-211}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+144}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+176}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+196}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(y2 \cdot y5 - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \end{array} \]

Alternative 28: 29.3% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{if}\;b \leq -6.6 \cdot 10^{+66}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-70}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-187}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-77}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+140}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+220}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y3 (- (* y0 y5) (* y1 y4))))))
   (if (<= b -6.6e+66)
     (* j (* x (- (* i y1) (* b y0))))
     (if (<= b -9.5e-70)
       (* c (* t (- (* z i) (* y2 y4))))
       (if (<= b -1.4e-187)
         (* (* y c) (- (* y3 y4) (* x i)))
         (if (<= b -4.4e-275)
           t_1
           (if (<= b 3e-77)
             (* c (* y4 (- (* y y3) (* t y2))))
             (if (<= b 1.05e+140)
               (* c (* x (- (* y0 y2) (* y i))))
               (if (<= b 1.85e+220)
                 t_1
                 (* (* t b) (- (* j y4) (* z 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 t_1 = j * (y3 * ((y0 * y5) - (y1 * y4)));
	double tmp;
	if (b <= -6.6e+66) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (b <= -9.5e-70) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (b <= -1.4e-187) {
		tmp = (y * c) * ((y3 * y4) - (x * i));
	} else if (b <= -4.4e-275) {
		tmp = t_1;
	} else if (b <= 3e-77) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (b <= 1.05e+140) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (b <= 1.85e+220) {
		tmp = t_1;
	} else {
		tmp = (t * b) * ((j * y4) - (z * 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) :: t_1
    real(8) :: tmp
    t_1 = j * (y3 * ((y0 * y5) - (y1 * y4)))
    if (b <= (-6.6d+66)) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (b <= (-9.5d-70)) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (b <= (-1.4d-187)) then
        tmp = (y * c) * ((y3 * y4) - (x * i))
    else if (b <= (-4.4d-275)) then
        tmp = t_1
    else if (b <= 3d-77) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (b <= 1.05d+140) then
        tmp = c * (x * ((y0 * y2) - (y * i)))
    else if (b <= 1.85d+220) then
        tmp = t_1
    else
        tmp = (t * b) * ((j * y4) - (z * 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 t_1 = j * (y3 * ((y0 * y5) - (y1 * y4)));
	double tmp;
	if (b <= -6.6e+66) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (b <= -9.5e-70) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (b <= -1.4e-187) {
		tmp = (y * c) * ((y3 * y4) - (x * i));
	} else if (b <= -4.4e-275) {
		tmp = t_1;
	} else if (b <= 3e-77) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (b <= 1.05e+140) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (b <= 1.85e+220) {
		tmp = t_1;
	} else {
		tmp = (t * b) * ((j * y4) - (z * a));
	}
	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)))
	tmp = 0
	if b <= -6.6e+66:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif b <= -9.5e-70:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif b <= -1.4e-187:
		tmp = (y * c) * ((y3 * y4) - (x * i))
	elif b <= -4.4e-275:
		tmp = t_1
	elif b <= 3e-77:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif b <= 1.05e+140:
		tmp = c * (x * ((y0 * y2) - (y * i)))
	elif b <= 1.85e+220:
		tmp = t_1
	else:
		tmp = (t * b) * ((j * y4) - (z * a))
	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(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))))
	tmp = 0.0
	if (b <= -6.6e+66)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (b <= -9.5e-70)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (b <= -1.4e-187)
		tmp = Float64(Float64(y * c) * Float64(Float64(y3 * y4) - Float64(x * i)));
	elseif (b <= -4.4e-275)
		tmp = t_1;
	elseif (b <= 3e-77)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (b <= 1.05e+140)
		tmp = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))));
	elseif (b <= 1.85e+220)
		tmp = t_1;
	else
		tmp = Float64(Float64(t * b) * Float64(Float64(j * y4) - Float64(z * 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)
	t_1 = j * (y3 * ((y0 * y5) - (y1 * y4)));
	tmp = 0.0;
	if (b <= -6.6e+66)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (b <= -9.5e-70)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (b <= -1.4e-187)
		tmp = (y * c) * ((y3 * y4) - (x * i));
	elseif (b <= -4.4e-275)
		tmp = t_1;
	elseif (b <= 3e-77)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (b <= 1.05e+140)
		tmp = c * (x * ((y0 * y2) - (y * i)));
	elseif (b <= 1.85e+220)
		tmp = t_1;
	else
		tmp = (t * b) * ((j * y4) - (z * a));
	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[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.6e+66], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -9.5e-70], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.4e-187], N[(N[(y * c), $MachinePrecision] * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.4e-275], t$95$1, If[LessEqual[b, 3e-77], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e+140], N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.85e+220], t$95$1, N[(N[(t * b), $MachinePrecision] * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -6.6000000000000003e66

   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. Taylor expanded in j around inf 46.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 46.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 46.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 46.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 46.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 46.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in x around inf 46.4%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   if -6.6000000000000003e66 < b < -9.4999999999999994e-70

   1. Initial program 37.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in t around inf 43.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in c around inf 38.1%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   if -9.4999999999999994e-70 < b < -1.4e-187

   1. Initial program 43.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 47.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 47.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 47.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 47.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 47.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 47.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 47.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 47.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 47.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y around -inf 51.4%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 51.4%

         \[\leadsto \color{blue}{\left(c \cdot y\right) \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)} \]

      2. +-commutative 51.4%

         \[\leadsto \left(c \cdot y\right) \cdot \color{blue}{\left(y3 \cdot y4 + -1 \cdot \left(i \cdot x\right)\right)} \]

      3. mul-1-neg 51.4%

         \[\leadsto \left(c \cdot y\right) \cdot \left(y3 \cdot y4 + \color{blue}{\left(-i \cdot x\right)}\right) \]

      4. unsub-neg 51.4%

         \[\leadsto \left(c \cdot y\right) \cdot \color{blue}{\left(y3 \cdot y4 - i \cdot x\right)} \]

      5. *-commutative 51.4%

         \[\leadsto \left(c \cdot y\right) \cdot \left(y3 \cdot y4 - \color{blue}{x \cdot i}\right) \]

   7. Simplified 51.4%

      \[\leadsto \color{blue}{\left(c \cdot y\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)} \]

   if -1.4e-187 < b < -4.39999999999999977e-275 or 1.0500000000000001e140 < b < 1.85e220

   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. Taylor expanded in j around inf 56.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 56.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 56.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 56.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 56.7%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 56.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y3 around inf 54.6%

      \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)} \]

   if -4.39999999999999977e-275 < b < 3.00000000000000016e-77

   1. Initial program 42.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 39.0%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 39.0%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 44.3%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 44.3%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 44.3%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in c around inf 45.8%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 45.8%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. neg-mul-1 45.8%

         \[\leadsto \color{blue}{\left(-c\right)} \cdot \left(y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. *-commutative 45.8%

         \[\leadsto \left(-c\right) \cdot \left(y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 45.8%

      \[\leadsto \color{blue}{\left(-c\right) \cdot \left(y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   if 3.00000000000000016e-77 < b < 1.0500000000000001e140

   1. Initial program 33.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 44.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 44.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 44.9%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 44.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 44.9%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 44.9%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 44.9%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 44.9%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 44.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in x around inf 48.2%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2 - i \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 48.2%

         \[\leadsto c \cdot \left(x \cdot \left(\color{blue}{y2 \cdot y0} - i \cdot y\right)\right) \]

   7. Simplified 48.2%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0 - i \cdot y\right)\right)} \]

   if 1.85e220 < b

   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. Taylor expanded in t around inf 38.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in b around inf 61.4%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 66.8%

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      2. *-commutative 66.8%

         \[\leadsto \color{blue}{\left(t \cdot b\right)} \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right) \]

      3. +-commutative 66.8%

         \[\leadsto \left(t \cdot b\right) \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)} \]

      4. mul-1-neg 66.8%

         \[\leadsto \left(t \cdot b\right) \cdot \left(j \cdot y4 + \color{blue}{\left(-a \cdot z\right)}\right) \]

      5. unsub-neg 66.8%

         \[\leadsto \left(t \cdot b\right) \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)} \]

      6. *-commutative 66.8%

         \[\leadsto \left(t \cdot b\right) \cdot \left(j \cdot y4 - \color{blue}{z \cdot a}\right) \]

   5. Simplified 66.8%

      \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+66}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-70}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-187}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{-275}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-77}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+140}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+220}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)\\ \end{array} \]

Alternative 29: 29.5% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ t_2 := i \cdot y1 - b \cdot y0\\ t_3 := k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{if}\;y5 \leq -6.3 \cdot 10^{-103}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y5 \leq -3.1 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq -6 \cdot 10^{-288}:\\ \;\;\;\;\left(x \cdot j\right) \cdot t_2\\ \mathbf{elif}\;y5 \leq 5 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq 1.95 \cdot 10^{-81}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 0.205:\\ \;\;\;\;j \cdot \left(x \cdot t_2\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* y c) (- (* y3 y4) (* x i))))
        (t_2 (- (* i y1) (* b y0)))
        (t_3 (* k (* y0 (- (* z b) (* y2 y5))))))
   (if (<= y5 -6.3e-103)
     t_3
     (if (<= y5 -3.1e-248)
       t_1
       (if (<= y5 -6e-288)
         (* (* x j) t_2)
         (if (<= y5 5e-205)
           t_1
           (if (<= y5 1.95e-81)
             (* c (* t (- (* z i) (* y2 y4))))
             (if (<= y5 0.205) (* j (* x t_2)) t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * c) * ((y3 * y4) - (x * i));
	double t_2 = (i * y1) - (b * y0);
	double t_3 = k * (y0 * ((z * b) - (y2 * y5)));
	double tmp;
	if (y5 <= -6.3e-103) {
		tmp = t_3;
	} else if (y5 <= -3.1e-248) {
		tmp = t_1;
	} else if (y5 <= -6e-288) {
		tmp = (x * j) * t_2;
	} else if (y5 <= 5e-205) {
		tmp = t_1;
	} else if (y5 <= 1.95e-81) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (y5 <= 0.205) {
		tmp = j * (x * t_2);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y * c) * ((y3 * y4) - (x * i))
    t_2 = (i * y1) - (b * y0)
    t_3 = k * (y0 * ((z * b) - (y2 * y5)))
    if (y5 <= (-6.3d-103)) then
        tmp = t_3
    else if (y5 <= (-3.1d-248)) then
        tmp = t_1
    else if (y5 <= (-6d-288)) then
        tmp = (x * j) * t_2
    else if (y5 <= 5d-205) then
        tmp = t_1
    else if (y5 <= 1.95d-81) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (y5 <= 0.205d0) then
        tmp = j * (x * t_2)
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * c) * ((y3 * y4) - (x * i));
	double t_2 = (i * y1) - (b * y0);
	double t_3 = k * (y0 * ((z * b) - (y2 * y5)));
	double tmp;
	if (y5 <= -6.3e-103) {
		tmp = t_3;
	} else if (y5 <= -3.1e-248) {
		tmp = t_1;
	} else if (y5 <= -6e-288) {
		tmp = (x * j) * t_2;
	} else if (y5 <= 5e-205) {
		tmp = t_1;
	} else if (y5 <= 1.95e-81) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (y5 <= 0.205) {
		tmp = j * (x * t_2);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y * c) * ((y3 * y4) - (x * i))
	t_2 = (i * y1) - (b * y0)
	t_3 = k * (y0 * ((z * b) - (y2 * y5)))
	tmp = 0
	if y5 <= -6.3e-103:
		tmp = t_3
	elif y5 <= -3.1e-248:
		tmp = t_1
	elif y5 <= -6e-288:
		tmp = (x * j) * t_2
	elif y5 <= 5e-205:
		tmp = t_1
	elif y5 <= 1.95e-81:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif y5 <= 0.205:
		tmp = j * (x * t_2)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * c) * Float64(Float64(y3 * y4) - Float64(x * i)))
	t_2 = Float64(Float64(i * y1) - Float64(b * y0))
	t_3 = Float64(k * Float64(y0 * Float64(Float64(z * b) - Float64(y2 * y5))))
	tmp = 0.0
	if (y5 <= -6.3e-103)
		tmp = t_3;
	elseif (y5 <= -3.1e-248)
		tmp = t_1;
	elseif (y5 <= -6e-288)
		tmp = Float64(Float64(x * j) * t_2);
	elseif (y5 <= 5e-205)
		tmp = t_1;
	elseif (y5 <= 1.95e-81)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (y5 <= 0.205)
		tmp = Float64(j * Float64(x * t_2));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y * c) * ((y3 * y4) - (x * i));
	t_2 = (i * y1) - (b * y0);
	t_3 = k * (y0 * ((z * b) - (y2 * y5)));
	tmp = 0.0;
	if (y5 <= -6.3e-103)
		tmp = t_3;
	elseif (y5 <= -3.1e-248)
		tmp = t_1;
	elseif (y5 <= -6e-288)
		tmp = (x * j) * t_2;
	elseif (y5 <= 5e-205)
		tmp = t_1;
	elseif (y5 <= 1.95e-81)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (y5 <= 0.205)
		tmp = j * (x * t_2);
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y * c), $MachinePrecision] * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(k * N[(y0 * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -6.3e-103], t$95$3, If[LessEqual[y5, -3.1e-248], t$95$1, If[LessEqual[y5, -6e-288], N[(N[(x * j), $MachinePrecision] * t$95$2), $MachinePrecision], If[LessEqual[y5, 5e-205], t$95$1, If[LessEqual[y5, 1.95e-81], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 0.205], N[(j * N[(x * t$95$2), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -6.3000000000000004e-103 or 0.204999999999999988 < y5

   1. Initial program 29.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in k around inf 36.8%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 36.8%

         \[\leadsto k \cdot \color{blue}{\left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. +-commutative 36.8%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      3. mul-1-neg 36.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      4. unsub-neg 36.8%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      5. *-commutative 36.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) + \left(--1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right) \]

      6. mul-1-neg 36.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + \left(-\color{blue}{\left(-z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right)\right) \]

      7. remove-double-neg 36.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + \color{blue}{z \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Simplified 36.8%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in y0 around inf 42.8%

      \[\leadsto \color{blue}{k \cdot \left(y0 \cdot \left(-1 \cdot \left(y2 \cdot y5\right) + b \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 42.8%

         \[\leadsto k \cdot \left(y0 \cdot \color{blue}{\left(b \cdot z + -1 \cdot \left(y2 \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 42.8%

         \[\leadsto k \cdot \left(y0 \cdot \left(b \cdot z + \color{blue}{\left(-y2 \cdot y5\right)}\right)\right) \]

      3. sub-neg 42.8%

         \[\leadsto k \cdot \left(y0 \cdot \color{blue}{\left(b \cdot z - y2 \cdot y5\right)}\right) \]

      4. *-commutative 42.8%

         \[\leadsto k \cdot \left(y0 \cdot \left(b \cdot z - \color{blue}{y5 \cdot y2}\right)\right) \]

   7. Simplified 42.8%

      \[\leadsto \color{blue}{k \cdot \left(y0 \cdot \left(b \cdot z - y5 \cdot y2\right)\right)} \]

   if -6.3000000000000004e-103 < y5 < -3.1000000000000002e-248 or -5.99999999999999998e-288 < y5 < 5.00000000000000001e-205

   1. Initial program 39.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 34.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 34.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 34.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 34.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 34.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 34.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 34.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 34.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 34.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y around -inf 47.7%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 46.0%

         \[\leadsto \color{blue}{\left(c \cdot y\right) \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)} \]

      2. +-commutative 46.0%

         \[\leadsto \left(c \cdot y\right) \cdot \color{blue}{\left(y3 \cdot y4 + -1 \cdot \left(i \cdot x\right)\right)} \]

      3. mul-1-neg 46.0%

         \[\leadsto \left(c \cdot y\right) \cdot \left(y3 \cdot y4 + \color{blue}{\left(-i \cdot x\right)}\right) \]

      4. unsub-neg 46.0%

         \[\leadsto \left(c \cdot y\right) \cdot \color{blue}{\left(y3 \cdot y4 - i \cdot x\right)} \]

      5. *-commutative 46.0%

         \[\leadsto \left(c \cdot y\right) \cdot \left(y3 \cdot y4 - \color{blue}{x \cdot i}\right) \]

   7. Simplified 46.0%

      \[\leadsto \color{blue}{\left(c \cdot y\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)} \]

   if -3.1000000000000002e-248 < y5 < -5.99999999999999998e-288

   1. Initial program 32.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 55.5%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 55.5%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 55.5%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 55.5%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 55.5%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 55.5%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in x around inf 48.4%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 55.7%

         \[\leadsto \color{blue}{\left(j \cdot x\right) \cdot \left(i \cdot y1 - b \cdot y0\right)} \]

   7. Simplified 55.7%

      \[\leadsto \color{blue}{\left(j \cdot x\right) \cdot \left(i \cdot y1 - b \cdot y0\right)} \]

   if 5.00000000000000001e-205 < y5 < 1.94999999999999992e-81

   1. Initial program 46.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in t around inf 46.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in c around inf 43.1%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]

   if 1.94999999999999992e-81 < y5 < 0.204999999999999988

   1. Initial program 45.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 55.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 55.0%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 55.0%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 55.0%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 55.0%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 55.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in x around inf 55.3%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -6.3 \cdot 10^{-103}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -3.1 \cdot 10^{-248}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{elif}\;y5 \leq -6 \cdot 10^{-288}:\\ \;\;\;\;\left(x \cdot j\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\\ \mathbf{elif}\;y5 \leq 5 \cdot 10^{-205}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{elif}\;y5 \leq 1.95 \cdot 10^{-81}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 0.205:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \end{array} \]

Alternative 30: 21.5% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -6.6 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -4.8 \cdot 10^{-289}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(k \cdot \left(-z\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 2.4 \cdot 10^{-205}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 6.2 \cdot 10^{-74}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 3.3 \cdot 10^{+14}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 1.2 \cdot 10^{+31}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -6.6e-12)
   (* x (* c (* y0 y2)))
   (if (<= y0 -4.8e-289)
     (* y1 (* i (* k (- z))))
     (if (<= y0 2.4e-205)
       (* a (* y5 (* t y2)))
       (if (<= y0 6.2e-74)
         (* k (* y1 (* y2 y4)))
         (if (<= y0 3.3e+14)
           (* j (* y0 (* y3 y5)))
           (if (<= y0 1.2e+31)
             (* c (* y0 (* z (- y3))))
             (* j (* y5 (* y0 y3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -6.6e-12) {
		tmp = x * (c * (y0 * y2));
	} else if (y0 <= -4.8e-289) {
		tmp = y1 * (i * (k * -z));
	} else if (y0 <= 2.4e-205) {
		tmp = a * (y5 * (t * y2));
	} else if (y0 <= 6.2e-74) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y0 <= 3.3e+14) {
		tmp = j * (y0 * (y3 * y5));
	} else if (y0 <= 1.2e+31) {
		tmp = c * (y0 * (z * -y3));
	} else {
		tmp = j * (y5 * (y0 * y3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y0 <= (-6.6d-12)) then
        tmp = x * (c * (y0 * y2))
    else if (y0 <= (-4.8d-289)) then
        tmp = y1 * (i * (k * -z))
    else if (y0 <= 2.4d-205) then
        tmp = a * (y5 * (t * y2))
    else if (y0 <= 6.2d-74) then
        tmp = k * (y1 * (y2 * y4))
    else if (y0 <= 3.3d+14) then
        tmp = j * (y0 * (y3 * y5))
    else if (y0 <= 1.2d+31) then
        tmp = c * (y0 * (z * -y3))
    else
        tmp = j * (y5 * (y0 * y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -6.6e-12) {
		tmp = x * (c * (y0 * y2));
	} else if (y0 <= -4.8e-289) {
		tmp = y1 * (i * (k * -z));
	} else if (y0 <= 2.4e-205) {
		tmp = a * (y5 * (t * y2));
	} else if (y0 <= 6.2e-74) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y0 <= 3.3e+14) {
		tmp = j * (y0 * (y3 * y5));
	} else if (y0 <= 1.2e+31) {
		tmp = c * (y0 * (z * -y3));
	} else {
		tmp = j * (y5 * (y0 * y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y0 <= -6.6e-12:
		tmp = x * (c * (y0 * y2))
	elif y0 <= -4.8e-289:
		tmp = y1 * (i * (k * -z))
	elif y0 <= 2.4e-205:
		tmp = a * (y5 * (t * y2))
	elif y0 <= 6.2e-74:
		tmp = k * (y1 * (y2 * y4))
	elif y0 <= 3.3e+14:
		tmp = j * (y0 * (y3 * y5))
	elif y0 <= 1.2e+31:
		tmp = c * (y0 * (z * -y3))
	else:
		tmp = j * (y5 * (y0 * y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -6.6e-12)
		tmp = Float64(x * Float64(c * Float64(y0 * y2)));
	elseif (y0 <= -4.8e-289)
		tmp = Float64(y1 * Float64(i * Float64(k * Float64(-z))));
	elseif (y0 <= 2.4e-205)
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	elseif (y0 <= 6.2e-74)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (y0 <= 3.3e+14)
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	elseif (y0 <= 1.2e+31)
		tmp = Float64(c * Float64(y0 * Float64(z * Float64(-y3))));
	else
		tmp = Float64(j * Float64(y5 * Float64(y0 * y3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y0 <= -6.6e-12)
		tmp = x * (c * (y0 * y2));
	elseif (y0 <= -4.8e-289)
		tmp = y1 * (i * (k * -z));
	elseif (y0 <= 2.4e-205)
		tmp = a * (y5 * (t * y2));
	elseif (y0 <= 6.2e-74)
		tmp = k * (y1 * (y2 * y4));
	elseif (y0 <= 3.3e+14)
		tmp = j * (y0 * (y3 * y5));
	elseif (y0 <= 1.2e+31)
		tmp = c * (y0 * (z * -y3));
	else
		tmp = j * (y5 * (y0 * y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -6.6e-12], N[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -4.8e-289], N[(y1 * N[(i * N[(k * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.4e-205], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 6.2e-74], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 3.3e+14], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.2e+31], N[(c * N[(y0 * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y5 * N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y0 < -6.6000000000000001e-12

   1. Initial program 31.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 33.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 33.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 33.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 33.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 33.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 33.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 33.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 33.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 33.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 60.7%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 60.7%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 60.7%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]

      3. *-commutative 60.7%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot y5}\right)\right) \]

      4. *-commutative 60.7%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(\color{blue}{y2 \cdot k} - j \cdot y3\right) \cdot y5\right)\right) \]

      5. *-commutative 60.7%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(y2 \cdot k - \color{blue}{y3 \cdot j}\right) \cdot y5\right)\right) \]

      6. unsub-neg 60.7%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right)} \]

      7. *-commutative 60.7%

         \[\leadsto y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right) \]

      8. *-commutative 60.7%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(\color{blue}{k \cdot y2} - y3 \cdot j\right) \cdot y5\right) \]

      9. *-commutative 60.7%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) \cdot y5\right) \]

      10. *-commutative 60.7%

          \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \color{blue}{y5 \cdot \left(k \cdot y2 - j \cdot y3\right)}\right) \]

   7. Simplified 60.7%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in x around inf 36.2%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 36.2%

         \[\leadsto \color{blue}{\left(c \cdot x\right) \cdot \left(y0 \cdot y2\right)} \]

      2. *-commutative 36.2%

         \[\leadsto \color{blue}{\left(x \cdot c\right)} \cdot \left(y0 \cdot y2\right) \]

      3. associate-*l* 43.3%

         \[\leadsto \color{blue}{x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)} \]

   10. Simplified 43.3%

       \[\leadsto \color{blue}{x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)} \]

   if -6.6000000000000001e-12 < y0 < -4.79999999999999988e-289

   1. Initial program 33.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 42.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 42.0%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 42.0%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 42.0%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 42.0%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in z around -inf 33.6%

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]

   6. Taylor expanded in a around 0 27.2%

      \[\leadsto y1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(k \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 27.2%

         \[\leadsto y1 \cdot \color{blue}{\left(\left(-1 \cdot i\right) \cdot \left(k \cdot z\right)\right)} \]

      2. neg-mul-1 27.2%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-i\right)} \cdot \left(k \cdot z\right)\right) \]

      3. *-commutative 27.2%

         \[\leadsto y1 \cdot \left(\left(-i\right) \cdot \color{blue}{\left(z \cdot k\right)}\right) \]

   8. Simplified 27.2%

      \[\leadsto y1 \cdot \color{blue}{\left(\left(-i\right) \cdot \left(z \cdot k\right)\right)} \]

   if -4.79999999999999988e-289 < y0 < 2.4000000000000002e-205

   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. Taylor expanded in y5 around inf 38.8%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 38.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 38.7%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 38.7%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 38.7%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 35.6%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 35.6%

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 35.6%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in t around inf 31.7%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
   9. Step-by-step derivation

      1. *-commutative 31.7%

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y2 \cdot t\right)}\right) \]

   10. Simplified 31.7%

       \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y2 \cdot t\right)}\right) \]

   if 2.4000000000000002e-205 < y0 < 6.2000000000000003e-74

   1. Initial program 37.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 38.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 38.0%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 38.0%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 38.0%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 38.0%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in y4 around -inf 30.9%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   6. Taylor expanded in k around inf 30.9%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]

   if 6.2000000000000003e-74 < y0 < 3.3e14

   1. Initial program 52.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 24.2%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 24.2%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 28.7%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 28.7%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 28.7%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 29.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 29.8%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

      2. neg-mul-1 29.8%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   7. Simplified 29.8%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in k around 0 34.4%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]

   if 3.3e14 < y0 < 1.19999999999999991e31

   1. Initial program 42.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 58.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 58.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 58.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 58.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 58.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 58.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 58.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 58.3%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 58.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 72.6%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 72.6%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 72.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]

      3. *-commutative 72.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot y5}\right)\right) \]

      4. *-commutative 72.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(\color{blue}{y2 \cdot k} - j \cdot y3\right) \cdot y5\right)\right) \]

      5. *-commutative 72.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(y2 \cdot k - \color{blue}{y3 \cdot j}\right) \cdot y5\right)\right) \]

      6. unsub-neg 72.6%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right)} \]

      7. *-commutative 72.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right) \]

      8. *-commutative 72.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(\color{blue}{k \cdot y2} - y3 \cdot j\right) \cdot y5\right) \]

      9. *-commutative 72.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) \cdot y5\right) \]

      10. *-commutative 72.6%

          \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \color{blue}{y5 \cdot \left(k \cdot y2 - j \cdot y3\right)}\right) \]

   7. Simplified 72.6%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in z around inf 58.0%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 58.0%

         \[\leadsto \color{blue}{-c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]

   10. Simplified 58.0%

       \[\leadsto \color{blue}{-c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]

   if 1.19999999999999991e31 < y0

   1. Initial program 32.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 31.9%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 31.9%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 34.8%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 34.8%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 34.8%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 39.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 39.3%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

      2. neg-mul-1 39.3%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   7. Simplified 39.3%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in k around 0 40.8%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 42.2%

         \[\leadsto j \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot y5\right)} \]

      2. *-commutative 42.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(y3 \cdot y0\right)} \cdot y5\right) \]

   10. Simplified 42.2%

       \[\leadsto \color{blue}{j \cdot \left(\left(y3 \cdot y0\right) \cdot y5\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -6.6 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -4.8 \cdot 10^{-289}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(k \cdot \left(-z\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 2.4 \cdot 10^{-205}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 6.2 \cdot 10^{-74}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 3.3 \cdot 10^{+14}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 1.2 \cdot 10^{+31}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \end{array} \]

Alternative 31: 26.2% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;c \leq -2.5 \cdot 10^{+243}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -2.7 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.6 \cdot 10^{-98}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 3.45 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y5 (- (* t y2) (* y y3))))))
   (if (<= c -2.5e+243)
     (* x (* c (* y0 y2)))
     (if (<= c -2.7e-14)
       t_1
       (if (<= c -2.6e-98)
         (* a (* y3 (* z y1)))
         (if (<= c 3.45e+49) t_1 (* y0 (* c (* z (- y3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (c <= -2.5e+243) {
		tmp = x * (c * (y0 * y2));
	} else if (c <= -2.7e-14) {
		tmp = t_1;
	} else if (c <= -2.6e-98) {
		tmp = a * (y3 * (z * y1));
	} else if (c <= 3.45e+49) {
		tmp = t_1;
	} else {
		tmp = y0 * (c * (z * -y3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y5 * ((t * y2) - (y * y3)))
    if (c <= (-2.5d+243)) then
        tmp = x * (c * (y0 * y2))
    else if (c <= (-2.7d-14)) then
        tmp = t_1
    else if (c <= (-2.6d-98)) then
        tmp = a * (y3 * (z * y1))
    else if (c <= 3.45d+49) then
        tmp = t_1
    else
        tmp = y0 * (c * (z * -y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (c <= -2.5e+243) {
		tmp = x * (c * (y0 * y2));
	} else if (c <= -2.7e-14) {
		tmp = t_1;
	} else if (c <= -2.6e-98) {
		tmp = a * (y3 * (z * y1));
	} else if (c <= 3.45e+49) {
		tmp = t_1;
	} else {
		tmp = y0 * (c * (z * -y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y5 * ((t * y2) - (y * y3)))
	tmp = 0
	if c <= -2.5e+243:
		tmp = x * (c * (y0 * y2))
	elif c <= -2.7e-14:
		tmp = t_1
	elif c <= -2.6e-98:
		tmp = a * (y3 * (z * y1))
	elif c <= 3.45e+49:
		tmp = t_1
	else:
		tmp = y0 * (c * (z * -y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	tmp = 0.0
	if (c <= -2.5e+243)
		tmp = Float64(x * Float64(c * Float64(y0 * y2)));
	elseif (c <= -2.7e-14)
		tmp = t_1;
	elseif (c <= -2.6e-98)
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	elseif (c <= 3.45e+49)
		tmp = t_1;
	else
		tmp = Float64(y0 * Float64(c * Float64(z * Float64(-y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y5 * ((t * y2) - (y * y3)));
	tmp = 0.0;
	if (c <= -2.5e+243)
		tmp = x * (c * (y0 * y2));
	elseif (c <= -2.7e-14)
		tmp = t_1;
	elseif (c <= -2.6e-98)
		tmp = a * (y3 * (z * y1));
	elseif (c <= 3.45e+49)
		tmp = t_1;
	else
		tmp = y0 * (c * (z * -y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.5e+243], N[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.7e-14], t$95$1, If[LessEqual[c, -2.6e-98], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.45e+49], t$95$1, N[(y0 * N[(c * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.50000000000000019e243

   1. Initial program 15.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 39.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 39.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 39.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 39.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 39.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 39.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 39.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 39.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 39.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 31.4%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 31.4%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 31.4%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]

      3. *-commutative 31.4%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot y5}\right)\right) \]

      4. *-commutative 31.4%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(\color{blue}{y2 \cdot k} - j \cdot y3\right) \cdot y5\right)\right) \]

      5. *-commutative 31.4%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(y2 \cdot k - \color{blue}{y3 \cdot j}\right) \cdot y5\right)\right) \]

      6. unsub-neg 31.4%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right)} \]

      7. *-commutative 31.4%

         \[\leadsto y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right) \]

      8. *-commutative 31.4%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(\color{blue}{k \cdot y2} - y3 \cdot j\right) \cdot y5\right) \]

      9. *-commutative 31.4%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) \cdot y5\right) \]

      10. *-commutative 31.4%

          \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \color{blue}{y5 \cdot \left(k \cdot y2 - j \cdot y3\right)}\right) \]

   7. Simplified 31.4%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in x around inf 47.6%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 47.7%

         \[\leadsto \color{blue}{\left(c \cdot x\right) \cdot \left(y0 \cdot y2\right)} \]

      2. *-commutative 47.7%

         \[\leadsto \color{blue}{\left(x \cdot c\right)} \cdot \left(y0 \cdot y2\right) \]

      3. associate-*l* 62.1%

         \[\leadsto \color{blue}{x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)} \]

   10. Simplified 62.1%

       \[\leadsto \color{blue}{x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)} \]

   if -2.50000000000000019e243 < c < -2.6999999999999999e-14 or -2.60000000000000013e-98 < c < 3.4500000000000002e49

   1. Initial program 38.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 40.9%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 40.9%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 42.5%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 42.5%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 42.5%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 33.5%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 33.5%

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 33.5%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   if -2.6999999999999999e-14 < c < -2.60000000000000013e-98

   1. Initial program 28.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 43.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 43.8%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 43.8%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 43.8%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 43.8%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in y3 around -inf 15.3%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 15.3%

         \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

      2. *-commutative 15.3%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \left(\color{blue}{z \cdot a} - j \cdot y4\right) \]

   7. Simplified 15.3%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(z \cdot a - j \cdot y4\right)} \]

   8. Taylor expanded in z around inf 29.6%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. expm1-log1p-u 0.9%

         \[\leadsto a \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y1 \cdot \left(y3 \cdot z\right)\right)\right)} \]

      2. expm1-udef 0.8%

         \[\leadsto a \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(y1 \cdot \left(y3 \cdot z\right)\right)} - 1\right)} \]

      3. *-commutative 0.8%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(y3 \cdot z\right) \cdot y1}\right)} - 1\right) \]

   10. Applied egg-rr 0.8%

       \[\leadsto a \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\left(y3 \cdot z\right) \cdot y1\right)} - 1\right)} \]
   11. Step-by-step derivation

       1. expm1-def 0.9%

          \[\leadsto a \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(y3 \cdot z\right) \cdot y1\right)\right)} \]

       2. expm1-log1p 29.6%

          \[\leadsto a \cdot \color{blue}{\left(\left(y3 \cdot z\right) \cdot y1\right)} \]

       3. associate-*l* 29.7%

          \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(z \cdot y1\right)\right)} \]

   12. Simplified 29.7%

       \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(z \cdot y1\right)\right)} \]

   if 3.4500000000000002e49 < c

   1. Initial program 30.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 50.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 50.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 50.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 50.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 50.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 50.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 50.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 50.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 50.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 54.7%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 54.7%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 54.7%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]

      3. *-commutative 54.7%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot y5}\right)\right) \]

      4. *-commutative 54.7%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(\color{blue}{y2 \cdot k} - j \cdot y3\right) \cdot y5\right)\right) \]

      5. *-commutative 54.7%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(y2 \cdot k - \color{blue}{y3 \cdot j}\right) \cdot y5\right)\right) \]

      6. unsub-neg 54.7%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right)} \]

      7. *-commutative 54.7%

         \[\leadsto y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right) \]

      8. *-commutative 54.7%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(\color{blue}{k \cdot y2} - y3 \cdot j\right) \cdot y5\right) \]

      9. *-commutative 54.7%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) \cdot y5\right) \]

      10. *-commutative 54.7%

          \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \color{blue}{y5 \cdot \left(k \cdot y2 - j \cdot y3\right)}\right) \]

   7. Simplified 54.7%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in z around inf 35.0%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 35.0%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]

      2. *-commutative 35.0%

         \[\leadsto \left(-1 \cdot c\right) \cdot \color{blue}{\left(\left(y3 \cdot z\right) \cdot y0\right)} \]

      3. associate-*r* 40.3%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot c\right) \cdot \left(y3 \cdot z\right)\right) \cdot y0} \]

      4. associate-*r* 40.3%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot \left(y3 \cdot z\right)\right)\right)} \cdot y0 \]

      5. mul-1-neg 40.3%

         \[\leadsto \color{blue}{\left(-c \cdot \left(y3 \cdot z\right)\right)} \cdot y0 \]

      6. distribute-rgt-neg-in 40.3%

         \[\leadsto \color{blue}{\left(c \cdot \left(-y3 \cdot z\right)\right)} \cdot y0 \]

      7. distribute-rgt-neg-in 40.3%

         \[\leadsto \left(c \cdot \color{blue}{\left(y3 \cdot \left(-z\right)\right)}\right) \cdot y0 \]

   10. Simplified 40.3%

       \[\leadsto \color{blue}{\left(c \cdot \left(y3 \cdot \left(-z\right)\right)\right) \cdot y0} \]
3. Recombined 4 regimes into one program.

4. Final simplification 36.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{+243}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -2.7 \cdot 10^{-14}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;c \leq -2.6 \cdot 10^{-98}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 3.45 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \end{array} \]

Alternative 32: 21.1% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{if}\;y0 \leq -1.85 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -2.7 \cdot 10^{-306}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq 2.6 \cdot 10^{-190}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 4.8 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* y1 (* y2 y4)))))
   (if (<= y0 -1.85e-13)
     (* x (* c (* y0 y2)))
     (if (<= y0 -2.7e-306)
       t_1
       (if (<= y0 2.6e-190)
         (* a (* y5 (* t y2)))
         (if (<= y0 4.8e-66) t_1 (* j (* y0 (* y3 y5)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y1 * (y2 * y4));
	double tmp;
	if (y0 <= -1.85e-13) {
		tmp = x * (c * (y0 * y2));
	} else if (y0 <= -2.7e-306) {
		tmp = t_1;
	} else if (y0 <= 2.6e-190) {
		tmp = a * (y5 * (t * y2));
	} else if (y0 <= 4.8e-66) {
		tmp = t_1;
	} else {
		tmp = j * (y0 * (y3 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (y1 * (y2 * y4))
    if (y0 <= (-1.85d-13)) then
        tmp = x * (c * (y0 * y2))
    else if (y0 <= (-2.7d-306)) then
        tmp = t_1
    else if (y0 <= 2.6d-190) then
        tmp = a * (y5 * (t * y2))
    else if (y0 <= 4.8d-66) then
        tmp = t_1
    else
        tmp = j * (y0 * (y3 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y1 * (y2 * y4));
	double tmp;
	if (y0 <= -1.85e-13) {
		tmp = x * (c * (y0 * y2));
	} else if (y0 <= -2.7e-306) {
		tmp = t_1;
	} else if (y0 <= 2.6e-190) {
		tmp = a * (y5 * (t * y2));
	} else if (y0 <= 4.8e-66) {
		tmp = t_1;
	} else {
		tmp = j * (y0 * (y3 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (y1 * (y2 * y4))
	tmp = 0
	if y0 <= -1.85e-13:
		tmp = x * (c * (y0 * y2))
	elif y0 <= -2.7e-306:
		tmp = t_1
	elif y0 <= 2.6e-190:
		tmp = a * (y5 * (t * y2))
	elif y0 <= 4.8e-66:
		tmp = t_1
	else:
		tmp = j * (y0 * (y3 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(y1 * Float64(y2 * y4)))
	tmp = 0.0
	if (y0 <= -1.85e-13)
		tmp = Float64(x * Float64(c * Float64(y0 * y2)));
	elseif (y0 <= -2.7e-306)
		tmp = t_1;
	elseif (y0 <= 2.6e-190)
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	elseif (y0 <= 4.8e-66)
		tmp = t_1;
	else
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (y1 * (y2 * y4));
	tmp = 0.0;
	if (y0 <= -1.85e-13)
		tmp = x * (c * (y0 * y2));
	elseif (y0 <= -2.7e-306)
		tmp = t_1;
	elseif (y0 <= 2.6e-190)
		tmp = a * (y5 * (t * y2));
	elseif (y0 <= 4.8e-66)
		tmp = t_1;
	else
		tmp = j * (y0 * (y3 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -1.85e-13], N[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -2.7e-306], t$95$1, If[LessEqual[y0, 2.6e-190], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.8e-66], t$95$1, N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y0 < -1.84999999999999994e-13

   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. Taylor expanded in c around inf 32.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 32.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 32.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 32.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 32.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 32.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 32.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 32.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 32.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 59.5%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 59.5%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 59.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]

      3. *-commutative 59.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot y5}\right)\right) \]

      4. *-commutative 59.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(\color{blue}{y2 \cdot k} - j \cdot y3\right) \cdot y5\right)\right) \]

      5. *-commutative 59.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(y2 \cdot k - \color{blue}{y3 \cdot j}\right) \cdot y5\right)\right) \]

      6. unsub-neg 59.5%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right)} \]

      7. *-commutative 59.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right) \]

      8. *-commutative 59.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(\color{blue}{k \cdot y2} - y3 \cdot j\right) \cdot y5\right) \]

      9. *-commutative 59.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) \cdot y5\right) \]

      10. *-commutative 59.5%

          \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \color{blue}{y5 \cdot \left(k \cdot y2 - j \cdot y3\right)}\right) \]

   7. Simplified 59.5%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in x around inf 35.5%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 35.6%

         \[\leadsto \color{blue}{\left(c \cdot x\right) \cdot \left(y0 \cdot y2\right)} \]

      2. *-commutative 35.6%

         \[\leadsto \color{blue}{\left(x \cdot c\right)} \cdot \left(y0 \cdot y2\right) \]

      3. associate-*l* 42.5%

         \[\leadsto \color{blue}{x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)} \]

   10. Simplified 42.5%

       \[\leadsto \color{blue}{x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)} \]

   if -1.84999999999999994e-13 < y0 < -2.70000000000000009e-306 or 2.5999999999999998e-190 < y0 < 4.80000000000000052e-66

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 40.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 40.6%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 40.6%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 40.6%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 40.6%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in y4 around -inf 30.6%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   6. Taylor expanded in k around inf 26.4%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]

   if -2.70000000000000009e-306 < y0 < 2.5999999999999998e-190

   1. Initial program 40.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 36.5%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 36.5%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 36.5%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 36.5%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 36.5%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 33.2%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 33.2%

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 33.2%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in t around inf 29.2%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
   9. Step-by-step derivation

      1. *-commutative 29.2%

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y2 \cdot t\right)}\right) \]

   10. Simplified 29.2%

       \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y2 \cdot t\right)}\right) \]

   if 4.80000000000000052e-66 < y0

   1. Initial program 36.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 28.8%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 28.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 30.9%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 30.9%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 30.9%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 36.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 36.6%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

      2. neg-mul-1 36.6%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   7. Simplified 36.6%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in k around 0 37.7%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.85 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -2.7 \cdot 10^{-306}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 2.6 \cdot 10^{-190}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 4.8 \cdot 10^{-66}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \]

Alternative 33: 21.1% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -5.3 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -1.95 \cdot 10^{-306}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.65 \cdot 10^{-193}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 1.1 \cdot 10^{-64}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -5.3e-14)
   (* x (* c (* y0 y2)))
   (if (<= y0 -1.95e-306)
     (* y1 (* k (* y2 y4)))
     (if (<= y0 1.65e-193)
       (* a (* y5 (* t y2)))
       (if (<= y0 1.1e-64) (* k (* y1 (* y2 y4))) (* j (* y0 (* y3 y5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -5.3e-14) {
		tmp = x * (c * (y0 * y2));
	} else if (y0 <= -1.95e-306) {
		tmp = y1 * (k * (y2 * y4));
	} else if (y0 <= 1.65e-193) {
		tmp = a * (y5 * (t * y2));
	} else if (y0 <= 1.1e-64) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = j * (y0 * (y3 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y0 <= (-5.3d-14)) then
        tmp = x * (c * (y0 * y2))
    else if (y0 <= (-1.95d-306)) then
        tmp = y1 * (k * (y2 * y4))
    else if (y0 <= 1.65d-193) then
        tmp = a * (y5 * (t * y2))
    else if (y0 <= 1.1d-64) then
        tmp = k * (y1 * (y2 * y4))
    else
        tmp = j * (y0 * (y3 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -5.3e-14) {
		tmp = x * (c * (y0 * y2));
	} else if (y0 <= -1.95e-306) {
		tmp = y1 * (k * (y2 * y4));
	} else if (y0 <= 1.65e-193) {
		tmp = a * (y5 * (t * y2));
	} else if (y0 <= 1.1e-64) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = j * (y0 * (y3 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y0 <= -5.3e-14:
		tmp = x * (c * (y0 * y2))
	elif y0 <= -1.95e-306:
		tmp = y1 * (k * (y2 * y4))
	elif y0 <= 1.65e-193:
		tmp = a * (y5 * (t * y2))
	elif y0 <= 1.1e-64:
		tmp = k * (y1 * (y2 * y4))
	else:
		tmp = j * (y0 * (y3 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -5.3e-14)
		tmp = Float64(x * Float64(c * Float64(y0 * y2)));
	elseif (y0 <= -1.95e-306)
		tmp = Float64(y1 * Float64(k * Float64(y2 * y4)));
	elseif (y0 <= 1.65e-193)
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	elseif (y0 <= 1.1e-64)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	else
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y0 <= -5.3e-14)
		tmp = x * (c * (y0 * y2));
	elseif (y0 <= -1.95e-306)
		tmp = y1 * (k * (y2 * y4));
	elseif (y0 <= 1.65e-193)
		tmp = a * (y5 * (t * y2));
	elseif (y0 <= 1.1e-64)
		tmp = k * (y1 * (y2 * y4));
	else
		tmp = j * (y0 * (y3 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -5.3e-14], N[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.95e-306], N[(y1 * N[(k * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.65e-193], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.1e-64], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y0 < -5.3000000000000001e-14

   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. Taylor expanded in c around inf 32.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 32.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 32.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 32.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 32.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 32.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 32.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 32.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 32.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 59.5%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 59.5%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 59.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]

      3. *-commutative 59.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot y5}\right)\right) \]

      4. *-commutative 59.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(\color{blue}{y2 \cdot k} - j \cdot y3\right) \cdot y5\right)\right) \]

      5. *-commutative 59.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(y2 \cdot k - \color{blue}{y3 \cdot j}\right) \cdot y5\right)\right) \]

      6. unsub-neg 59.5%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right)} \]

      7. *-commutative 59.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right) \]

      8. *-commutative 59.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(\color{blue}{k \cdot y2} - y3 \cdot j\right) \cdot y5\right) \]

      9. *-commutative 59.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) \cdot y5\right) \]

      10. *-commutative 59.5%

          \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \color{blue}{y5 \cdot \left(k \cdot y2 - j \cdot y3\right)}\right) \]

   7. Simplified 59.5%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in x around inf 35.5%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 35.6%

         \[\leadsto \color{blue}{\left(c \cdot x\right) \cdot \left(y0 \cdot y2\right)} \]

      2. *-commutative 35.6%

         \[\leadsto \color{blue}{\left(x \cdot c\right)} \cdot \left(y0 \cdot y2\right) \]

      3. associate-*l* 42.5%

         \[\leadsto \color{blue}{x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)} \]

   10. Simplified 42.5%

       \[\leadsto \color{blue}{x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)} \]

   if -5.3000000000000001e-14 < y0 < -1.95e-306

   1. Initial program 33.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 41.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 41.6%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 41.6%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 41.6%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 41.6%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in y4 around -inf 28.9%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   6. Taylor expanded in k around inf 24.0%

      \[\leadsto y1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y4\right)\right)} \]

   if -1.95e-306 < y0 < 1.6499999999999999e-193

   1. Initial program 40.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 36.5%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 36.5%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 36.5%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 36.5%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 36.5%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 33.2%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 33.2%

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 33.2%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in t around inf 29.2%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
   9. Step-by-step derivation

      1. *-commutative 29.2%

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y2 \cdot t\right)}\right) \]

   10. Simplified 29.2%

       \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y2 \cdot t\right)}\right) \]

   if 1.6499999999999999e-193 < y0 < 1.1e-64

   1. Initial program 37.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 37.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 37.9%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 37.9%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 37.9%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 37.9%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in y4 around -inf 34.8%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   6. Taylor expanded in k around inf 39.2%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]

   if 1.1e-64 < y0

   1. Initial program 36.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 28.8%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 28.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 30.9%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 30.9%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 30.9%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 36.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 36.6%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

      2. neg-mul-1 36.6%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   7. Simplified 36.6%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in k around 0 37.7%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 34.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -5.3 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -1.95 \cdot 10^{-306}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.65 \cdot 10^{-193}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 1.1 \cdot 10^{-64}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \]

Alternative 34: 20.8% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -3.1 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -2.9 \cdot 10^{-292}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(i \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 4.9 \cdot 10^{-178}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 1.3 \cdot 10^{-64}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -3.1e-12)
   (* x (* c (* y0 y2)))
   (if (<= y0 -2.9e-292)
     (* y1 (* z (* i (- k))))
     (if (<= y0 4.9e-178)
       (* a (* y5 (* t y2)))
       (if (<= y0 1.3e-64) (* k (* y1 (* y2 y4))) (* j (* y0 (* y3 y5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -3.1e-12) {
		tmp = x * (c * (y0 * y2));
	} else if (y0 <= -2.9e-292) {
		tmp = y1 * (z * (i * -k));
	} else if (y0 <= 4.9e-178) {
		tmp = a * (y5 * (t * y2));
	} else if (y0 <= 1.3e-64) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = j * (y0 * (y3 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y0 <= (-3.1d-12)) then
        tmp = x * (c * (y0 * y2))
    else if (y0 <= (-2.9d-292)) then
        tmp = y1 * (z * (i * -k))
    else if (y0 <= 4.9d-178) then
        tmp = a * (y5 * (t * y2))
    else if (y0 <= 1.3d-64) then
        tmp = k * (y1 * (y2 * y4))
    else
        tmp = j * (y0 * (y3 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -3.1e-12) {
		tmp = x * (c * (y0 * y2));
	} else if (y0 <= -2.9e-292) {
		tmp = y1 * (z * (i * -k));
	} else if (y0 <= 4.9e-178) {
		tmp = a * (y5 * (t * y2));
	} else if (y0 <= 1.3e-64) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = j * (y0 * (y3 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y0 <= -3.1e-12:
		tmp = x * (c * (y0 * y2))
	elif y0 <= -2.9e-292:
		tmp = y1 * (z * (i * -k))
	elif y0 <= 4.9e-178:
		tmp = a * (y5 * (t * y2))
	elif y0 <= 1.3e-64:
		tmp = k * (y1 * (y2 * y4))
	else:
		tmp = j * (y0 * (y3 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -3.1e-12)
		tmp = Float64(x * Float64(c * Float64(y0 * y2)));
	elseif (y0 <= -2.9e-292)
		tmp = Float64(y1 * Float64(z * Float64(i * Float64(-k))));
	elseif (y0 <= 4.9e-178)
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	elseif (y0 <= 1.3e-64)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	else
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y0 <= -3.1e-12)
		tmp = x * (c * (y0 * y2));
	elseif (y0 <= -2.9e-292)
		tmp = y1 * (z * (i * -k));
	elseif (y0 <= 4.9e-178)
		tmp = a * (y5 * (t * y2));
	elseif (y0 <= 1.3e-64)
		tmp = k * (y1 * (y2 * y4));
	else
		tmp = j * (y0 * (y3 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -3.1e-12], N[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -2.9e-292], N[(y1 * N[(z * N[(i * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.9e-178], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.3e-64], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y0 < -3.1000000000000001e-12

   1. Initial program 31.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 33.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 33.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 33.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 33.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 33.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 33.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 33.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 33.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 33.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 60.7%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 60.7%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 60.7%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]

      3. *-commutative 60.7%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot y5}\right)\right) \]

      4. *-commutative 60.7%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(\color{blue}{y2 \cdot k} - j \cdot y3\right) \cdot y5\right)\right) \]

      5. *-commutative 60.7%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(y2 \cdot k - \color{blue}{y3 \cdot j}\right) \cdot y5\right)\right) \]

      6. unsub-neg 60.7%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right)} \]

      7. *-commutative 60.7%

         \[\leadsto y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right) \]

      8. *-commutative 60.7%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(\color{blue}{k \cdot y2} - y3 \cdot j\right) \cdot y5\right) \]

      9. *-commutative 60.7%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) \cdot y5\right) \]

      10. *-commutative 60.7%

          \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \color{blue}{y5 \cdot \left(k \cdot y2 - j \cdot y3\right)}\right) \]

   7. Simplified 60.7%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in x around inf 36.2%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 36.2%

         \[\leadsto \color{blue}{\left(c \cdot x\right) \cdot \left(y0 \cdot y2\right)} \]

      2. *-commutative 36.2%

         \[\leadsto \color{blue}{\left(x \cdot c\right)} \cdot \left(y0 \cdot y2\right) \]

      3. associate-*l* 43.3%

         \[\leadsto \color{blue}{x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)} \]

   10. Simplified 43.3%

       \[\leadsto \color{blue}{x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)} \]

   if -3.1000000000000001e-12 < y0 < -2.89999999999999993e-292

   1. Initial program 33.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 42.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 42.0%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 42.0%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 42.0%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 42.0%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in z around -inf 33.6%

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]

   6. Taylor expanded in a around 0 25.6%

      \[\leadsto y1 \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(i \cdot k\right)\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg 25.6%

         \[\leadsto y1 \cdot \left(z \cdot \color{blue}{\left(-i \cdot k\right)}\right) \]

      2. distribute-lft-neg-out 25.6%

         \[\leadsto y1 \cdot \left(z \cdot \color{blue}{\left(\left(-i\right) \cdot k\right)}\right) \]

      3. *-commutative 25.6%

         \[\leadsto y1 \cdot \left(z \cdot \color{blue}{\left(k \cdot \left(-i\right)\right)}\right) \]

   8. Simplified 25.6%

      \[\leadsto y1 \cdot \left(z \cdot \color{blue}{\left(k \cdot \left(-i\right)\right)}\right) \]

   if -2.89999999999999993e-292 < y0 < 4.9000000000000002e-178

   1. Initial program 38.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 38.4%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 38.4%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 38.4%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 38.4%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 38.4%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 32.1%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 32.1%

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 32.1%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in t around inf 28.7%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
   9. Step-by-step derivation

      1. *-commutative 28.7%

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y2 \cdot t\right)}\right) \]

   10. Simplified 28.7%

       \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y2 \cdot t\right)}\right) \]

   if 4.9000000000000002e-178 < y0 < 1.3e-64

   1. Initial program 37.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 37.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 37.9%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 37.9%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 37.9%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 37.9%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in y4 around -inf 34.8%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   6. Taylor expanded in k around inf 39.2%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]

   if 1.3e-64 < y0

   1. Initial program 36.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 28.8%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 28.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 30.9%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 30.9%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 30.9%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 36.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 36.6%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

      2. neg-mul-1 36.6%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   7. Simplified 36.6%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in k around 0 37.7%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -3.1 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -2.9 \cdot 10^{-292}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(i \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 4.9 \cdot 10^{-178}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 1.3 \cdot 10^{-64}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \]

Alternative 35: 19.8% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -1.4 \cdot 10^{+49}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y0 \leq -1.4 \cdot 10^{-293}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(k \cdot \left(-z\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 1.55 \cdot 10^{-190}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 7.6 \cdot 10^{-66}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -1.4e+49)
   (* y0 (* k (* y2 (- y5))))
   (if (<= y0 -1.4e-293)
     (* y1 (* i (* k (- z))))
     (if (<= y0 1.55e-190)
       (* a (* y5 (* t y2)))
       (if (<= y0 7.6e-66) (* k (* y1 (* y2 y4))) (* j (* y0 (* y3 y5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -1.4e+49) {
		tmp = y0 * (k * (y2 * -y5));
	} else if (y0 <= -1.4e-293) {
		tmp = y1 * (i * (k * -z));
	} else if (y0 <= 1.55e-190) {
		tmp = a * (y5 * (t * y2));
	} else if (y0 <= 7.6e-66) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = j * (y0 * (y3 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y0 <= (-1.4d+49)) then
        tmp = y0 * (k * (y2 * -y5))
    else if (y0 <= (-1.4d-293)) then
        tmp = y1 * (i * (k * -z))
    else if (y0 <= 1.55d-190) then
        tmp = a * (y5 * (t * y2))
    else if (y0 <= 7.6d-66) then
        tmp = k * (y1 * (y2 * y4))
    else
        tmp = j * (y0 * (y3 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -1.4e+49) {
		tmp = y0 * (k * (y2 * -y5));
	} else if (y0 <= -1.4e-293) {
		tmp = y1 * (i * (k * -z));
	} else if (y0 <= 1.55e-190) {
		tmp = a * (y5 * (t * y2));
	} else if (y0 <= 7.6e-66) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = j * (y0 * (y3 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y0 <= -1.4e+49:
		tmp = y0 * (k * (y2 * -y5))
	elif y0 <= -1.4e-293:
		tmp = y1 * (i * (k * -z))
	elif y0 <= 1.55e-190:
		tmp = a * (y5 * (t * y2))
	elif y0 <= 7.6e-66:
		tmp = k * (y1 * (y2 * y4))
	else:
		tmp = j * (y0 * (y3 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -1.4e+49)
		tmp = Float64(y0 * Float64(k * Float64(y2 * Float64(-y5))));
	elseif (y0 <= -1.4e-293)
		tmp = Float64(y1 * Float64(i * Float64(k * Float64(-z))));
	elseif (y0 <= 1.55e-190)
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	elseif (y0 <= 7.6e-66)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	else
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y0 <= -1.4e+49)
		tmp = y0 * (k * (y2 * -y5));
	elseif (y0 <= -1.4e-293)
		tmp = y1 * (i * (k * -z));
	elseif (y0 <= 1.55e-190)
		tmp = a * (y5 * (t * y2));
	elseif (y0 <= 7.6e-66)
		tmp = k * (y1 * (y2 * y4));
	else
		tmp = j * (y0 * (y3 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -1.4e+49], N[(y0 * N[(k * N[(y2 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.4e-293], N[(y1 * N[(i * N[(k * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.55e-190], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 7.6e-66], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y0 < -1.3999999999999999e49

   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. Taylor expanded in y5 around inf 38.7%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 38.7%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 38.7%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 38.7%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 38.7%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 56.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 56.8%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

      2. neg-mul-1 56.8%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   7. Simplified 56.8%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in k around inf 50.3%

      \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y5\right)\right)} \]

   if -1.3999999999999999e49 < y0 < -1.40000000000000013e-293

   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. Taylor expanded in y1 around -inf 42.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 42.2%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 42.2%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 42.2%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 42.2%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in z around -inf 33.2%

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]

   6. Taylor expanded in a around 0 26.0%

      \[\leadsto y1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(k \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 26.0%

         \[\leadsto y1 \cdot \color{blue}{\left(\left(-1 \cdot i\right) \cdot \left(k \cdot z\right)\right)} \]

      2. neg-mul-1 26.0%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-i\right)} \cdot \left(k \cdot z\right)\right) \]

      3. *-commutative 26.0%

         \[\leadsto y1 \cdot \left(\left(-i\right) \cdot \color{blue}{\left(z \cdot k\right)}\right) \]

   8. Simplified 26.0%

      \[\leadsto y1 \cdot \color{blue}{\left(\left(-i\right) \cdot \left(z \cdot k\right)\right)} \]

   if -1.40000000000000013e-293 < y0 < 1.54999999999999997e-190

   1. Initial program 38.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 38.4%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 38.4%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 38.4%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 38.4%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 38.4%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 32.1%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 32.1%

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 32.1%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in t around inf 28.7%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
   9. Step-by-step derivation

      1. *-commutative 28.7%

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y2 \cdot t\right)}\right) \]

   10. Simplified 28.7%

       \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y2 \cdot t\right)}\right) \]

   if 1.54999999999999997e-190 < y0 < 7.5999999999999995e-66

   1. Initial program 37.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 37.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 37.9%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 37.9%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 37.9%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 37.9%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in y4 around -inf 34.8%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   6. Taylor expanded in k around inf 39.2%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]

   if 7.5999999999999995e-66 < y0

   1. Initial program 36.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 28.8%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 28.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 30.9%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 30.9%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 30.9%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 36.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 36.6%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

      2. neg-mul-1 36.6%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   7. Simplified 36.6%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in k around 0 37.7%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 36.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.4 \cdot 10^{+49}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y0 \leq -1.4 \cdot 10^{-293}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(k \cdot \left(-z\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 1.55 \cdot 10^{-190}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 7.6 \cdot 10^{-66}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \]

Alternative 36: 20.3% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -1.9 \cdot 10^{+33}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y0 \leq -2.2 \cdot 10^{-288}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(k \cdot \left(-z\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 8 \cdot 10^{-186}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 1.2 \cdot 10^{-64}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -1.9e+33)
   (* k (* y0 (* y2 (- y5))))
   (if (<= y0 -2.2e-288)
     (* y1 (* i (* k (- z))))
     (if (<= y0 8e-186)
       (* a (* y5 (* t y2)))
       (if (<= y0 1.2e-64) (* k (* y1 (* y2 y4))) (* j (* y0 (* y3 y5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -1.9e+33) {
		tmp = k * (y0 * (y2 * -y5));
	} else if (y0 <= -2.2e-288) {
		tmp = y1 * (i * (k * -z));
	} else if (y0 <= 8e-186) {
		tmp = a * (y5 * (t * y2));
	} else if (y0 <= 1.2e-64) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = j * (y0 * (y3 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y0 <= (-1.9d+33)) then
        tmp = k * (y0 * (y2 * -y5))
    else if (y0 <= (-2.2d-288)) then
        tmp = y1 * (i * (k * -z))
    else if (y0 <= 8d-186) then
        tmp = a * (y5 * (t * y2))
    else if (y0 <= 1.2d-64) then
        tmp = k * (y1 * (y2 * y4))
    else
        tmp = j * (y0 * (y3 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -1.9e+33) {
		tmp = k * (y0 * (y2 * -y5));
	} else if (y0 <= -2.2e-288) {
		tmp = y1 * (i * (k * -z));
	} else if (y0 <= 8e-186) {
		tmp = a * (y5 * (t * y2));
	} else if (y0 <= 1.2e-64) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = j * (y0 * (y3 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y0 <= -1.9e+33:
		tmp = k * (y0 * (y2 * -y5))
	elif y0 <= -2.2e-288:
		tmp = y1 * (i * (k * -z))
	elif y0 <= 8e-186:
		tmp = a * (y5 * (t * y2))
	elif y0 <= 1.2e-64:
		tmp = k * (y1 * (y2 * y4))
	else:
		tmp = j * (y0 * (y3 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -1.9e+33)
		tmp = Float64(k * Float64(y0 * Float64(y2 * Float64(-y5))));
	elseif (y0 <= -2.2e-288)
		tmp = Float64(y1 * Float64(i * Float64(k * Float64(-z))));
	elseif (y0 <= 8e-186)
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	elseif (y0 <= 1.2e-64)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	else
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y0 <= -1.9e+33)
		tmp = k * (y0 * (y2 * -y5));
	elseif (y0 <= -2.2e-288)
		tmp = y1 * (i * (k * -z));
	elseif (y0 <= 8e-186)
		tmp = a * (y5 * (t * y2));
	elseif (y0 <= 1.2e-64)
		tmp = k * (y1 * (y2 * y4));
	else
		tmp = j * (y0 * (y3 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -1.9e+33], N[(k * N[(y0 * N[(y2 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -2.2e-288], N[(y1 * N[(i * N[(k * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 8e-186], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.2e-64], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y0 < -1.90000000000000001e33

   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. Taylor expanded in y5 around inf 38.7%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 38.7%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 38.7%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 38.7%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 38.7%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 56.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 56.8%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

      2. neg-mul-1 56.8%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   7. Simplified 56.8%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in k around inf 50.3%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 50.3%

         \[\leadsto \color{blue}{-k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)} \]

      2. *-commutative 50.3%

         \[\leadsto -\color{blue}{\left(y0 \cdot \left(y2 \cdot y5\right)\right) \cdot k} \]

      3. distribute-rgt-neg-in 50.3%

         \[\leadsto \color{blue}{\left(y0 \cdot \left(y2 \cdot y5\right)\right) \cdot \left(-k\right)} \]

   10. Simplified 50.3%

       \[\leadsto \color{blue}{\left(y0 \cdot \left(y2 \cdot y5\right)\right) \cdot \left(-k\right)} \]

   if -1.90000000000000001e33 < y0 < -2.2000000000000002e-288

   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. Taylor expanded in y1 around -inf 42.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 42.2%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 42.2%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 42.2%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 42.2%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in z around -inf 33.2%

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]

   6. Taylor expanded in a around 0 26.0%

      \[\leadsto y1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(k \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 26.0%

         \[\leadsto y1 \cdot \color{blue}{\left(\left(-1 \cdot i\right) \cdot \left(k \cdot z\right)\right)} \]

      2. neg-mul-1 26.0%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-i\right)} \cdot \left(k \cdot z\right)\right) \]

      3. *-commutative 26.0%

         \[\leadsto y1 \cdot \left(\left(-i\right) \cdot \color{blue}{\left(z \cdot k\right)}\right) \]

   8. Simplified 26.0%

      \[\leadsto y1 \cdot \color{blue}{\left(\left(-i\right) \cdot \left(z \cdot k\right)\right)} \]

   if -2.2000000000000002e-288 < y0 < 7.9999999999999993e-186

   1. Initial program 38.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 38.4%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 38.4%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 38.4%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 38.4%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 38.4%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 32.1%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 32.1%

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 32.1%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in t around inf 28.7%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
   9. Step-by-step derivation

      1. *-commutative 28.7%

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y2 \cdot t\right)}\right) \]

   10. Simplified 28.7%

       \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y2 \cdot t\right)}\right) \]

   if 7.9999999999999993e-186 < y0 < 1.19999999999999999e-64

   1. Initial program 37.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 37.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 37.9%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 37.9%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 37.9%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 37.9%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in y4 around -inf 34.8%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   6. Taylor expanded in k around inf 39.2%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]

   if 1.19999999999999999e-64 < y0

   1. Initial program 36.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 28.8%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 28.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 30.9%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 30.9%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 30.9%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 36.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 36.6%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

      2. neg-mul-1 36.6%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   7. Simplified 36.6%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in k around 0 37.7%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 36.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.9 \cdot 10^{+33}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y0 \leq -2.2 \cdot 10^{-288}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(k \cdot \left(-z\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 8 \cdot 10^{-186}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 1.2 \cdot 10^{-64}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \]

Alternative 37: 21.9% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -4.2 \cdot 10^{+107} \lor \neg \left(y2 \leq 1.8 \cdot 10^{-8}\right):\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y2 -4.2e+107) (not (<= y2 1.8e-8)))
   (* a (* y5 (* t y2)))
   (* a (* y3 (* z y1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y2 <= -4.2e+107) || !(y2 <= 1.8e-8)) {
		tmp = a * (y5 * (t * y2));
	} else {
		tmp = a * (y3 * (z * y1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y2 <= (-4.2d+107)) .or. (.not. (y2 <= 1.8d-8))) then
        tmp = a * (y5 * (t * y2))
    else
        tmp = a * (y3 * (z * y1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y2 <= -4.2e+107) || !(y2 <= 1.8e-8)) {
		tmp = a * (y5 * (t * y2));
	} else {
		tmp = a * (y3 * (z * y1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y2 <= -4.2e+107) or not (y2 <= 1.8e-8):
		tmp = a * (y5 * (t * y2))
	else:
		tmp = a * (y3 * (z * y1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y2 <= -4.2e+107) || !(y2 <= 1.8e-8))
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	else
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y2 <= -4.2e+107) || ~((y2 <= 1.8e-8)))
		tmp = a * (y5 * (t * y2));
	else
		tmp = a * (y3 * (z * y1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y2, -4.2e+107], N[Not[LessEqual[y2, 1.8e-8]], $MachinePrecision]], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y2 < -4.1999999999999999e107 or 1.79999999999999991e-8 < y2

   1. Initial program 31.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 43.9%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 43.9%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 43.9%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 43.9%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 43.9%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 38.4%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 38.4%

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 38.4%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in t around inf 33.2%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
   9. Step-by-step derivation

      1. *-commutative 33.2%

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y2 \cdot t\right)}\right) \]

   10. Simplified 33.2%

       \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y2 \cdot t\right)}\right) \]

   if -4.1999999999999999e107 < y2 < 1.79999999999999991e-8

   1. Initial program 37.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 34.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 34.3%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 34.3%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 34.3%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 34.3%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in y3 around -inf 22.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 22.7%

         \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

      2. *-commutative 22.7%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \left(\color{blue}{z \cdot a} - j \cdot y4\right) \]

   7. Simplified 22.7%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(z \cdot a - j \cdot y4\right)} \]

   8. Taylor expanded in z around inf 17.0%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. expm1-log1p-u 7.5%

         \[\leadsto a \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y1 \cdot \left(y3 \cdot z\right)\right)\right)} \]

      2. expm1-udef 7.5%

         \[\leadsto a \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(y1 \cdot \left(y3 \cdot z\right)\right)} - 1\right)} \]

      3. *-commutative 7.5%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(y3 \cdot z\right) \cdot y1}\right)} - 1\right) \]

   10. Applied egg-rr 7.5%

       \[\leadsto a \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\left(y3 \cdot z\right) \cdot y1\right)} - 1\right)} \]
   11. Step-by-step derivation

       1. expm1-def 7.5%

          \[\leadsto a \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(y3 \cdot z\right) \cdot y1\right)\right)} \]

       2. expm1-log1p 17.0%

          \[\leadsto a \cdot \color{blue}{\left(\left(y3 \cdot z\right) \cdot y1\right)} \]

       3. associate-*l* 17.1%

          \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(z \cdot y1\right)\right)} \]

   12. Simplified 17.1%

       \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(z \cdot y1\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 24.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -4.2 \cdot 10^{+107} \lor \neg \left(y2 \leq 1.8 \cdot 10^{-8}\right):\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \end{array} \]

Alternative 38: 21.8% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -2 \cdot 10^{-15}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 2.7 \cdot 10^{-10}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -2e-15)
   (* c (* x (* y0 y2)))
   (if (<= y2 2.7e-10) (* a (* y3 (* z y1))) (* a (* y5 (* t y2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -2e-15) {
		tmp = c * (x * (y0 * y2));
	} else if (y2 <= 2.7e-10) {
		tmp = a * (y3 * (z * y1));
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-2d-15)) then
        tmp = c * (x * (y0 * y2))
    else if (y2 <= 2.7d-10) then
        tmp = a * (y3 * (z * y1))
    else
        tmp = a * (y5 * (t * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -2e-15) {
		tmp = c * (x * (y0 * y2));
	} else if (y2 <= 2.7e-10) {
		tmp = a * (y3 * (z * y1));
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -2e-15:
		tmp = c * (x * (y0 * y2))
	elif y2 <= 2.7e-10:
		tmp = a * (y3 * (z * y1))
	else:
		tmp = a * (y5 * (t * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -2e-15)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (y2 <= 2.7e-10)
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	else
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -2e-15)
		tmp = c * (x * (y0 * y2));
	elseif (y2 <= 2.7e-10)
		tmp = a * (y3 * (z * y1));
	else
		tmp = a * (y5 * (t * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -2e-15], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.7e-10], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y2 < -2.0000000000000002e-15

   1. Initial program 42.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in c around inf 44.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 44.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 44.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 44.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 44.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 44.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 44.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 44.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 44.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 49.1%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 49.1%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 49.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]

      3. *-commutative 49.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot y5}\right)\right) \]

      4. *-commutative 49.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(\color{blue}{y2 \cdot k} - j \cdot y3\right) \cdot y5\right)\right) \]

      5. *-commutative 49.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(y2 \cdot k - \color{blue}{y3 \cdot j}\right) \cdot y5\right)\right) \]

      6. unsub-neg 49.1%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right)} \]

      7. *-commutative 49.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right) \]

      8. *-commutative 49.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(\color{blue}{k \cdot y2} - y3 \cdot j\right) \cdot y5\right) \]

      9. *-commutative 49.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) \cdot y5\right) \]

      10. *-commutative 49.1%

          \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \color{blue}{y5 \cdot \left(k \cdot y2 - j \cdot y3\right)}\right) \]

   7. Simplified 49.1%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in x around inf 31.0%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if -2.0000000000000002e-15 < y2 < 2.7e-10

   1. Initial program 36.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 35.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 35.5%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 35.5%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 35.5%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 35.5%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in y3 around -inf 24.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 24.7%

         \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

      2. *-commutative 24.7%

         \[\leadsto \left(y1 \cdot y3\right) \cdot \left(\color{blue}{z \cdot a} - j \cdot y4\right) \]

   7. Simplified 24.7%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(z \cdot a - j \cdot y4\right)} \]

   8. Taylor expanded in z around inf 18.7%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. expm1-log1p-u 8.0%

         \[\leadsto a \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y1 \cdot \left(y3 \cdot z\right)\right)\right)} \]

      2. expm1-udef 8.0%

         \[\leadsto a \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(y1 \cdot \left(y3 \cdot z\right)\right)} - 1\right)} \]

      3. *-commutative 8.0%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(y3 \cdot z\right) \cdot y1}\right)} - 1\right) \]

   10. Applied egg-rr 8.0%

       \[\leadsto a \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\left(y3 \cdot z\right) \cdot y1\right)} - 1\right)} \]
   11. Step-by-step derivation

       1. expm1-def 8.0%

          \[\leadsto a \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(y3 \cdot z\right) \cdot y1\right)\right)} \]

       2. expm1-log1p 18.7%

          \[\leadsto a \cdot \color{blue}{\left(\left(y3 \cdot z\right) \cdot y1\right)} \]

       3. associate-*l* 18.8%

          \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(z \cdot y1\right)\right)} \]

   12. Simplified 18.8%

       \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(z \cdot y1\right)\right)} \]

   if 2.7e-10 < y2

   1. Initial program 25.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 38.1%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 38.1%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 38.1%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 38.1%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 38.1%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 37.1%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 37.1%

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 37.1%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in t around inf 31.7%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
   9. Step-by-step derivation

      1. *-commutative 31.7%

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y2 \cdot t\right)}\right) \]

   10. Simplified 31.7%

       \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y2 \cdot t\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 25.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2 \cdot 10^{-15}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 2.7 \cdot 10^{-10}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \]

Alternative 39: 20.7% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -4.7 \cdot 10^{+36}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 2.3 \cdot 10^{-87}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -4.7e+36)
   (* c (* x (* y0 y2)))
   (if (<= y0 2.3e-87) (* a (* y5 (* t y2))) (* j (* y0 (* y3 y5))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -4.7e+36) {
		tmp = c * (x * (y0 * y2));
	} else if (y0 <= 2.3e-87) {
		tmp = a * (y5 * (t * y2));
	} else {
		tmp = j * (y0 * (y3 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y0 <= (-4.7d+36)) then
        tmp = c * (x * (y0 * y2))
    else if (y0 <= 2.3d-87) then
        tmp = a * (y5 * (t * y2))
    else
        tmp = j * (y0 * (y3 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -4.7e+36) {
		tmp = c * (x * (y0 * y2));
	} else if (y0 <= 2.3e-87) {
		tmp = a * (y5 * (t * y2));
	} else {
		tmp = j * (y0 * (y3 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y0 <= -4.7e+36:
		tmp = c * (x * (y0 * y2))
	elif y0 <= 2.3e-87:
		tmp = a * (y5 * (t * y2))
	else:
		tmp = j * (y0 * (y3 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -4.7e+36)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (y0 <= 2.3e-87)
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	else
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y0 <= -4.7e+36)
		tmp = c * (x * (y0 * y2));
	elseif (y0 <= 2.3e-87)
		tmp = a * (y5 * (t * y2));
	else
		tmp = j * (y0 * (y3 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -4.7e+36], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.3e-87], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y0 < -4.69999999999999989e36

   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. Taylor expanded in c around inf 36.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 36.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 36.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 36.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 36.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 36.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 36.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 36.2%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 36.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 67.6%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 67.6%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 67.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]

      3. *-commutative 67.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot y5}\right)\right) \]

      4. *-commutative 67.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(\color{blue}{y2 \cdot k} - j \cdot y3\right) \cdot y5\right)\right) \]

      5. *-commutative 67.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(y2 \cdot k - \color{blue}{y3 \cdot j}\right) \cdot y5\right)\right) \]

      6. unsub-neg 67.6%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right)} \]

      7. *-commutative 67.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right) \]

      8. *-commutative 67.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(\color{blue}{k \cdot y2} - y3 \cdot j\right) \cdot y5\right) \]

      9. *-commutative 67.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) \cdot y5\right) \]

      10. *-commutative 67.6%

          \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \color{blue}{y5 \cdot \left(k \cdot y2 - j \cdot y3\right)}\right) \]

   7. Simplified 67.6%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in x around inf 41.5%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if -4.69999999999999989e36 < y0 < 2.3000000000000001e-87

   1. Initial program 32.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 38.5%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 38.5%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 38.5%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 38.5%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 38.5%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 27.4%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 27.4%

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 27.4%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in t around inf 17.6%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
   9. Step-by-step derivation

      1. *-commutative 17.6%

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y2 \cdot t\right)}\right) \]

   10. Simplified 17.6%

       \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y2 \cdot t\right)}\right) \]

   if 2.3000000000000001e-87 < y0

   1. Initial program 37.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 28.8%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 28.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 31.8%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 31.8%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 31.8%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 36.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 36.1%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

      2. neg-mul-1 36.1%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   7. Simplified 36.1%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in k around 0 37.1%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 29.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -4.7 \cdot 10^{+36}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 2.3 \cdot 10^{-87}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \]

Alternative 40: 21.1% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -3.7 \cdot 10^{-16}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 9 \cdot 10^{-66}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -3.7e-16)
   (* c (* x (* y0 y2)))
   (if (<= y0 9e-66) (* k (* y1 (* y2 y4))) (* j (* y0 (* y3 y5))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -3.7e-16) {
		tmp = c * (x * (y0 * y2));
	} else if (y0 <= 9e-66) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = j * (y0 * (y3 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y0 <= (-3.7d-16)) then
        tmp = c * (x * (y0 * y2))
    else if (y0 <= 9d-66) then
        tmp = k * (y1 * (y2 * y4))
    else
        tmp = j * (y0 * (y3 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -3.7e-16) {
		tmp = c * (x * (y0 * y2));
	} else if (y0 <= 9e-66) {
		tmp = k * (y1 * (y2 * y4));
	} else {
		tmp = j * (y0 * (y3 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y0 <= -3.7e-16:
		tmp = c * (x * (y0 * y2))
	elif y0 <= 9e-66:
		tmp = k * (y1 * (y2 * y4))
	else:
		tmp = j * (y0 * (y3 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -3.7e-16)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (y0 <= 9e-66)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	else
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y0 <= -3.7e-16)
		tmp = c * (x * (y0 * y2));
	elseif (y0 <= 9e-66)
		tmp = k * (y1 * (y2 * y4));
	else
		tmp = j * (y0 * (y3 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -3.7e-16], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 9e-66], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y0 < -3.7e-16

   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. Taylor expanded in c around inf 32.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. +-commutative 32.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. mul-1-neg 32.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-i \cdot \left(x \cdot y - t \cdot z\right)\right)}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. unsub-neg 32.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 32.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 32.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 32.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. *-commutative 32.7%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 32.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 59.5%

      \[\leadsto \color{blue}{y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 59.5%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 59.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]

      3. *-commutative 59.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot y5}\right)\right) \]

      4. *-commutative 59.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(\color{blue}{y2 \cdot k} - j \cdot y3\right) \cdot y5\right)\right) \]

      5. *-commutative 59.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-\left(y2 \cdot k - \color{blue}{y3 \cdot j}\right) \cdot y5\right)\right) \]

      6. unsub-neg 59.5%

         \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right)} \]

      7. *-commutative 59.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - \left(y2 \cdot k - y3 \cdot j\right) \cdot y5\right) \]

      8. *-commutative 59.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(\color{blue}{k \cdot y2} - y3 \cdot j\right) \cdot y5\right) \]

      9. *-commutative 59.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) \cdot y5\right) \]

      10. *-commutative 59.5%

          \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - \color{blue}{y5 \cdot \left(k \cdot y2 - j \cdot y3\right)}\right) \]

   7. Simplified 59.5%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in x around inf 35.5%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if -3.7e-16 < y0 < 8.9999999999999995e-66

   1. Initial program 35.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y1 around -inf 41.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 41.4%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 41.4%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 41.4%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   4. Simplified 41.4%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   5. Taylor expanded in y4 around -inf 29.3%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   6. Taylor expanded in k around inf 23.4%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]

   if 8.9999999999999995e-66 < y0

   1. Initial program 36.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around inf 28.8%

      \[\leadsto \left(\color{blue}{-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 28.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 30.9%

         \[\leadsto \left(\left(-\color{blue}{\left(i \cdot y5\right) \cdot \left(j \cdot t - k \cdot y\right)}\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. *-commutative 30.9%

         \[\leadsto \left(\left(-\left(i \cdot y5\right) \cdot \left(\color{blue}{t \cdot j} - k \cdot y\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 30.9%

      \[\leadsto \left(\color{blue}{\left(-\left(i \cdot y5\right) \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y0 around inf 36.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 36.6%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

      2. neg-mul-1 36.6%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) \]

   7. Simplified 36.6%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Taylor expanded in k around 0 37.7%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -3.7 \cdot 10^{-16}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 9 \cdot 10^{-66}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \]

Alternative 41: 17.2% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* y1 (* z y3))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y1 * (z * y3));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * (y1 * (z * y3))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y1 * (z * y3));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (y1 * (z * y3))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(y1 * Float64(z * y3)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (y1 * (z * y3));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 35.0%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

2. Taylor expanded in y1 around -inf 35.6%

   \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
3. Step-by-step derivation

   1. mul-1-neg 35.6%

      \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   2. *-commutative 35.6%

      \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

   3. distribute-rgt-neg-in 35.6%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

4. Simplified 35.6%

   \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

5. Taylor expanded in y3 around -inf 22.0%

   \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]
6. Step-by-step derivation

   1. associate-*r* 19.8%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

   2. *-commutative 19.8%

      \[\leadsto \left(y1 \cdot y3\right) \cdot \left(\color{blue}{z \cdot a} - j \cdot y4\right) \]

7. Simplified 19.8%

   \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(z \cdot a - j \cdot y4\right)} \]

8. Taylor expanded in z around inf 14.3%

   \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

9. Final simplification 14.3%

   \[\leadsto a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right) \]

Alternative 42: 17.2% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* y3 (* z y1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y3 * (z * y1));
}

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 * (y3 * (z * y1))
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 * (y3 * (z * y1));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (y3 * (z * y1))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(y3 * Float64(z * y1)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (y3 * (z * y1));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 35.0%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

2. Taylor expanded in y1 around -inf 35.6%

   \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
3. Step-by-step derivation

   1. mul-1-neg 35.6%

      \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   2. *-commutative 35.6%

      \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

   3. distribute-rgt-neg-in 35.6%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

4. Simplified 35.6%

   \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

5. Taylor expanded in y3 around -inf 22.0%

   \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]
6. Step-by-step derivation

   1. associate-*r* 19.8%

      \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(a \cdot z - j \cdot y4\right)} \]

   2. *-commutative 19.8%

      \[\leadsto \left(y1 \cdot y3\right) \cdot \left(\color{blue}{z \cdot a} - j \cdot y4\right) \]

7. Simplified 19.8%

   \[\leadsto \color{blue}{\left(y1 \cdot y3\right) \cdot \left(z \cdot a - j \cdot y4\right)} \]

8. Taylor expanded in z around inf 14.3%

   \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
9. Step-by-step derivation

   1. expm1-log1p-u 5.5%

      \[\leadsto a \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y1 \cdot \left(y3 \cdot z\right)\right)\right)} \]

   2. expm1-udef 5.5%

      \[\leadsto a \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(y1 \cdot \left(y3 \cdot z\right)\right)} - 1\right)} \]

   3. *-commutative 5.5%

      \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(y3 \cdot z\right) \cdot y1}\right)} - 1\right) \]

10. Applied egg-rr 5.5%

    \[\leadsto a \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\left(y3 \cdot z\right) \cdot y1\right)} - 1\right)} \]
11. Step-by-step derivation

    1. expm1-def 5.5%

       \[\leadsto a \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(y3 \cdot z\right) \cdot y1\right)\right)} \]

    2. expm1-log1p 14.3%

       \[\leadsto a \cdot \color{blue}{\left(\left(y3 \cdot z\right) \cdot y1\right)} \]

    3. associate-*l* 14.7%

       \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(z \cdot y1\right)\right)} \]

12. Simplified 14.7%

    \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(z \cdot y1\right)\right)} \]

13. Final simplification 14.7%

    \[\leadsto a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right) \]

Developer target: 27.8% accurate, 0.8× 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 2023308 
(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

  :herbie-target
  (if (< y4 -7.206256231996481e+60) (- (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))))) (- (/ (- (* y2 t) (* y3 y)) (/ 1.0 (- (* y4 c) (* y5 a)))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (if (< y4 -3.364603505246317e-66) (+ (- (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x))) (* (- (* b y0) (* i y1)) (- (* j x) (* k z)))) (- (* (- (* y0 c) (* a y1)) (- (* x y2) (* z y3))) (- (* (- (* t y2) (* y y3)) (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) (- (* k y2) (* j y3)))))) (if (< y4 -1.2000065055686116e-105) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 6.718963124057495e-279) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (if (< y4 4.77962681403792e-222) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 2.2852241541266835e-175) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (- (* k (* i (* z y1))) (+ (* j (* i (* x y1))) (* y0 (* k (* z b)))))) (- (* z (* y3 (* a y1))) (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3)))))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))))))))

  (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (* (- (* x j) (* z k)) (- (* y0 b) (* y1 i)))) (* (- (* x y2) (* z y3)) (- (* y0 c) (* y1 a)))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))