Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 29.4% → 41.4%

Time: 1.8min

Alternatives: 35

Speedup: 4.9×

• 89.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 29.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 41.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := y0 \cdot y5 - y1 \cdot y4\\ t_3 := t \cdot j - y \cdot k\\ t_4 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t_3\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_5 := y1 \cdot y4 - y0 \cdot y5\\ t_6 := y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - \left(i \cdot t_3 + y0 \cdot t_1\right)\right)\\ \mathbf{if}\;y2 \leq -5.8 \cdot 10^{+159}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot t_5 + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -3 \cdot 10^{+31}:\\ \;\;\;\;t_1 \cdot t_5 + y2 \cdot \left(y5 \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq -1.65 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq -9 \cdot 10^{-175}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y2 \leq -4.2 \cdot 10^{-190}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y2 \leq -9.6 \cdot 10^{-225}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot t_2 + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -5.8 \cdot 10^{-254}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y2 \leq 2.4 \cdot 10^{-256}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot t_2\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 1.3 \cdot 10^{-90}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y2 \leq 4500000000000:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y2 \leq 6.8 \cdot 10^{+122}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(y \cdot b - y1 \cdot y2\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y2) (* j y3)))
        (t_2 (- (* y0 y5) (* y1 y4)))
        (t_3 (- (* t j) (* y k)))
        (t_4
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 t_3))
           (* y0 (- (* z k) (* x j))))))
        (t_5 (- (* y1 y4) (* y0 y5)))
        (t_6 (* y5 (- (* a (- (* t y2) (* y y3))) (+ (* i t_3) (* y0 t_1))))))
   (if (<= y2 -5.8e+159)
     (*
      y2
      (+
       (+ (* k t_5) (* x (- (* c y0) (* a y1))))
       (* t (- (* a y5) (* c y4)))))
     (if (<= y2 -3e+31)
       (+ (* t_1 t_5) (* y2 (* y5 (* t a))))
       (if (<= y2 -1.65e-10)
         (* b (* j (- (* t y4) (* x y0))))
         (if (<= y2 -9e-175)
           t_4
           (if (<= y2 -4.2e-190)
             t_6
             (if (<= y2 -9.6e-225)
               (*
                y3
                (+
                 (* y (- (* c y4) (* a y5)))
                 (+ (* j t_2) (* z (- (* a y1) (* c y0))))))
               (if (<= y2 -5.8e-254)
                 t_4
                 (if (<= y2 2.4e-256)
                   (*
                    j
                    (+
                     (+ (* t (- (* b y4) (* i y5))) (* y3 t_2))
                     (* x (- (* i y1) (* b y0)))))
                   (if (<= y2 1.3e-90)
                     t_4
                     (if (<= y2 4500000000000.0)
                       t_6
                       (if (<= y2 6.8e+122)
                         (* (* x a) (- (* y b) (* y1 y2)))
                         (* a (* y2 (- (* t y5) (* x y1)))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = (y0 * y5) - (y1 * y4);
	double t_3 = (t * j) - (y * k);
	double t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))));
	double t_5 = (y1 * y4) - (y0 * y5);
	double t_6 = y5 * ((a * ((t * y2) - (y * y3))) - ((i * t_3) + (y0 * t_1)));
	double tmp;
	if (y2 <= -5.8e+159) {
		tmp = y2 * (((k * t_5) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (y2 <= -3e+31) {
		tmp = (t_1 * t_5) + (y2 * (y5 * (t * a)));
	} else if (y2 <= -1.65e-10) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y2 <= -9e-175) {
		tmp = t_4;
	} else if (y2 <= -4.2e-190) {
		tmp = t_6;
	} else if (y2 <= -9.6e-225) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_2) + (z * ((a * y1) - (c * y0)))));
	} else if (y2 <= -5.8e-254) {
		tmp = t_4;
	} else if (y2 <= 2.4e-256) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * t_2)) + (x * ((i * y1) - (b * y0))));
	} else if (y2 <= 1.3e-90) {
		tmp = t_4;
	} else if (y2 <= 4500000000000.0) {
		tmp = t_6;
	} else if (y2 <= 6.8e+122) {
		tmp = (x * a) * ((y * b) - (y1 * y2));
	} else {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = (k * y2) - (j * y3)
    t_2 = (y0 * y5) - (y1 * y4)
    t_3 = (t * j) - (y * k)
    t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))))
    t_5 = (y1 * y4) - (y0 * y5)
    t_6 = y5 * ((a * ((t * y2) - (y * y3))) - ((i * t_3) + (y0 * t_1)))
    if (y2 <= (-5.8d+159)) then
        tmp = y2 * (((k * t_5) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    else if (y2 <= (-3d+31)) then
        tmp = (t_1 * t_5) + (y2 * (y5 * (t * a)))
    else if (y2 <= (-1.65d-10)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y2 <= (-9d-175)) then
        tmp = t_4
    else if (y2 <= (-4.2d-190)) then
        tmp = t_6
    else if (y2 <= (-9.6d-225)) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_2) + (z * ((a * y1) - (c * y0)))))
    else if (y2 <= (-5.8d-254)) then
        tmp = t_4
    else if (y2 <= 2.4d-256) then
        tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * t_2)) + (x * ((i * y1) - (b * y0))))
    else if (y2 <= 1.3d-90) then
        tmp = t_4
    else if (y2 <= 4500000000000.0d0) then
        tmp = t_6
    else if (y2 <= 6.8d+122) then
        tmp = (x * a) * ((y * b) - (y1 * y2))
    else
        tmp = a * (y2 * ((t * y5) - (x * y1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = (y0 * y5) - (y1 * y4);
	double t_3 = (t * j) - (y * k);
	double t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))));
	double t_5 = (y1 * y4) - (y0 * y5);
	double t_6 = y5 * ((a * ((t * y2) - (y * y3))) - ((i * t_3) + (y0 * t_1)));
	double tmp;
	if (y2 <= -5.8e+159) {
		tmp = y2 * (((k * t_5) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (y2 <= -3e+31) {
		tmp = (t_1 * t_5) + (y2 * (y5 * (t * a)));
	} else if (y2 <= -1.65e-10) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y2 <= -9e-175) {
		tmp = t_4;
	} else if (y2 <= -4.2e-190) {
		tmp = t_6;
	} else if (y2 <= -9.6e-225) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_2) + (z * ((a * y1) - (c * y0)))));
	} else if (y2 <= -5.8e-254) {
		tmp = t_4;
	} else if (y2 <= 2.4e-256) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * t_2)) + (x * ((i * y1) - (b * y0))));
	} else if (y2 <= 1.3e-90) {
		tmp = t_4;
	} else if (y2 <= 4500000000000.0) {
		tmp = t_6;
	} else if (y2 <= 6.8e+122) {
		tmp = (x * a) * ((y * b) - (y1 * y2));
	} else {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	}
	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 = (y0 * y5) - (y1 * y4)
	t_3 = (t * j) - (y * k)
	t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))))
	t_5 = (y1 * y4) - (y0 * y5)
	t_6 = y5 * ((a * ((t * y2) - (y * y3))) - ((i * t_3) + (y0 * t_1)))
	tmp = 0
	if y2 <= -5.8e+159:
		tmp = y2 * (((k * t_5) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	elif y2 <= -3e+31:
		tmp = (t_1 * t_5) + (y2 * (y5 * (t * a)))
	elif y2 <= -1.65e-10:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y2 <= -9e-175:
		tmp = t_4
	elif y2 <= -4.2e-190:
		tmp = t_6
	elif y2 <= -9.6e-225:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_2) + (z * ((a * y1) - (c * y0)))))
	elif y2 <= -5.8e-254:
		tmp = t_4
	elif y2 <= 2.4e-256:
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * t_2)) + (x * ((i * y1) - (b * y0))))
	elif y2 <= 1.3e-90:
		tmp = t_4
	elif y2 <= 4500000000000.0:
		tmp = t_6
	elif y2 <= 6.8e+122:
		tmp = (x * a) * ((y * b) - (y1 * y2))
	else:
		tmp = a * (y2 * ((t * y5) - (x * y1)))
	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(y0 * y5) - Float64(y1 * y4))
	t_3 = Float64(Float64(t * j) - Float64(y * k))
	t_4 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * t_3)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	t_5 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_6 = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) - Float64(Float64(i * t_3) + Float64(y0 * t_1))))
	tmp = 0.0
	if (y2 <= -5.8e+159)
		tmp = Float64(y2 * Float64(Float64(Float64(k * t_5) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y2 <= -3e+31)
		tmp = Float64(Float64(t_1 * t_5) + Float64(y2 * Float64(y5 * Float64(t * a))));
	elseif (y2 <= -1.65e-10)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y2 <= -9e-175)
		tmp = t_4;
	elseif (y2 <= -4.2e-190)
		tmp = t_6;
	elseif (y2 <= -9.6e-225)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * t_2) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (y2 <= -5.8e-254)
		tmp = t_4;
	elseif (y2 <= 2.4e-256)
		tmp = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * t_2)) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y2 <= 1.3e-90)
		tmp = t_4;
	elseif (y2 <= 4500000000000.0)
		tmp = t_6;
	elseif (y2 <= 6.8e+122)
		tmp = Float64(Float64(x * a) * Float64(Float64(y * b) - Float64(y1 * y2)));
	else
		tmp = Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (k * y2) - (j * y3);
	t_2 = (y0 * y5) - (y1 * y4);
	t_3 = (t * j) - (y * k);
	t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * ((z * k) - (x * j))));
	t_5 = (y1 * y4) - (y0 * y5);
	t_6 = y5 * ((a * ((t * y2) - (y * y3))) - ((i * t_3) + (y0 * t_1)));
	tmp = 0.0;
	if (y2 <= -5.8e+159)
		tmp = y2 * (((k * t_5) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	elseif (y2 <= -3e+31)
		tmp = (t_1 * t_5) + (y2 * (y5 * (t * a)));
	elseif (y2 <= -1.65e-10)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y2 <= -9e-175)
		tmp = t_4;
	elseif (y2 <= -4.2e-190)
		tmp = t_6;
	elseif (y2 <= -9.6e-225)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_2) + (z * ((a * y1) - (c * y0)))));
	elseif (y2 <= -5.8e-254)
		tmp = t_4;
	elseif (y2 <= 2.4e-256)
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * t_2)) + (x * ((i * y1) - (b * y0))));
	elseif (y2 <= 1.3e-90)
		tmp = t_4;
	elseif (y2 <= 4500000000000.0)
		tmp = t_6;
	elseif (y2 <= 6.8e+122)
		tmp = (x * a) * ((y * b) - (y1 * y2));
	else
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(i * t$95$3), $MachinePrecision] + N[(y0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -5.8e+159], N[(y2 * N[(N[(N[(k * t$95$5), $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[y2, -3e+31], N[(N[(t$95$1 * t$95$5), $MachinePrecision] + N[(y2 * N[(y5 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.65e-10], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -9e-175], t$95$4, If[LessEqual[y2, -4.2e-190], t$95$6, If[LessEqual[y2, -9.6e-225], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * t$95$2), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -5.8e-254], t$95$4, If[LessEqual[y2, 2.4e-256], N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.3e-90], t$95$4, If[LessEqual[y2, 4500000000000.0], t$95$6, If[LessEqual[y2, 6.8e+122], N[(N[(x * a), $MachinePrecision] * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y2 < -5.80000000000000029e159

   1. Initial program 31.0%

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

   2. Taylor expanded in y2 around inf 75.9%

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

   if -5.80000000000000029e159 < y2 < -2.99999999999999989e31

   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 a around inf 55.2%

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

      1. sub-neg 55.2%

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

      2. +-commutative 55.2%

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

      3. mul-1-neg 55.2%

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

      4. unsub-neg 55.2%

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

      5. *-commutative 55.2%

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

      6. *-commutative 55.2%

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

      7. mul-1-neg 55.2%

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

      8. remove-double-neg 55.2%

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

      9. *-commutative 55.2%

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

   4. Simplified 55.2%

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

   5. Taylor expanded in y1 around 0 55.2%

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

   6. Taylor expanded in y2 around inf 54.9%

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

      1. *-commutative 54.9%

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

      2. associate-*r* 59.5%

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

      3. associate-*r* 59.5%

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

      4. *-commutative 59.5%

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

      5. associate-*r* 64.1%

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

      6. *-commutative 64.1%

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

   8. Simplified 64.1%

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

   if -2.99999999999999989e31 < y2 < -1.65e-10

   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 37.9%

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

      1. +-commutative 37.9%

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

      2. mul-1-neg 37.9%

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

      3. unsub-neg 37.9%

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

      4. *-commutative 37.9%

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

   4. Simplified 37.9%

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

   5. Taylor expanded in b around inf 75.3%

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

   if -1.65e-10 < y2 < -8.99999999999999996e-175 or -9.59999999999999985e-225 < y2 < -5.7999999999999999e-254 or 2.3999999999999999e-256 < y2 < 1.3e-90

   1. Initial program 34.8%

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

   3. Simplified 34.8%

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

   4. Taylor expanded in b around inf 52.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)} \]

   if -8.99999999999999996e-175 < y2 < -4.19999999999999983e-190 or 1.3e-90 < y2 < 4.5e12

   1. Initial program 20.7%

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

   2. Taylor expanded in y5 around -inf 62.9%

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

   if -4.19999999999999983e-190 < y2 < -9.59999999999999985e-225

   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 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 -5.7999999999999999e-254 < y2 < 2.3999999999999999e-256

   1. Initial program 23.8%

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

   2. Taylor expanded in j around inf 71.5%

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

      1. +-commutative 71.5%

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

      2. mul-1-neg 71.5%

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

      3. unsub-neg 71.5%

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

      4. *-commutative 71.5%

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

   4. Simplified 71.5%

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

   if 4.5e12 < y2 < 6.8e122

   1. Initial program 26.3%

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

   2. Taylor expanded in a around inf 48.3%

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

      1. sub-neg 48.3%

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

      2. +-commutative 48.3%

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

      3. mul-1-neg 48.3%

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

      4. unsub-neg 48.3%

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

      5. *-commutative 48.3%

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

      6. *-commutative 48.3%

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

      7. mul-1-neg 48.3%

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

      8. remove-double-neg 48.3%

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

      9. *-commutative 48.3%

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

   4. Simplified 48.3%

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

   5. Taylor expanded in x around inf 53.0%

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

      1. associate-*r* 61.2%

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

      2. *-commutative 61.2%

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

   7. Simplified 61.2%

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

   if 6.8e122 < y2

   1. Initial program 26.5%

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

   2. Taylor expanded in y2 around inf 63.7%

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

      1. sub-neg 63.7%

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

      2. +-commutative 63.7%

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

      3. mul-1-neg 63.7%

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

      4. fma-def 63.7%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 63.7%

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

      6. +-commutative 63.7%

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

      7. sub-neg 63.7%

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

      8. *-commutative 63.7%

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

   4. Simplified 63.7%

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

   5. Taylor expanded in a around -inf 68.1%

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

      1. associate-*r* 68.1%

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

      2. neg-mul-1 68.1%

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

      3. *-commutative 68.1%

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

      4. *-commutative 68.1%

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

   7. Simplified 68.1%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y2 \cdot \left(y1 \cdot x - y5 \cdot t\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -5.8 \cdot 10^{+159}:\\ \;\;\;\;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}\;y2 \leq -3 \cdot 10^{+31}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y2 \cdot \left(y5 \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq -1.65 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq -9 \cdot 10^{-175}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq -4.2 \cdot 10^{-190}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - \left(i \cdot \left(t \cdot j - y \cdot k\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -9.6 \cdot 10^{-225}:\\ \;\;\;\;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}\;y2 \leq -5.8 \cdot 10^{-254}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 2.4 \cdot 10^{-256}:\\ \;\;\;\;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}\;y2 \leq 1.3 \cdot 10^{-90}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 4500000000000:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - \left(i \cdot \left(t \cdot j - y \cdot k\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 6.8 \cdot 10^{+122}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(y \cdot b - y1 \cdot y2\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \end{array} \]

Alternative 2: 52.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.4%

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

   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 a around inf 32.3%

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

      1. sub-neg 32.3%

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

      2. +-commutative 32.3%

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

      3. mul-1-neg 32.3%

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

      4. unsub-neg 32.3%

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

      5. *-commutative 32.3%

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

      6. *-commutative 32.3%

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

      7. mul-1-neg 32.3%

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

      8. remove-double-neg 32.3%

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

      9. *-commutative 32.3%

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

   4. Simplified 32.3%

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

   5. Taylor expanded in y1 around 0 38.1%

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

   6. Taylor expanded in x around inf 38.3%

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

      1. associate-*r* 39.5%

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

   8. Simplified 39.5%

      \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot x\right) \cdot y} + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.8%

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

Alternative 3: 38.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := t \cdot y2 - y \cdot y3\\ t_3 := y5 \cdot t_2\\ t_4 := x \cdot y2 - z \cdot y3\\ t_5 := y1 \cdot y4 - y0 \cdot y5\\ t_6 := \left(k \cdot y2 - j \cdot y3\right) \cdot t_5\\ t_7 := b \cdot \left(x \cdot y - z \cdot t\right)\\ \mathbf{if}\;y0 \leq -3.7 \cdot 10^{+184}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot t_4 + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -2 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(y2 \cdot t_1\right)\\ \mathbf{elif}\;y0 \leq -7.4 \cdot 10^{-112}:\\ \;\;\;\;t_6 + a \cdot \left(y \cdot \left(x \cdot b\right) + t_3\right)\\ \mathbf{elif}\;y0 \leq -4.8 \cdot 10^{-259}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot t_5 + x \cdot t_1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 5.5 \cdot 10^{-209}:\\ \;\;\;\;t_6 + a \cdot \left(t_3 + t_7\right)\\ \mathbf{elif}\;y0 \leq 4.8 \cdot 10^{-130}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq 1.15 \cdot 10^{+77}:\\ \;\;\;\;t_6 + y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + a \cdot t_2\right)\\ \mathbf{elif}\;y0 \leq 5 \cdot 10^{+139}:\\ \;\;\;\;t_4 \cdot \left(c \cdot y0\right)\\ \mathbf{elif}\;y0 \leq 8 \cdot 10^{+265}:\\ \;\;\;\;t_6 + a \cdot \left(t_3 + \left(t_7 + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1)))
        (t_2 (- (* t y2) (* y y3)))
        (t_3 (* y5 t_2))
        (t_4 (- (* x y2) (* z y3)))
        (t_5 (- (* y1 y4) (* y0 y5)))
        (t_6 (* (- (* k y2) (* j y3)) t_5))
        (t_7 (* b (- (* x y) (* z t)))))
   (if (<= y0 -3.7e+184)
     (*
      y0
      (+ (+ (* c t_4) (* y5 (- (* j y3) (* k y2)))) (* b (- (* z k) (* x j)))))
     (if (<= y0 -2e+17)
       (* x (* y2 t_1))
       (if (<= y0 -7.4e-112)
         (+ t_6 (* a (+ (* y (* x b)) t_3)))
         (if (<= y0 -4.8e-259)
           (* y2 (+ (+ (* k t_5) (* x t_1)) (* t (- (* a y5) (* c y4)))))
           (if (<= y0 5.5e-209)
             (+ t_6 (* a (+ t_3 t_7)))
             (if (<= y0 4.8e-130)
               (*
                j
                (+
                 (+ (* t (- (* b y4) (* i y5))) (* y3 (- (* y0 y5) (* y1 y4))))
                 (* x (- (* i y1) (* b y0)))))
               (if (<= y0 1.15e+77)
                 (+ t_6 (* y5 (+ (* i (- (* y k) (* t j))) (* a t_2))))
                 (if (<= y0 5e+139)
                   (* t_4 (* c y0))
                   (if (<= y0 8e+265)
                     (+ t_6 (* a (+ t_3 (+ t_7 (* y1 (- (* z y3) (* x y2)))))))
                     (* 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 = (c * y0) - (a * y1);
	double t_2 = (t * y2) - (y * y3);
	double t_3 = y5 * t_2;
	double t_4 = (x * y2) - (z * y3);
	double t_5 = (y1 * y4) - (y0 * y5);
	double t_6 = ((k * y2) - (j * y3)) * t_5;
	double t_7 = b * ((x * y) - (z * t));
	double tmp;
	if (y0 <= -3.7e+184) {
		tmp = y0 * (((c * t_4) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	} else if (y0 <= -2e+17) {
		tmp = x * (y2 * t_1);
	} else if (y0 <= -7.4e-112) {
		tmp = t_6 + (a * ((y * (x * b)) + t_3));
	} else if (y0 <= -4.8e-259) {
		tmp = y2 * (((k * t_5) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	} else if (y0 <= 5.5e-209) {
		tmp = t_6 + (a * (t_3 + t_7));
	} else if (y0 <= 4.8e-130) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	} else if (y0 <= 1.15e+77) {
		tmp = t_6 + (y5 * ((i * ((y * k) - (t * j))) + (a * t_2)));
	} else if (y0 <= 5e+139) {
		tmp = t_4 * (c * y0);
	} else if (y0 <= 8e+265) {
		tmp = t_6 + (a * (t_3 + (t_7 + (y1 * ((z * y3) - (x * y2))))));
	} 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) :: 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 = (t * y2) - (y * y3)
    t_3 = y5 * t_2
    t_4 = (x * y2) - (z * y3)
    t_5 = (y1 * y4) - (y0 * y5)
    t_6 = ((k * y2) - (j * y3)) * t_5
    t_7 = b * ((x * y) - (z * t))
    if (y0 <= (-3.7d+184)) then
        tmp = y0 * (((c * t_4) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))))
    else if (y0 <= (-2d+17)) then
        tmp = x * (y2 * t_1)
    else if (y0 <= (-7.4d-112)) then
        tmp = t_6 + (a * ((y * (x * b)) + t_3))
    else if (y0 <= (-4.8d-259)) then
        tmp = y2 * (((k * t_5) + (x * t_1)) + (t * ((a * y5) - (c * y4))))
    else if (y0 <= 5.5d-209) then
        tmp = t_6 + (a * (t_3 + t_7))
    else if (y0 <= 4.8d-130) then
        tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
    else if (y0 <= 1.15d+77) then
        tmp = t_6 + (y5 * ((i * ((y * k) - (t * j))) + (a * t_2)))
    else if (y0 <= 5d+139) then
        tmp = t_4 * (c * y0)
    else if (y0 <= 8d+265) then
        tmp = t_6 + (a * (t_3 + (t_7 + (y1 * ((z * y3) - (x * y2))))))
    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 = (c * y0) - (a * y1);
	double t_2 = (t * y2) - (y * y3);
	double t_3 = y5 * t_2;
	double t_4 = (x * y2) - (z * y3);
	double t_5 = (y1 * y4) - (y0 * y5);
	double t_6 = ((k * y2) - (j * y3)) * t_5;
	double t_7 = b * ((x * y) - (z * t));
	double tmp;
	if (y0 <= -3.7e+184) {
		tmp = y0 * (((c * t_4) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	} else if (y0 <= -2e+17) {
		tmp = x * (y2 * t_1);
	} else if (y0 <= -7.4e-112) {
		tmp = t_6 + (a * ((y * (x * b)) + t_3));
	} else if (y0 <= -4.8e-259) {
		tmp = y2 * (((k * t_5) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	} else if (y0 <= 5.5e-209) {
		tmp = t_6 + (a * (t_3 + t_7));
	} else if (y0 <= 4.8e-130) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	} else if (y0 <= 1.15e+77) {
		tmp = t_6 + (y5 * ((i * ((y * k) - (t * j))) + (a * t_2)));
	} else if (y0 <= 5e+139) {
		tmp = t_4 * (c * y0);
	} else if (y0 <= 8e+265) {
		tmp = t_6 + (a * (t_3 + (t_7 + (y1 * ((z * y3) - (x * y2))))));
	} 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 = (c * y0) - (a * y1)
	t_2 = (t * y2) - (y * y3)
	t_3 = y5 * t_2
	t_4 = (x * y2) - (z * y3)
	t_5 = (y1 * y4) - (y0 * y5)
	t_6 = ((k * y2) - (j * y3)) * t_5
	t_7 = b * ((x * y) - (z * t))
	tmp = 0
	if y0 <= -3.7e+184:
		tmp = y0 * (((c * t_4) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))))
	elif y0 <= -2e+17:
		tmp = x * (y2 * t_1)
	elif y0 <= -7.4e-112:
		tmp = t_6 + (a * ((y * (x * b)) + t_3))
	elif y0 <= -4.8e-259:
		tmp = y2 * (((k * t_5) + (x * t_1)) + (t * ((a * y5) - (c * y4))))
	elif y0 <= 5.5e-209:
		tmp = t_6 + (a * (t_3 + t_7))
	elif y0 <= 4.8e-130:
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
	elif y0 <= 1.15e+77:
		tmp = t_6 + (y5 * ((i * ((y * k) - (t * j))) + (a * t_2)))
	elif y0 <= 5e+139:
		tmp = t_4 * (c * y0)
	elif y0 <= 8e+265:
		tmp = t_6 + (a * (t_3 + (t_7 + (y1 * ((z * y3) - (x * y2))))))
	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(Float64(c * y0) - Float64(a * y1))
	t_2 = Float64(Float64(t * y2) - Float64(y * y3))
	t_3 = Float64(y5 * t_2)
	t_4 = Float64(Float64(x * y2) - Float64(z * y3))
	t_5 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_6 = Float64(Float64(Float64(k * y2) - Float64(j * y3)) * t_5)
	t_7 = Float64(b * Float64(Float64(x * y) - Float64(z * t)))
	tmp = 0.0
	if (y0 <= -3.7e+184)
		tmp = Float64(y0 * Float64(Float64(Float64(c * t_4) + Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2)))) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y0 <= -2e+17)
		tmp = Float64(x * Float64(y2 * t_1));
	elseif (y0 <= -7.4e-112)
		tmp = Float64(t_6 + Float64(a * Float64(Float64(y * Float64(x * b)) + t_3)));
	elseif (y0 <= -4.8e-259)
		tmp = Float64(y2 * Float64(Float64(Float64(k * t_5) + Float64(x * t_1)) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y0 <= 5.5e-209)
		tmp = Float64(t_6 + Float64(a * Float64(t_3 + t_7)));
	elseif (y0 <= 4.8e-130)
		tmp = 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)))));
	elseif (y0 <= 1.15e+77)
		tmp = Float64(t_6 + Float64(y5 * Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(a * t_2))));
	elseif (y0 <= 5e+139)
		tmp = Float64(t_4 * Float64(c * y0));
	elseif (y0 <= 8e+265)
		tmp = Float64(t_6 + Float64(a * Float64(t_3 + Float64(t_7 + Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2)))))));
	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 = (c * y0) - (a * y1);
	t_2 = (t * y2) - (y * y3);
	t_3 = y5 * t_2;
	t_4 = (x * y2) - (z * y3);
	t_5 = (y1 * y4) - (y0 * y5);
	t_6 = ((k * y2) - (j * y3)) * t_5;
	t_7 = b * ((x * y) - (z * t));
	tmp = 0.0;
	if (y0 <= -3.7e+184)
		tmp = y0 * (((c * t_4) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	elseif (y0 <= -2e+17)
		tmp = x * (y2 * t_1);
	elseif (y0 <= -7.4e-112)
		tmp = t_6 + (a * ((y * (x * b)) + t_3));
	elseif (y0 <= -4.8e-259)
		tmp = y2 * (((k * t_5) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	elseif (y0 <= 5.5e-209)
		tmp = t_6 + (a * (t_3 + t_7));
	elseif (y0 <= 4.8e-130)
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	elseif (y0 <= 1.15e+77)
		tmp = t_6 + (y5 * ((i * ((y * k) - (t * j))) + (a * t_2)));
	elseif (y0 <= 5e+139)
		tmp = t_4 * (c * y0);
	elseif (y0 <= 8e+265)
		tmp = t_6 + (a * (t_3 + (t_7 + (y1 * ((z * y3) - (x * y2))))));
	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[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y5 * t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -3.7e+184], N[(y0 * N[(N[(N[(c * t$95$4), $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], If[LessEqual[y0, -2e+17], N[(x * N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -7.4e-112], N[(t$95$6 + N[(a * N[(N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -4.8e-259], N[(y2 * N[(N[(N[(k * t$95$5), $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[y0, 5.5e-209], N[(t$95$6 + N[(a * N[(t$95$3 + t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.8e-130], 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], If[LessEqual[y0, 1.15e+77], N[(t$95$6 + N[(y5 * N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 5e+139], N[(t$95$4 * N[(c * y0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 8e+265], N[(t$95$6 + N[(a * N[(t$95$3 + N[(t$95$7 + N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y0 < -3.6999999999999997e184

   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 y0 around inf 70.4%

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

      1. sub-neg 70.4%

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

      2. +-commutative 70.4%

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

      3. mul-1-neg 70.4%

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

      4. +-commutative 70.4%

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

      5. mul-1-neg 70.4%

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

      6. unsub-neg 70.4%

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

      7. *-commutative 70.4%

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

      8. *-commutative 70.4%

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

   4. Simplified 70.4%

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

   if -3.6999999999999997e184 < y0 < -2e17

   1. Initial program 11.4%

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

   2. Taylor expanded in y2 around inf 31.8%

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

      1. sub-neg 31.8%

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

      2. +-commutative 31.8%

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

      3. mul-1-neg 31.8%

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

      4. fma-def 31.8%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 31.8%

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

      6. +-commutative 31.8%

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

      7. sub-neg 31.8%

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

      8. *-commutative 31.8%

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

   4. Simplified 31.8%

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

   5. Taylor expanded in x around inf 49.5%

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

      1. *-commutative 49.5%

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

      2. *-commutative 49.5%

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

   7. Simplified 49.5%

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

   if -2e17 < y0 < -7.3999999999999996e-112

   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 a around inf 56.0%

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

      1. sub-neg 56.0%

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

      2. +-commutative 56.0%

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

      3. mul-1-neg 56.0%

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

      4. unsub-neg 56.0%

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

      5. *-commutative 56.0%

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

      6. *-commutative 56.0%

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

      7. mul-1-neg 56.0%

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

      8. remove-double-neg 56.0%

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

      9. *-commutative 56.0%

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

   4. Simplified 56.0%

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

   5. Taylor expanded in y1 around 0 60.4%

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

   6. Taylor expanded in x around inf 60.6%

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

      1. associate-*r* 61.0%

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

   8. Simplified 61.0%

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

   if -7.3999999999999996e-112 < y0 < -4.8000000000000001e-259

   1. Initial program 39.0%

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

   2. Taylor expanded in y2 around inf 54.9%

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

   if -4.8000000000000001e-259 < y0 < 5.5000000000000001e-209

   1. Initial program 37.6%

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

   2. Taylor expanded in a around inf 53.4%

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

      1. sub-neg 53.4%

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

      2. +-commutative 53.4%

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

      3. mul-1-neg 53.4%

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

      4. unsub-neg 53.4%

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

      5. *-commutative 53.4%

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

      6. *-commutative 53.4%

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

      7. mul-1-neg 53.4%

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

      8. remove-double-neg 53.4%

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

      9. *-commutative 53.4%

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

   4. Simplified 53.4%

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

   5. Taylor expanded in y1 around 0 59.6%

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

   if 5.5000000000000001e-209 < y0 < 4.79999999999999993e-130

   1. Initial program 17.6%

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

   2. Taylor expanded in j around inf 65.1%

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

      1. +-commutative 65.1%

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

      2. mul-1-neg 65.1%

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

      3. unsub-neg 65.1%

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

      4. *-commutative 65.1%

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

   4. Simplified 65.1%

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

   if 4.79999999999999993e-130 < y0 < 1.14999999999999997e77

   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 y5 around -inf 59.1%

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

   if 1.14999999999999997e77 < y0 < 5.0000000000000003e139

   1. Initial program 23.1%

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

   2. Taylor expanded in y0 around inf 46.2%

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

      1. sub-neg 46.2%

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

      2. +-commutative 46.2%

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

      3. mul-1-neg 46.2%

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

      4. +-commutative 46.2%

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

      5. mul-1-neg 46.2%

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

      6. unsub-neg 46.2%

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

      7. *-commutative 46.2%

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

      8. *-commutative 46.2%

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

   4. Simplified 46.2%

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

   5. Taylor expanded in c around inf 62.3%

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

      1. associate-*r* 62.3%

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

      2. *-commutative 62.3%

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

   7. Simplified 62.3%

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

   if 5.0000000000000003e139 < y0 < 8.00000000000000053e265

   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 a around inf 63.2%

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

      1. sub-neg 63.2%

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

      2. +-commutative 63.2%

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

      3. mul-1-neg 63.2%

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

      4. unsub-neg 63.2%

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

      5. *-commutative 63.2%

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

      6. *-commutative 63.2%

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

      7. mul-1-neg 63.2%

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

      8. remove-double-neg 63.2%

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

      9. *-commutative 63.2%

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

   4. Simplified 63.2%

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

   if 8.00000000000000053e265 < y0

   1. Initial program 25.0%

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

   2. Taylor expanded in k around -inf 42.0%

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

      1. mul-1-neg 42.0%

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

      2. *-commutative 42.0%

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

      3. distribute-rgt-neg-in 42.0%

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

      4. +-commutative 42.0%

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

      5. mul-1-neg 42.0%

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

      6. unsub-neg 42.0%

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

      7. *-commutative 42.0%

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

   4. Simplified 42.0%

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

   5. Taylor expanded in b around inf 75.5%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -3.7 \cdot 10^{+184}:\\ \;\;\;\;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}\;y0 \leq -2 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq -7.4 \cdot 10^{-112}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + a \cdot \left(y \cdot \left(x \cdot b\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -4.8 \cdot 10^{-259}:\\ \;\;\;\;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}\;y0 \leq 5.5 \cdot 10^{-209}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y0 \leq 4.8 \cdot 10^{-130}:\\ \;\;\;\;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}\;y0 \leq 1.15 \cdot 10^{+77}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 5 \cdot 10^{+139}:\\ \;\;\;\;\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0\right)\\ \mathbf{elif}\;y0 \leq 8 \cdot 10^{+265}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(b \cdot \left(x \cdot y - z \cdot t\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \end{array} \]

Alternative 4: 39.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := y2 \cdot t_1\\ t_3 := k \cdot y2 - j \cdot y3\\ t_4 := t \cdot j - y \cdot k\\ t_5 := y1 \cdot y4 - y0 \cdot y5\\ t_6 := t_3 \cdot t_5\\ t_7 := a \cdot y5 - c \cdot y4\\ t_8 := t \cdot y2 - y \cdot y3\\ t_9 := y5 \cdot \left(a \cdot t_8 - \left(i \cdot t_4 + y0 \cdot t_3\right)\right)\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+237}:\\ \;\;\;\;t_6 + \left(x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + t_2\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right) + t_8 \cdot t_7\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{+127}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t_4 + y1 \cdot t_3\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-32}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot t_5 + x \cdot t_1\right) + t \cdot t_7\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-209}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-303}:\\ \;\;\;\;t_6 + t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot t_7\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-200}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-72}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+194}:\\ \;\;\;\;t_6 + a \cdot \left(y5 \cdot t_8 + b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1)))
        (t_2 (* y2 t_1))
        (t_3 (- (* k y2) (* j y3)))
        (t_4 (- (* t j) (* y k)))
        (t_5 (- (* y1 y4) (* y0 y5)))
        (t_6 (* t_3 t_5))
        (t_7 (- (* a y5) (* c y4)))
        (t_8 (- (* t y2) (* y y3)))
        (t_9 (* y5 (- (* a t_8) (+ (* i t_4) (* y0 t_3))))))
   (if (<= x -2.1e+237)
     (+
      t_6
      (+
       (* x (+ (+ (* y (- (* a b) (* c i))) t_2) (* j (- (* i y1) (* b y0)))))
       (* t_8 t_7)))
     (if (<= x -8.5e+127)
       (* y4 (+ (+ (* b t_4) (* y1 t_3)) (* c (- (* y y3) (* t y2)))))
       (if (<= x -2.6e-32)
         (* y2 (+ (+ (* k t_5) (* x t_1)) (* t t_7)))
         (if (<= x -8e-209)
           t_9
           (if (<= x -1.55e-303)
             (+
              t_6
              (*
               t
               (+
                (+ (* j (- (* b y4) (* i y5))) (* z (- (* c i) (* a b))))
                (* y2 t_7))))
             (if (<= x 3.5e-200)
               (*
                y3
                (+
                 (* y (- (* c y4) (* a y5)))
                 (+
                  (* j (- (* y0 y5) (* y1 y4)))
                  (* z (- (* a y1) (* c y0))))))
               (if (<= x 3.7e-72)
                 t_9
                 (if (<= x 2.6e+194)
                   (+ t_6 (* a (+ (* y5 t_8) (* b (- (* x y) (* z t))))))
                   (* x 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 * y0) - (a * y1);
	double t_2 = y2 * t_1;
	double t_3 = (k * y2) - (j * y3);
	double t_4 = (t * j) - (y * k);
	double t_5 = (y1 * y4) - (y0 * y5);
	double t_6 = t_3 * t_5;
	double t_7 = (a * y5) - (c * y4);
	double t_8 = (t * y2) - (y * y3);
	double t_9 = y5 * ((a * t_8) - ((i * t_4) + (y0 * t_3)));
	double tmp;
	if (x <= -2.1e+237) {
		tmp = t_6 + ((x * (((y * ((a * b) - (c * i))) + t_2) + (j * ((i * y1) - (b * y0))))) + (t_8 * t_7));
	} else if (x <= -8.5e+127) {
		tmp = y4 * (((b * t_4) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))));
	} else if (x <= -2.6e-32) {
		tmp = y2 * (((k * t_5) + (x * t_1)) + (t * t_7));
	} else if (x <= -8e-209) {
		tmp = t_9;
	} else if (x <= -1.55e-303) {
		tmp = t_6 + (t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * t_7)));
	} else if (x <= 3.5e-200) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else if (x <= 3.7e-72) {
		tmp = t_9;
	} else if (x <= 2.6e+194) {
		tmp = t_6 + (a * ((y5 * t_8) + (b * ((x * y) - (z * t)))));
	} else {
		tmp = x * 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) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (c * y0) - (a * y1)
    t_2 = y2 * t_1
    t_3 = (k * y2) - (j * y3)
    t_4 = (t * j) - (y * k)
    t_5 = (y1 * y4) - (y0 * y5)
    t_6 = t_3 * t_5
    t_7 = (a * y5) - (c * y4)
    t_8 = (t * y2) - (y * y3)
    t_9 = y5 * ((a * t_8) - ((i * t_4) + (y0 * t_3)))
    if (x <= (-2.1d+237)) then
        tmp = t_6 + ((x * (((y * ((a * b) - (c * i))) + t_2) + (j * ((i * y1) - (b * y0))))) + (t_8 * t_7))
    else if (x <= (-8.5d+127)) then
        tmp = y4 * (((b * t_4) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))))
    else if (x <= (-2.6d-32)) then
        tmp = y2 * (((k * t_5) + (x * t_1)) + (t * t_7))
    else if (x <= (-8d-209)) then
        tmp = t_9
    else if (x <= (-1.55d-303)) then
        tmp = t_6 + (t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * t_7)))
    else if (x <= 3.5d-200) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
    else if (x <= 3.7d-72) then
        tmp = t_9
    else if (x <= 2.6d+194) then
        tmp = t_6 + (a * ((y5 * t_8) + (b * ((x * y) - (z * t)))))
    else
        tmp = x * 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 * y0) - (a * y1);
	double t_2 = y2 * t_1;
	double t_3 = (k * y2) - (j * y3);
	double t_4 = (t * j) - (y * k);
	double t_5 = (y1 * y4) - (y0 * y5);
	double t_6 = t_3 * t_5;
	double t_7 = (a * y5) - (c * y4);
	double t_8 = (t * y2) - (y * y3);
	double t_9 = y5 * ((a * t_8) - ((i * t_4) + (y0 * t_3)));
	double tmp;
	if (x <= -2.1e+237) {
		tmp = t_6 + ((x * (((y * ((a * b) - (c * i))) + t_2) + (j * ((i * y1) - (b * y0))))) + (t_8 * t_7));
	} else if (x <= -8.5e+127) {
		tmp = y4 * (((b * t_4) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))));
	} else if (x <= -2.6e-32) {
		tmp = y2 * (((k * t_5) + (x * t_1)) + (t * t_7));
	} else if (x <= -8e-209) {
		tmp = t_9;
	} else if (x <= -1.55e-303) {
		tmp = t_6 + (t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * t_7)));
	} else if (x <= 3.5e-200) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else if (x <= 3.7e-72) {
		tmp = t_9;
	} else if (x <= 2.6e+194) {
		tmp = t_6 + (a * ((y5 * t_8) + (b * ((x * y) - (z * t)))));
	} else {
		tmp = x * 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 * y0) - (a * y1)
	t_2 = y2 * t_1
	t_3 = (k * y2) - (j * y3)
	t_4 = (t * j) - (y * k)
	t_5 = (y1 * y4) - (y0 * y5)
	t_6 = t_3 * t_5
	t_7 = (a * y5) - (c * y4)
	t_8 = (t * y2) - (y * y3)
	t_9 = y5 * ((a * t_8) - ((i * t_4) + (y0 * t_3)))
	tmp = 0
	if x <= -2.1e+237:
		tmp = t_6 + ((x * (((y * ((a * b) - (c * i))) + t_2) + (j * ((i * y1) - (b * y0))))) + (t_8 * t_7))
	elif x <= -8.5e+127:
		tmp = y4 * (((b * t_4) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))))
	elif x <= -2.6e-32:
		tmp = y2 * (((k * t_5) + (x * t_1)) + (t * t_7))
	elif x <= -8e-209:
		tmp = t_9
	elif x <= -1.55e-303:
		tmp = t_6 + (t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * t_7)))
	elif x <= 3.5e-200:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
	elif x <= 3.7e-72:
		tmp = t_9
	elif x <= 2.6e+194:
		tmp = t_6 + (a * ((y5 * t_8) + (b * ((x * y) - (z * t)))))
	else:
		tmp = x * 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 * y0) - Float64(a * y1))
	t_2 = Float64(y2 * t_1)
	t_3 = Float64(Float64(k * y2) - Float64(j * y3))
	t_4 = Float64(Float64(t * j) - Float64(y * k))
	t_5 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_6 = Float64(t_3 * t_5)
	t_7 = Float64(Float64(a * y5) - Float64(c * y4))
	t_8 = Float64(Float64(t * y2) - Float64(y * y3))
	t_9 = Float64(y5 * Float64(Float64(a * t_8) - Float64(Float64(i * t_4) + Float64(y0 * t_3))))
	tmp = 0.0
	if (x <= -2.1e+237)
		tmp = Float64(t_6 + Float64(Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + t_2) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0))))) + Float64(t_8 * t_7)));
	elseif (x <= -8.5e+127)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_4) + Float64(y1 * t_3)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (x <= -2.6e-32)
		tmp = Float64(y2 * Float64(Float64(Float64(k * t_5) + Float64(x * t_1)) + Float64(t * t_7)));
	elseif (x <= -8e-209)
		tmp = t_9;
	elseif (x <= -1.55e-303)
		tmp = Float64(t_6 + Float64(t * Float64(Float64(Float64(j * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(z * Float64(Float64(c * i) - Float64(a * b)))) + Float64(y2 * t_7))));
	elseif (x <= 3.5e-200)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (x <= 3.7e-72)
		tmp = t_9;
	elseif (x <= 2.6e+194)
		tmp = Float64(t_6 + Float64(a * Float64(Float64(y5 * t_8) + Float64(b * Float64(Float64(x * y) - Float64(z * t))))));
	else
		tmp = Float64(x * 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 * y0) - (a * y1);
	t_2 = y2 * t_1;
	t_3 = (k * y2) - (j * y3);
	t_4 = (t * j) - (y * k);
	t_5 = (y1 * y4) - (y0 * y5);
	t_6 = t_3 * t_5;
	t_7 = (a * y5) - (c * y4);
	t_8 = (t * y2) - (y * y3);
	t_9 = y5 * ((a * t_8) - ((i * t_4) + (y0 * t_3)));
	tmp = 0.0;
	if (x <= -2.1e+237)
		tmp = t_6 + ((x * (((y * ((a * b) - (c * i))) + t_2) + (j * ((i * y1) - (b * y0))))) + (t_8 * t_7));
	elseif (x <= -8.5e+127)
		tmp = y4 * (((b * t_4) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))));
	elseif (x <= -2.6e-32)
		tmp = y2 * (((k * t_5) + (x * t_1)) + (t * t_7));
	elseif (x <= -8e-209)
		tmp = t_9;
	elseif (x <= -1.55e-303)
		tmp = t_6 + (t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * t_7)));
	elseif (x <= 3.5e-200)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	elseif (x <= 3.7e-72)
		tmp = t_9;
	elseif (x <= 2.6e+194)
		tmp = t_6 + (a * ((y5 * t_8) + (b * ((x * y) - (z * t)))));
	else
		tmp = x * 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 * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y2 * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$3 * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(y5 * N[(N[(a * t$95$8), $MachinePrecision] - N[(N[(i * t$95$4), $MachinePrecision] + N[(y0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.1e+237], N[(t$95$6 + N[(N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$8 * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8.5e+127], N[(y4 * N[(N[(N[(b * t$95$4), $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[x, -2.6e-32], N[(y2 * N[(N[(N[(k * t$95$5), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8e-209], t$95$9, If[LessEqual[x, -1.55e-303], N[(t$95$6 + N[(t * N[(N[(N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e-200], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $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[x, 3.7e-72], t$95$9, If[LessEqual[x, 2.6e+194], N[(t$95$6 + N[(a * N[(N[(y5 * t$95$8), $MachinePrecision] + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * t$95$2), $MachinePrecision]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if x < -2.10000000000000015e237

   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 x around inf 73.3%

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

   if -2.10000000000000015e237 < x < -8.4999999999999997e127

   1. Initial program 20.0%

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

   2. Taylor expanded in y4 around inf 68.0%

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

   if -8.4999999999999997e127 < x < -2.5999999999999997e-32

   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 y2 around inf 58.8%

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

   if -2.5999999999999997e-32 < x < -8.0000000000000004e-209 or 3.50000000000000023e-200 < x < 3.6999999999999998e-72

   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 y5 around -inf 62.3%

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

   if -8.0000000000000004e-209 < x < -1.55e-303

   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 t around inf 60.6%

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

      1. +-commutative 60.6%

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

      2. mul-1-neg 60.6%

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

      3. unsub-neg 60.6%

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

      4. *-commutative 60.6%

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

   4. Simplified 60.6%

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

   if -1.55e-303 < x < 3.50000000000000023e-200

   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 y3 around -inf 66.7%

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

   if 3.6999999999999998e-72 < x < 2.5999999999999999e194

   1. Initial program 22.9%

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

   2. Taylor expanded in a around inf 48.4%

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

      1. sub-neg 48.4%

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

      2. +-commutative 48.4%

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

      3. mul-1-neg 48.4%

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

      4. unsub-neg 48.4%

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

      5. *-commutative 48.4%

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

      6. *-commutative 48.4%

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

      7. mul-1-neg 48.4%

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

      8. remove-double-neg 48.4%

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

      9. *-commutative 48.4%

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

   4. Simplified 48.4%

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

   5. Taylor expanded in y1 around 0 57.0%

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

   if 2.5999999999999999e194 < x

   1. Initial program 20.3%

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

   2. Taylor expanded in y2 around inf 40.6%

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

      1. sub-neg 40.6%

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

      2. +-commutative 40.6%

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

      3. mul-1-neg 40.6%

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

      4. fma-def 44.6%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 44.6%

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

      6. +-commutative 44.6%

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

      7. sub-neg 44.6%

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

      8. *-commutative 44.6%

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

   4. Simplified 44.6%

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

   5. Taylor expanded in x around inf 60.5%

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

      1. *-commutative 60.5%

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

      2. *-commutative 60.5%

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

   7. Simplified 60.5%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(y0 \cdot c - y1 \cdot a\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+237}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{+127}:\\ \;\;\;\;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}\;x \leq -2.6 \cdot 10^{-32}:\\ \;\;\;\;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}\;x \leq -8 \cdot 10^{-209}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - \left(i \cdot \left(t \cdot j - y \cdot k\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-303}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-200}:\\ \;\;\;\;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}\;x \leq 3.7 \cdot 10^{-72}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - \left(i \cdot \left(t \cdot j - y \cdot k\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+194}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \]

Alternative 5: 39.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot y2 - y \cdot y3\\ t_2 := t \cdot j - y \cdot k\\ t_3 := k \cdot y2 - j \cdot y3\\ t_4 := y5 \cdot \left(a \cdot t_1 - \left(i \cdot t_2 + y0 \cdot t_3\right)\right)\\ t_5 := y1 \cdot y4 - y0 \cdot y5\\ t_6 := t_3 \cdot t_5\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{+235}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(y \cdot b - y1 \cdot y2\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{+127}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t_2 + y1 \cdot t_3\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+65}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot t_3 + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-32}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot t_5 + c \cdot \left(x \cdot y0\right)\right) - c \cdot \left(t \cdot y4\right)\right) + a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -1.18 \cdot 10^{-209}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-303}:\\ \;\;\;\;t_6 + t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-193}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-71}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+194}:\\ \;\;\;\;t_6 + a \cdot \left(y5 \cdot t_1 + b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* t y2) (* y y3)))
        (t_2 (- (* t j) (* y k)))
        (t_3 (- (* k y2) (* j y3)))
        (t_4 (* y5 (- (* a t_1) (+ (* i t_2) (* y0 t_3)))))
        (t_5 (- (* y1 y4) (* y0 y5)))
        (t_6 (* t_3 t_5)))
   (if (<= x -1.45e+235)
     (* (* x a) (- (* y b) (* y1 y2)))
     (if (<= x -8e+127)
       (* y4 (+ (+ (* b t_2) (* y1 t_3)) (* c (- (* y y3) (* t y2)))))
       (if (<= x -5e+65)
         (*
          y1
          (+
           (* i (- (* x j) (* z k)))
           (+ (* y4 t_3) (* a (- (* z y3) (* x y2))))))
         (if (<= x -7e-32)
           (+
            (* y2 (- (+ (* k t_5) (* c (* x y0))) (* c (* t y4))))
            (* a (* y2 (- (* t y5) (* x y1)))))
           (if (<= x -1.18e-209)
             t_4
             (if (<= x -1.6e-303)
               (+
                t_6
                (*
                 t
                 (+
                  (+ (* j (- (* b y4) (* i y5))) (* z (- (* c i) (* a b))))
                  (* y2 (- (* a y5) (* c y4))))))
               (if (<= x 3e-193)
                 (*
                  y3
                  (+
                   (* y (- (* c y4) (* a y5)))
                   (+
                    (* j (- (* y0 y5) (* y1 y4)))
                    (* z (- (* a y1) (* c y0))))))
                 (if (<= x 3.8e-71)
                   t_4
                   (if (<= x 1.9e+194)
                     (+ t_6 (* a (+ (* y5 t_1) (* b (- (* x y) (* z t))))))
                     (* x (* y2 (- (* c y0) (* a 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 t_1 = (t * y2) - (y * y3);
	double t_2 = (t * j) - (y * k);
	double t_3 = (k * y2) - (j * y3);
	double t_4 = y5 * ((a * t_1) - ((i * t_2) + (y0 * t_3)));
	double t_5 = (y1 * y4) - (y0 * y5);
	double t_6 = t_3 * t_5;
	double tmp;
	if (x <= -1.45e+235) {
		tmp = (x * a) * ((y * b) - (y1 * y2));
	} else if (x <= -8e+127) {
		tmp = y4 * (((b * t_2) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))));
	} else if (x <= -5e+65) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_3) + (a * ((z * y3) - (x * y2)))));
	} else if (x <= -7e-32) {
		tmp = (y2 * (((k * t_5) + (c * (x * y0))) - (c * (t * y4)))) + (a * (y2 * ((t * y5) - (x * y1))));
	} else if (x <= -1.18e-209) {
		tmp = t_4;
	} else if (x <= -1.6e-303) {
		tmp = t_6 + (t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4)))));
	} else if (x <= 3e-193) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else if (x <= 3.8e-71) {
		tmp = t_4;
	} else if (x <= 1.9e+194) {
		tmp = t_6 + (a * ((y5 * t_1) + (b * ((x * y) - (z * t)))));
	} else {
		tmp = x * (y2 * ((c * y0) - (a * 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = (t * y2) - (y * y3)
    t_2 = (t * j) - (y * k)
    t_3 = (k * y2) - (j * y3)
    t_4 = y5 * ((a * t_1) - ((i * t_2) + (y0 * t_3)))
    t_5 = (y1 * y4) - (y0 * y5)
    t_6 = t_3 * t_5
    if (x <= (-1.45d+235)) then
        tmp = (x * a) * ((y * b) - (y1 * y2))
    else if (x <= (-8d+127)) then
        tmp = y4 * (((b * t_2) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))))
    else if (x <= (-5d+65)) then
        tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_3) + (a * ((z * y3) - (x * y2)))))
    else if (x <= (-7d-32)) then
        tmp = (y2 * (((k * t_5) + (c * (x * y0))) - (c * (t * y4)))) + (a * (y2 * ((t * y5) - (x * y1))))
    else if (x <= (-1.18d-209)) then
        tmp = t_4
    else if (x <= (-1.6d-303)) then
        tmp = t_6 + (t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4)))))
    else if (x <= 3d-193) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
    else if (x <= 3.8d-71) then
        tmp = t_4
    else if (x <= 1.9d+194) then
        tmp = t_6 + (a * ((y5 * t_1) + (b * ((x * y) - (z * t)))))
    else
        tmp = x * (y2 * ((c * y0) - (a * 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 t_1 = (t * y2) - (y * y3);
	double t_2 = (t * j) - (y * k);
	double t_3 = (k * y2) - (j * y3);
	double t_4 = y5 * ((a * t_1) - ((i * t_2) + (y0 * t_3)));
	double t_5 = (y1 * y4) - (y0 * y5);
	double t_6 = t_3 * t_5;
	double tmp;
	if (x <= -1.45e+235) {
		tmp = (x * a) * ((y * b) - (y1 * y2));
	} else if (x <= -8e+127) {
		tmp = y4 * (((b * t_2) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))));
	} else if (x <= -5e+65) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_3) + (a * ((z * y3) - (x * y2)))));
	} else if (x <= -7e-32) {
		tmp = (y2 * (((k * t_5) + (c * (x * y0))) - (c * (t * y4)))) + (a * (y2 * ((t * y5) - (x * y1))));
	} else if (x <= -1.18e-209) {
		tmp = t_4;
	} else if (x <= -1.6e-303) {
		tmp = t_6 + (t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4)))));
	} else if (x <= 3e-193) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else if (x <= 3.8e-71) {
		tmp = t_4;
	} else if (x <= 1.9e+194) {
		tmp = t_6 + (a * ((y5 * t_1) + (b * ((x * y) - (z * t)))));
	} else {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (t * y2) - (y * y3)
	t_2 = (t * j) - (y * k)
	t_3 = (k * y2) - (j * y3)
	t_4 = y5 * ((a * t_1) - ((i * t_2) + (y0 * t_3)))
	t_5 = (y1 * y4) - (y0 * y5)
	t_6 = t_3 * t_5
	tmp = 0
	if x <= -1.45e+235:
		tmp = (x * a) * ((y * b) - (y1 * y2))
	elif x <= -8e+127:
		tmp = y4 * (((b * t_2) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))))
	elif x <= -5e+65:
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_3) + (a * ((z * y3) - (x * y2)))))
	elif x <= -7e-32:
		tmp = (y2 * (((k * t_5) + (c * (x * y0))) - (c * (t * y4)))) + (a * (y2 * ((t * y5) - (x * y1))))
	elif x <= -1.18e-209:
		tmp = t_4
	elif x <= -1.6e-303:
		tmp = t_6 + (t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4)))))
	elif x <= 3e-193:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
	elif x <= 3.8e-71:
		tmp = t_4
	elif x <= 1.9e+194:
		tmp = t_6 + (a * ((y5 * t_1) + (b * ((x * y) - (z * t)))))
	else:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * y2) - Float64(y * y3))
	t_2 = Float64(Float64(t * j) - Float64(y * k))
	t_3 = Float64(Float64(k * y2) - Float64(j * y3))
	t_4 = Float64(y5 * Float64(Float64(a * t_1) - Float64(Float64(i * t_2) + Float64(y0 * t_3))))
	t_5 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_6 = Float64(t_3 * t_5)
	tmp = 0.0
	if (x <= -1.45e+235)
		tmp = Float64(Float64(x * a) * Float64(Float64(y * b) - Float64(y1 * y2)));
	elseif (x <= -8e+127)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_2) + Float64(y1 * t_3)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (x <= -5e+65)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(y4 * t_3) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2))))));
	elseif (x <= -7e-32)
		tmp = Float64(Float64(y2 * Float64(Float64(Float64(k * t_5) + Float64(c * Float64(x * y0))) - Float64(c * Float64(t * y4)))) + Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1)))));
	elseif (x <= -1.18e-209)
		tmp = t_4;
	elseif (x <= -1.6e-303)
		tmp = Float64(t_6 + Float64(t * Float64(Float64(Float64(j * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(z * Float64(Float64(c * i) - Float64(a * b)))) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))))));
	elseif (x <= 3e-193)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (x <= 3.8e-71)
		tmp = t_4;
	elseif (x <= 1.9e+194)
		tmp = Float64(t_6 + Float64(a * Float64(Float64(y5 * t_1) + Float64(b * Float64(Float64(x * y) - Float64(z * t))))));
	else
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * 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)
	t_1 = (t * y2) - (y * y3);
	t_2 = (t * j) - (y * k);
	t_3 = (k * y2) - (j * y3);
	t_4 = y5 * ((a * t_1) - ((i * t_2) + (y0 * t_3)));
	t_5 = (y1 * y4) - (y0 * y5);
	t_6 = t_3 * t_5;
	tmp = 0.0;
	if (x <= -1.45e+235)
		tmp = (x * a) * ((y * b) - (y1 * y2));
	elseif (x <= -8e+127)
		tmp = y4 * (((b * t_2) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))));
	elseif (x <= -5e+65)
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_3) + (a * ((z * y3) - (x * y2)))));
	elseif (x <= -7e-32)
		tmp = (y2 * (((k * t_5) + (c * (x * y0))) - (c * (t * y4)))) + (a * (y2 * ((t * y5) - (x * y1))));
	elseif (x <= -1.18e-209)
		tmp = t_4;
	elseif (x <= -1.6e-303)
		tmp = t_6 + (t * (((j * ((b * y4) - (i * y5))) + (z * ((c * i) - (a * b)))) + (y2 * ((a * y5) - (c * y4)))));
	elseif (x <= 3e-193)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	elseif (x <= 3.8e-71)
		tmp = t_4;
	elseif (x <= 1.9e+194)
		tmp = t_6 + (a * ((y5 * t_1) + (b * ((x * y) - (z * t)))));
	else
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y5 * N[(N[(a * t$95$1), $MachinePrecision] - N[(N[(i * t$95$2), $MachinePrecision] + N[(y0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$3 * t$95$5), $MachinePrecision]}, If[LessEqual[x, -1.45e+235], N[(N[(x * a), $MachinePrecision] * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8e+127], N[(y4 * N[(N[(N[(b * t$95$2), $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[x, -5e+65], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y4 * t$95$3), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7e-32], N[(N[(y2 * N[(N[(N[(k * t$95$5), $MachinePrecision] + N[(c * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.18e-209], t$95$4, If[LessEqual[x, -1.6e-303], N[(t$95$6 + N[(t * N[(N[(N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e-193], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $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[x, 3.8e-71], t$95$4, If[LessEqual[x, 1.9e+194], N[(t$95$6 + N[(a * N[(N[(y5 * t$95$1), $MachinePrecision] + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if x < -1.45000000000000011e235

   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 a around inf 41.0%

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

      1. sub-neg 41.0%

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

      2. +-commutative 41.0%

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

      3. mul-1-neg 41.0%

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

      4. unsub-neg 41.0%

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

      5. *-commutative 41.0%

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

      6. *-commutative 41.0%

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

      7. mul-1-neg 41.0%

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

      8. remove-double-neg 41.0%

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

      9. *-commutative 41.0%

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

   4. Simplified 41.0%

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

   5. Taylor expanded in x around inf 54.5%

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

      1. associate-*r* 60.8%

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

      2. *-commutative 60.8%

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

   7. Simplified 60.8%

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

   if -1.45000000000000011e235 < x < -7.99999999999999964e127

   1. Initial program 20.0%

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

   2. Taylor expanded in y4 around inf 68.0%

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

   if -7.99999999999999964e127 < x < -4.99999999999999973e65

   1. Initial program 22.2%

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

   2. Taylor expanded in y1 around -inf 67.3%

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

      1. mul-1-neg 67.3%

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

      2. distribute-rgt-neg-in 67.3%

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

      3. sub-neg 67.3%

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

      4. +-commutative 67.3%

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

      5. mul-1-neg 67.3%

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

   4. Simplified 67.3%

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

   if -4.99999999999999973e65 < x < -6.9999999999999997e-32

   1. Initial program 25.0%

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

   2. Taylor expanded in y2 around inf 60.1%

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

      1. sub-neg 60.1%

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

      2. +-commutative 60.1%

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

      3. mul-1-neg 60.1%

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

      4. fma-def 60.1%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 60.1%

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

      6. +-commutative 60.1%

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

      7. sub-neg 60.1%

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

      8. *-commutative 60.1%

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

   4. Simplified 60.1%

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

   5. Taylor expanded in a around -inf 60.1%

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

   if -6.9999999999999997e-32 < x < -1.18e-209 or 2.9999999999999999e-193 < x < 3.79999999999999992e-71

   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 y5 around -inf 62.3%

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

   if -1.18e-209 < x < -1.59999999999999995e-303

   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 t around inf 60.6%

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

      1. +-commutative 60.6%

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

      2. mul-1-neg 60.6%

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

      3. unsub-neg 60.6%

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

      4. *-commutative 60.6%

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

   4. Simplified 60.6%

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

   if -1.59999999999999995e-303 < x < 2.9999999999999999e-193

   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 y3 around -inf 66.7%

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

   if 3.79999999999999992e-71 < x < 1.8999999999999999e194

   1. Initial program 22.9%

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

   2. Taylor expanded in a around inf 48.4%

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

      1. sub-neg 48.4%

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

      2. +-commutative 48.4%

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

      3. mul-1-neg 48.4%

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

      4. unsub-neg 48.4%

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

      5. *-commutative 48.4%

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

      6. *-commutative 48.4%

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

      7. mul-1-neg 48.4%

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

      8. remove-double-neg 48.4%

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

      9. *-commutative 48.4%

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

   4. Simplified 48.4%

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

   5. Taylor expanded in y1 around 0 57.0%

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

   if 1.8999999999999999e194 < x

   1. Initial program 20.3%

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

   2. Taylor expanded in y2 around inf 40.6%

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

      1. sub-neg 40.6%

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

      2. +-commutative 40.6%

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

      3. mul-1-neg 40.6%

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

      4. fma-def 44.6%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 44.6%

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

      6. +-commutative 44.6%

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

      7. sub-neg 44.6%

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

      8. *-commutative 44.6%

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

   4. Simplified 44.6%

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

   5. Taylor expanded in x around inf 60.5%

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

      1. *-commutative 60.5%

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

      2. *-commutative 60.5%

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

   7. Simplified 60.5%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(y0 \cdot c - y1 \cdot a\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+235}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(y \cdot b - y1 \cdot y2\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{+127}:\\ \;\;\;\;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}\;x \leq -5 \cdot 10^{+65}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-32}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + c \cdot \left(x \cdot y0\right)\right) - c \cdot \left(t \cdot y4\right)\right) + a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -1.18 \cdot 10^{-209}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - \left(i \cdot \left(t \cdot j - y \cdot k\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-303}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + z \cdot \left(c \cdot i - a \cdot b\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-193}:\\ \;\;\;\;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}\;x \leq 3.8 \cdot 10^{-71}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - \left(i \cdot \left(t \cdot j - y \cdot k\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+194}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \]

Alternative 6: 39.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot y2 - y \cdot y3\\ t_2 := t \cdot j - y \cdot k\\ t_3 := k \cdot y2 - j \cdot y3\\ t_4 := y5 \cdot \left(a \cdot t_1 - \left(i \cdot t_2 + y0 \cdot t_3\right)\right)\\ t_5 := x \cdot y - z \cdot t\\ t_6 := y1 \cdot y4 - y0 \cdot y5\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+232}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(y \cdot b - y1 \cdot y2\right)\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{+127}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t_2 + y1 \cdot t_3\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{+68}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot t_3 + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-32}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot t_6 + c \cdot \left(x \cdot y0\right)\right) - c \cdot \left(t \cdot y4\right)\right) + a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-210}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -8.8 \cdot 10^{-289}:\\ \;\;\;\;b \cdot \left(\left(a \cdot t_5 + y4 \cdot t_2\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{-200}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-70}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+194}:\\ \;\;\;\;t_3 \cdot t_6 + a \cdot \left(y5 \cdot t_1 + b \cdot t_5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* t y2) (* y y3)))
        (t_2 (- (* t j) (* y k)))
        (t_3 (- (* k y2) (* j y3)))
        (t_4 (* y5 (- (* a t_1) (+ (* i t_2) (* y0 t_3)))))
        (t_5 (- (* x y) (* z t)))
        (t_6 (- (* y1 y4) (* y0 y5))))
   (if (<= x -4.5e+232)
     (* (* x a) (- (* y b) (* y1 y2)))
     (if (<= x -7.8e+127)
       (* y4 (+ (+ (* b t_2) (* y1 t_3)) (* c (- (* y y3) (* t y2)))))
       (if (<= x -5.2e+68)
         (*
          y1
          (+
           (* i (- (* x j) (* z k)))
           (+ (* y4 t_3) (* a (- (* z y3) (* x y2))))))
         (if (<= x -1.55e-32)
           (+
            (* y2 (- (+ (* k t_6) (* c (* x y0))) (* c (* t y4))))
            (* a (* y2 (- (* t y5) (* x y1)))))
           (if (<= x -5.3e-210)
             t_4
             (if (<= x -8.8e-289)
               (* b (+ (+ (* a t_5) (* y4 t_2)) (* y0 (- (* z k) (* x j)))))
               (if (<= x 4.9e-200)
                 (*
                  y3
                  (+
                   (* y (- (* c y4) (* a y5)))
                   (+
                    (* j (- (* y0 y5) (* y1 y4)))
                    (* z (- (* a y1) (* c y0))))))
                 (if (<= x 8.8e-70)
                   t_4
                   (if (<= x 6.2e+194)
                     (+ (* t_3 t_6) (* a (+ (* y5 t_1) (* b t_5))))
                     (* x (* y2 (- (* c y0) (* a 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 t_1 = (t * y2) - (y * y3);
	double t_2 = (t * j) - (y * k);
	double t_3 = (k * y2) - (j * y3);
	double t_4 = y5 * ((a * t_1) - ((i * t_2) + (y0 * t_3)));
	double t_5 = (x * y) - (z * t);
	double t_6 = (y1 * y4) - (y0 * y5);
	double tmp;
	if (x <= -4.5e+232) {
		tmp = (x * a) * ((y * b) - (y1 * y2));
	} else if (x <= -7.8e+127) {
		tmp = y4 * (((b * t_2) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))));
	} else if (x <= -5.2e+68) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_3) + (a * ((z * y3) - (x * y2)))));
	} else if (x <= -1.55e-32) {
		tmp = (y2 * (((k * t_6) + (c * (x * y0))) - (c * (t * y4)))) + (a * (y2 * ((t * y5) - (x * y1))));
	} else if (x <= -5.3e-210) {
		tmp = t_4;
	} else if (x <= -8.8e-289) {
		tmp = b * (((a * t_5) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	} else if (x <= 4.9e-200) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else if (x <= 8.8e-70) {
		tmp = t_4;
	} else if (x <= 6.2e+194) {
		tmp = (t_3 * t_6) + (a * ((y5 * t_1) + (b * t_5)));
	} else {
		tmp = x * (y2 * ((c * y0) - (a * 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = (t * y2) - (y * y3)
    t_2 = (t * j) - (y * k)
    t_3 = (k * y2) - (j * y3)
    t_4 = y5 * ((a * t_1) - ((i * t_2) + (y0 * t_3)))
    t_5 = (x * y) - (z * t)
    t_6 = (y1 * y4) - (y0 * y5)
    if (x <= (-4.5d+232)) then
        tmp = (x * a) * ((y * b) - (y1 * y2))
    else if (x <= (-7.8d+127)) then
        tmp = y4 * (((b * t_2) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))))
    else if (x <= (-5.2d+68)) then
        tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_3) + (a * ((z * y3) - (x * y2)))))
    else if (x <= (-1.55d-32)) then
        tmp = (y2 * (((k * t_6) + (c * (x * y0))) - (c * (t * y4)))) + (a * (y2 * ((t * y5) - (x * y1))))
    else if (x <= (-5.3d-210)) then
        tmp = t_4
    else if (x <= (-8.8d-289)) then
        tmp = b * (((a * t_5) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))))
    else if (x <= 4.9d-200) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
    else if (x <= 8.8d-70) then
        tmp = t_4
    else if (x <= 6.2d+194) then
        tmp = (t_3 * t_6) + (a * ((y5 * t_1) + (b * t_5)))
    else
        tmp = x * (y2 * ((c * y0) - (a * 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 t_1 = (t * y2) - (y * y3);
	double t_2 = (t * j) - (y * k);
	double t_3 = (k * y2) - (j * y3);
	double t_4 = y5 * ((a * t_1) - ((i * t_2) + (y0 * t_3)));
	double t_5 = (x * y) - (z * t);
	double t_6 = (y1 * y4) - (y0 * y5);
	double tmp;
	if (x <= -4.5e+232) {
		tmp = (x * a) * ((y * b) - (y1 * y2));
	} else if (x <= -7.8e+127) {
		tmp = y4 * (((b * t_2) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))));
	} else if (x <= -5.2e+68) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_3) + (a * ((z * y3) - (x * y2)))));
	} else if (x <= -1.55e-32) {
		tmp = (y2 * (((k * t_6) + (c * (x * y0))) - (c * (t * y4)))) + (a * (y2 * ((t * y5) - (x * y1))));
	} else if (x <= -5.3e-210) {
		tmp = t_4;
	} else if (x <= -8.8e-289) {
		tmp = b * (((a * t_5) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	} else if (x <= 4.9e-200) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else if (x <= 8.8e-70) {
		tmp = t_4;
	} else if (x <= 6.2e+194) {
		tmp = (t_3 * t_6) + (a * ((y5 * t_1) + (b * t_5)));
	} else {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (t * y2) - (y * y3)
	t_2 = (t * j) - (y * k)
	t_3 = (k * y2) - (j * y3)
	t_4 = y5 * ((a * t_1) - ((i * t_2) + (y0 * t_3)))
	t_5 = (x * y) - (z * t)
	t_6 = (y1 * y4) - (y0 * y5)
	tmp = 0
	if x <= -4.5e+232:
		tmp = (x * a) * ((y * b) - (y1 * y2))
	elif x <= -7.8e+127:
		tmp = y4 * (((b * t_2) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))))
	elif x <= -5.2e+68:
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_3) + (a * ((z * y3) - (x * y2)))))
	elif x <= -1.55e-32:
		tmp = (y2 * (((k * t_6) + (c * (x * y0))) - (c * (t * y4)))) + (a * (y2 * ((t * y5) - (x * y1))))
	elif x <= -5.3e-210:
		tmp = t_4
	elif x <= -8.8e-289:
		tmp = b * (((a * t_5) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))))
	elif x <= 4.9e-200:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
	elif x <= 8.8e-70:
		tmp = t_4
	elif x <= 6.2e+194:
		tmp = (t_3 * t_6) + (a * ((y5 * t_1) + (b * t_5)))
	else:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * y2) - Float64(y * y3))
	t_2 = Float64(Float64(t * j) - Float64(y * k))
	t_3 = Float64(Float64(k * y2) - Float64(j * y3))
	t_4 = Float64(y5 * Float64(Float64(a * t_1) - Float64(Float64(i * t_2) + Float64(y0 * t_3))))
	t_5 = Float64(Float64(x * y) - Float64(z * t))
	t_6 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	tmp = 0.0
	if (x <= -4.5e+232)
		tmp = Float64(Float64(x * a) * Float64(Float64(y * b) - Float64(y1 * y2)));
	elseif (x <= -7.8e+127)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_2) + Float64(y1 * t_3)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (x <= -5.2e+68)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(y4 * t_3) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2))))));
	elseif (x <= -1.55e-32)
		tmp = Float64(Float64(y2 * Float64(Float64(Float64(k * t_6) + Float64(c * Float64(x * y0))) - Float64(c * Float64(t * y4)))) + Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1)))));
	elseif (x <= -5.3e-210)
		tmp = t_4;
	elseif (x <= -8.8e-289)
		tmp = Float64(b * Float64(Float64(Float64(a * t_5) + Float64(y4 * t_2)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (x <= 4.9e-200)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (x <= 8.8e-70)
		tmp = t_4;
	elseif (x <= 6.2e+194)
		tmp = Float64(Float64(t_3 * t_6) + Float64(a * Float64(Float64(y5 * t_1) + Float64(b * t_5))));
	else
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * 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)
	t_1 = (t * y2) - (y * y3);
	t_2 = (t * j) - (y * k);
	t_3 = (k * y2) - (j * y3);
	t_4 = y5 * ((a * t_1) - ((i * t_2) + (y0 * t_3)));
	t_5 = (x * y) - (z * t);
	t_6 = (y1 * y4) - (y0 * y5);
	tmp = 0.0;
	if (x <= -4.5e+232)
		tmp = (x * a) * ((y * b) - (y1 * y2));
	elseif (x <= -7.8e+127)
		tmp = y4 * (((b * t_2) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))));
	elseif (x <= -5.2e+68)
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_3) + (a * ((z * y3) - (x * y2)))));
	elseif (x <= -1.55e-32)
		tmp = (y2 * (((k * t_6) + (c * (x * y0))) - (c * (t * y4)))) + (a * (y2 * ((t * y5) - (x * y1))));
	elseif (x <= -5.3e-210)
		tmp = t_4;
	elseif (x <= -8.8e-289)
		tmp = b * (((a * t_5) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	elseif (x <= 4.9e-200)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	elseif (x <= 8.8e-70)
		tmp = t_4;
	elseif (x <= 6.2e+194)
		tmp = (t_3 * t_6) + (a * ((y5 * t_1) + (b * t_5)));
	else
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y5 * N[(N[(a * t$95$1), $MachinePrecision] - N[(N[(i * t$95$2), $MachinePrecision] + N[(y0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.5e+232], N[(N[(x * a), $MachinePrecision] * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.8e+127], N[(y4 * N[(N[(N[(b * t$95$2), $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[x, -5.2e+68], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y4 * t$95$3), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.55e-32], N[(N[(y2 * N[(N[(N[(k * t$95$6), $MachinePrecision] + N[(c * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.3e-210], t$95$4, If[LessEqual[x, -8.8e-289], N[(b * N[(N[(N[(a * t$95$5), $MachinePrecision] + N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.9e-200], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $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[x, 8.8e-70], t$95$4, If[LessEqual[x, 6.2e+194], N[(N[(t$95$3 * t$95$6), $MachinePrecision] + N[(a * N[(N[(y5 * t$95$1), $MachinePrecision] + N[(b * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if x < -4.4999999999999998e232

   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 a around inf 41.0%

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

      1. sub-neg 41.0%

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

      2. +-commutative 41.0%

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

      3. mul-1-neg 41.0%

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

      4. unsub-neg 41.0%

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

      5. *-commutative 41.0%

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

      6. *-commutative 41.0%

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

      7. mul-1-neg 41.0%

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

      8. remove-double-neg 41.0%

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

      9. *-commutative 41.0%

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

   4. Simplified 41.0%

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

   5. Taylor expanded in x around inf 54.5%

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

      1. associate-*r* 60.8%

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

      2. *-commutative 60.8%

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

   7. Simplified 60.8%

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

   if -4.4999999999999998e232 < x < -7.79999999999999962e127

   1. Initial program 20.0%

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

   2. Taylor expanded in y4 around inf 68.0%

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

   if -7.79999999999999962e127 < x < -5.1999999999999996e68

   1. Initial program 22.2%

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

   2. Taylor expanded in y1 around -inf 67.3%

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

      1. mul-1-neg 67.3%

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

      2. distribute-rgt-neg-in 67.3%

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

      3. sub-neg 67.3%

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

      4. +-commutative 67.3%

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

      5. mul-1-neg 67.3%

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

   4. Simplified 67.3%

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

   if -5.1999999999999996e68 < x < -1.55000000000000005e-32

   1. Initial program 25.0%

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

   2. Taylor expanded in y2 around inf 60.1%

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

      1. sub-neg 60.1%

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

      2. +-commutative 60.1%

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

      3. mul-1-neg 60.1%

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

      4. fma-def 60.1%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 60.1%

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

      6. +-commutative 60.1%

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

      7. sub-neg 60.1%

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

      8. *-commutative 60.1%

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

   4. Simplified 60.1%

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

   5. Taylor expanded in a around -inf 60.1%

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

   if -1.55000000000000005e-32 < x < -5.3000000000000001e-210 or 4.9e-200 < x < 8.7999999999999996e-70

   1. Initial program 41.2%

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

   2. Taylor expanded in y5 around -inf 61.1%

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

   if -5.3000000000000001e-210 < x < -8.7999999999999999e-289

   1. Initial program 44.3%

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

   3. Simplified 44.3%

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

   4. Taylor expanded in b around inf 62.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)} \]

   if -8.7999999999999999e-289 < x < 4.9e-200

   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 y3 around -inf 60.6%

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

   if 8.7999999999999996e-70 < x < 6.1999999999999999e194

   1. Initial program 22.9%

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

   2. Taylor expanded in a around inf 48.4%

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

      1. sub-neg 48.4%

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

      2. +-commutative 48.4%

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

      3. mul-1-neg 48.4%

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

      4. unsub-neg 48.4%

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

      5. *-commutative 48.4%

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

      6. *-commutative 48.4%

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

      7. mul-1-neg 48.4%

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

      8. remove-double-neg 48.4%

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

      9. *-commutative 48.4%

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

   4. Simplified 48.4%

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

   5. Taylor expanded in y1 around 0 57.0%

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

   if 6.1999999999999999e194 < x

   1. Initial program 20.3%

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

   2. Taylor expanded in y2 around inf 40.6%

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

      1. sub-neg 40.6%

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

      2. +-commutative 40.6%

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

      3. mul-1-neg 40.6%

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

      4. fma-def 44.6%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 44.6%

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

      6. +-commutative 44.6%

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

      7. sub-neg 44.6%

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

      8. *-commutative 44.6%

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

   4. Simplified 44.6%

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

   5. Taylor expanded in x around inf 60.5%

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

      1. *-commutative 60.5%

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

      2. *-commutative 60.5%

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

   7. Simplified 60.5%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(y0 \cdot c - y1 \cdot a\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+232}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(y \cdot b - y1 \cdot y2\right)\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{+127}:\\ \;\;\;\;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}\;x \leq -5.2 \cdot 10^{+68}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-32}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + c \cdot \left(x \cdot y0\right)\right) - c \cdot \left(t \cdot y4\right)\right) + a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-210}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - \left(i \cdot \left(t \cdot j - y \cdot k\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;x \leq -8.8 \cdot 10^{-289}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{-200}:\\ \;\;\;\;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}\;x \leq 8.8 \cdot 10^{-70}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - \left(i \cdot \left(t \cdot j - y \cdot k\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+194}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \]

Alternative 7: 38.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - \left(i \cdot \left(t \cdot j - y \cdot k\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ t_2 := y \cdot \left(c \cdot y4 - a \cdot y5\right)\\ t_3 := c \cdot y0 - a \cdot y1\\ t_4 := y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot t_3\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ t_5 := y0 \cdot y5 - y1 \cdot y4\\ t_6 := j \cdot t_5\\ t_7 := y3 \cdot \left(t_2 + t_6\right)\\ \mathbf{if}\;b \leq -3.7 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -4.15 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-199}:\\ \;\;\;\;x \cdot \left(y2 \cdot t_3\right)\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-290}:\\ \;\;\;\;y3 \cdot \left(t_2 + \left(t_6 + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-275}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-255}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;b \leq 7.1 \cdot 10^{-214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-148}:\\ \;\;\;\;\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-8}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 8.3 \cdot 10^{+37}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{+98}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot t_5\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y5
          (-
           (* a (- (* t y2) (* y y3)))
           (+ (* i (- (* t j) (* y k))) (* y0 (- (* k y2) (* j y3)))))))
        (t_2 (* y (- (* c y4) (* a y5))))
        (t_3 (- (* c y0) (* a y1)))
        (t_4
         (*
          y2
          (+
           (+ (* k (- (* y1 y4) (* y0 y5))) (* x t_3))
           (* t (- (* a y5) (* c y4))))))
        (t_5 (- (* y0 y5) (* y1 y4)))
        (t_6 (* j t_5))
        (t_7 (* y3 (+ t_2 t_6))))
   (if (<= b -3.7e+81)
     (* b (* j (- (* t y4) (* x y0))))
     (if (<= b -4.15e-122)
       t_1
       (if (<= b -1.95e-199)
         (* x (* y2 t_3))
         (if (<= b -6.5e-290)
           (* y3 (+ t_2 (+ t_6 (* z (- (* a y1) (* c y0))))))
           (if (<= b 7.2e-275)
             t_4
             (if (<= b 1.75e-255)
               t_7
               (if (<= b 7.1e-214)
                 t_1
                 (if (<= b 2e-148)
                   (* (- (* x y2) (* z y3)) (* c y0))
                   (if (<= b 8.5e-8)
                     t_4
                     (if (<= b 8.3e+37)
                       t_7
                       (if (<= b 2.35e+98)
                         (*
                          j
                          (+
                           (+ (* t (- (* b y4) (* i y5))) (* y3 t_5))
                           (* x (- (* i y1) (* b y0)))))
                         (* a (* b (- (* x y) (* z t)))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y5 * ((a * ((t * y2) - (y * y3))) - ((i * ((t * j) - (y * k))) + (y0 * ((k * y2) - (j * y3)))));
	double t_2 = y * ((c * y4) - (a * y5));
	double t_3 = (c * y0) - (a * y1);
	double t_4 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_3)) + (t * ((a * y5) - (c * y4))));
	double t_5 = (y0 * y5) - (y1 * y4);
	double t_6 = j * t_5;
	double t_7 = y3 * (t_2 + t_6);
	double tmp;
	if (b <= -3.7e+81) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -4.15e-122) {
		tmp = t_1;
	} else if (b <= -1.95e-199) {
		tmp = x * (y2 * t_3);
	} else if (b <= -6.5e-290) {
		tmp = y3 * (t_2 + (t_6 + (z * ((a * y1) - (c * y0)))));
	} else if (b <= 7.2e-275) {
		tmp = t_4;
	} else if (b <= 1.75e-255) {
		tmp = t_7;
	} else if (b <= 7.1e-214) {
		tmp = t_1;
	} else if (b <= 2e-148) {
		tmp = ((x * y2) - (z * y3)) * (c * y0);
	} else if (b <= 8.5e-8) {
		tmp = t_4;
	} else if (b <= 8.3e+37) {
		tmp = t_7;
	} else if (b <= 2.35e+98) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * t_5)) + (x * ((i * y1) - (b * y0))));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: 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 = y5 * ((a * ((t * y2) - (y * y3))) - ((i * ((t * j) - (y * k))) + (y0 * ((k * y2) - (j * y3)))))
    t_2 = y * ((c * y4) - (a * y5))
    t_3 = (c * y0) - (a * y1)
    t_4 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_3)) + (t * ((a * y5) - (c * y4))))
    t_5 = (y0 * y5) - (y1 * y4)
    t_6 = j * t_5
    t_7 = y3 * (t_2 + t_6)
    if (b <= (-3.7d+81)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (b <= (-4.15d-122)) then
        tmp = t_1
    else if (b <= (-1.95d-199)) then
        tmp = x * (y2 * t_3)
    else if (b <= (-6.5d-290)) then
        tmp = y3 * (t_2 + (t_6 + (z * ((a * y1) - (c * y0)))))
    else if (b <= 7.2d-275) then
        tmp = t_4
    else if (b <= 1.75d-255) then
        tmp = t_7
    else if (b <= 7.1d-214) then
        tmp = t_1
    else if (b <= 2d-148) then
        tmp = ((x * y2) - (z * y3)) * (c * y0)
    else if (b <= 8.5d-8) then
        tmp = t_4
    else if (b <= 8.3d+37) then
        tmp = t_7
    else if (b <= 2.35d+98) then
        tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * t_5)) + (x * ((i * y1) - (b * y0))))
    else
        tmp = a * (b * ((x * y) - (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y5 * ((a * ((t * y2) - (y * y3))) - ((i * ((t * j) - (y * k))) + (y0 * ((k * y2) - (j * y3)))));
	double t_2 = y * ((c * y4) - (a * y5));
	double t_3 = (c * y0) - (a * y1);
	double t_4 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_3)) + (t * ((a * y5) - (c * y4))));
	double t_5 = (y0 * y5) - (y1 * y4);
	double t_6 = j * t_5;
	double t_7 = y3 * (t_2 + t_6);
	double tmp;
	if (b <= -3.7e+81) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -4.15e-122) {
		tmp = t_1;
	} else if (b <= -1.95e-199) {
		tmp = x * (y2 * t_3);
	} else if (b <= -6.5e-290) {
		tmp = y3 * (t_2 + (t_6 + (z * ((a * y1) - (c * y0)))));
	} else if (b <= 7.2e-275) {
		tmp = t_4;
	} else if (b <= 1.75e-255) {
		tmp = t_7;
	} else if (b <= 7.1e-214) {
		tmp = t_1;
	} else if (b <= 2e-148) {
		tmp = ((x * y2) - (z * y3)) * (c * y0);
	} else if (b <= 8.5e-8) {
		tmp = t_4;
	} else if (b <= 8.3e+37) {
		tmp = t_7;
	} else if (b <= 2.35e+98) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * t_5)) + (x * ((i * y1) - (b * y0))));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y5 * ((a * ((t * y2) - (y * y3))) - ((i * ((t * j) - (y * k))) + (y0 * ((k * y2) - (j * y3)))))
	t_2 = y * ((c * y4) - (a * y5))
	t_3 = (c * y0) - (a * y1)
	t_4 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_3)) + (t * ((a * y5) - (c * y4))))
	t_5 = (y0 * y5) - (y1 * y4)
	t_6 = j * t_5
	t_7 = y3 * (t_2 + t_6)
	tmp = 0
	if b <= -3.7e+81:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif b <= -4.15e-122:
		tmp = t_1
	elif b <= -1.95e-199:
		tmp = x * (y2 * t_3)
	elif b <= -6.5e-290:
		tmp = y3 * (t_2 + (t_6 + (z * ((a * y1) - (c * y0)))))
	elif b <= 7.2e-275:
		tmp = t_4
	elif b <= 1.75e-255:
		tmp = t_7
	elif b <= 7.1e-214:
		tmp = t_1
	elif b <= 2e-148:
		tmp = ((x * y2) - (z * y3)) * (c * y0)
	elif b <= 8.5e-8:
		tmp = t_4
	elif b <= 8.3e+37:
		tmp = t_7
	elif b <= 2.35e+98:
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * t_5)) + (x * ((i * y1) - (b * y0))))
	else:
		tmp = a * (b * ((x * y) - (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) - Float64(Float64(i * Float64(Float64(t * j) - Float64(y * k))) + Float64(y0 * Float64(Float64(k * y2) - Float64(j * y3))))))
	t_2 = Float64(y * Float64(Float64(c * y4) - Float64(a * y5)))
	t_3 = Float64(Float64(c * y0) - Float64(a * y1))
	t_4 = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * t_3)) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))))
	t_5 = Float64(Float64(y0 * y5) - Float64(y1 * y4))
	t_6 = Float64(j * t_5)
	t_7 = Float64(y3 * Float64(t_2 + t_6))
	tmp = 0.0
	if (b <= -3.7e+81)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (b <= -4.15e-122)
		tmp = t_1;
	elseif (b <= -1.95e-199)
		tmp = Float64(x * Float64(y2 * t_3));
	elseif (b <= -6.5e-290)
		tmp = Float64(y3 * Float64(t_2 + Float64(t_6 + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (b <= 7.2e-275)
		tmp = t_4;
	elseif (b <= 1.75e-255)
		tmp = t_7;
	elseif (b <= 7.1e-214)
		tmp = t_1;
	elseif (b <= 2e-148)
		tmp = Float64(Float64(Float64(x * y2) - Float64(z * y3)) * Float64(c * y0));
	elseif (b <= 8.5e-8)
		tmp = t_4;
	elseif (b <= 8.3e+37)
		tmp = t_7;
	elseif (b <= 2.35e+98)
		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)))));
	else
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y5 * ((a * ((t * y2) - (y * y3))) - ((i * ((t * j) - (y * k))) + (y0 * ((k * y2) - (j * y3)))));
	t_2 = y * ((c * y4) - (a * y5));
	t_3 = (c * y0) - (a * y1);
	t_4 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_3)) + (t * ((a * y5) - (c * y4))));
	t_5 = (y0 * y5) - (y1 * y4);
	t_6 = j * t_5;
	t_7 = y3 * (t_2 + t_6);
	tmp = 0.0;
	if (b <= -3.7e+81)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (b <= -4.15e-122)
		tmp = t_1;
	elseif (b <= -1.95e-199)
		tmp = x * (y2 * t_3);
	elseif (b <= -6.5e-290)
		tmp = y3 * (t_2 + (t_6 + (z * ((a * y1) - (c * y0)))));
	elseif (b <= 7.2e-275)
		tmp = t_4;
	elseif (b <= 1.75e-255)
		tmp = t_7;
	elseif (b <= 7.1e-214)
		tmp = t_1;
	elseif (b <= 2e-148)
		tmp = ((x * y2) - (z * y3)) * (c * y0);
	elseif (b <= 8.5e-8)
		tmp = t_4;
	elseif (b <= 8.3e+37)
		tmp = t_7;
	elseif (b <= 2.35e+98)
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * t_5)) + (x * ((i * y1) - (b * y0))));
	else
		tmp = a * (b * ((x * y) - (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(i * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(j * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(y3 * N[(t$95$2 + t$95$6), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.7e+81], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.15e-122], t$95$1, If[LessEqual[b, -1.95e-199], N[(x * N[(y2 * t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.5e-290], N[(y3 * N[(t$95$2 + N[(t$95$6 + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.2e-275], t$95$4, If[LessEqual[b, 1.75e-255], t$95$7, If[LessEqual[b, 7.1e-214], t$95$1, If[LessEqual[b, 2e-148], N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * N[(c * y0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e-8], t$95$4, If[LessEqual[b, 8.3e+37], t$95$7, If[LessEqual[b, 2.35e+98], 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], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if b < -3.7000000000000001e81

   1. Initial program 26.1%

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

   2. Taylor expanded in j around inf 35.1%

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

      1. +-commutative 35.1%

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

      2. mul-1-neg 35.1%

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

      3. unsub-neg 35.1%

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

      4. *-commutative 35.1%

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

   4. Simplified 35.1%

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

   5. Taylor expanded in b around inf 54.7%

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

   if -3.7000000000000001e81 < b < -4.1500000000000002e-122 or 1.74999999999999989e-255 < b < 7.1000000000000001e-214

   1. Initial program 29.0%

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

   2. Taylor expanded in y5 around -inf 63.9%

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

   if -4.1500000000000002e-122 < b < -1.9500000000000001e-199

   1. Initial program 47.1%

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

   2. Taylor expanded in y2 around inf 42.1%

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

      1. sub-neg 42.1%

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

      2. +-commutative 42.1%

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

      3. mul-1-neg 42.1%

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

      4. fma-def 48.0%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 48.0%

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

      6. +-commutative 48.0%

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

      7. sub-neg 48.0%

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

      8. *-commutative 48.0%

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

   4. Simplified 48.0%

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

   5. Taylor expanded in x around inf 71.2%

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

      1. *-commutative 71.2%

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

      2. *-commutative 71.2%

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

   7. Simplified 71.2%

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

   if -1.9500000000000001e-199 < b < -6.4999999999999997e-290

   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 y3 around -inf 69.7%

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

   if -6.4999999999999997e-290 < b < 7.1999999999999994e-275 or 1.99999999999999987e-148 < b < 8.49999999999999935e-8

   1. Initial program 23.8%

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

   2. Taylor expanded in y2 around inf 55.1%

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

   if 7.1999999999999994e-275 < b < 1.74999999999999989e-255 or 8.49999999999999935e-8 < b < 8.3e37

   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 j around inf 37.2%

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

      1. mul-1-neg 37.2%

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

      2. associate-*r* 37.2%

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

   4. Simplified 37.2%

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

   5. Taylor expanded in y3 around inf 74.4%

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

      1. distribute-lft-out-- 74.4%

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

      2. *-commutative 74.4%

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

      3. *-commutative 74.4%

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

      4. *-commutative 74.4%

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

      5. *-commutative 74.4%

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

   7. Simplified 74.4%

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

   if 7.1000000000000001e-214 < b < 1.99999999999999987e-148

   1. Initial program 43.8%

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

   2. Taylor expanded in y0 around inf 44.4%

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

      1. sub-neg 44.4%

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

      2. +-commutative 44.4%

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

      3. mul-1-neg 44.4%

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

      4. +-commutative 44.4%

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

      5. mul-1-neg 44.4%

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

      6. unsub-neg 44.4%

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

      7. *-commutative 44.4%

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

      8. *-commutative 44.4%

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

   4. Simplified 44.4%

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

   5. Taylor expanded in c around inf 45.3%

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

      1. associate-*r* 51.3%

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

      2. *-commutative 51.3%

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

   7. Simplified 51.3%

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

   if 8.3e37 < b < 2.34999999999999985e98

   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 j around inf 66.9%

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

      1. +-commutative 66.9%

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

      2. mul-1-neg 66.9%

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

      3. unsub-neg 66.9%

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

      4. *-commutative 66.9%

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

   4. Simplified 66.9%

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

   if 2.34999999999999985e98 < b

   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 a around inf 47.7%

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

      1. sub-neg 47.7%

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

      2. +-commutative 47.7%

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

      3. mul-1-neg 47.7%

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

      4. unsub-neg 47.7%

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

      5. *-commutative 47.7%

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

      6. *-commutative 47.7%

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

      7. mul-1-neg 47.7%

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

      8. remove-double-neg 47.7%

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

      9. *-commutative 47.7%

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

   4. Simplified 47.7%

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

   5. Taylor expanded in b around inf 65.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -4.15 \cdot 10^{-122}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - \left(i \cdot \left(t \cdot j - y \cdot k\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-199}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-290}:\\ \;\;\;\;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}\;b \leq 7.2 \cdot 10^{-275}:\\ \;\;\;\;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}\;b \leq 1.75 \cdot 10^{-255}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 7.1 \cdot 10^{-214}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - \left(i \cdot \left(t \cdot j - y \cdot k\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-148}:\\ \;\;\;\;\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-8}:\\ \;\;\;\;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}\;b \leq 8.3 \cdot 10^{+37}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{+98}:\\ \;\;\;\;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{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]

Alternative 8: 37.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := y1 \cdot y4 - y0 \cdot y5\\ t_3 := y2 \cdot \left(\left(k \cdot t_2 + x \cdot t_1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := t_4 \cdot t_2 + y2 \cdot \left(y5 \cdot \left(t \cdot a\right)\right)\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -2.45 \cdot 10^{-113}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{-197}:\\ \;\;\;\;x \cdot \left(y2 \cdot t_1\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-290}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-249}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-226}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot t_4 + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-137}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{-51}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{+109}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1)))
        (t_2 (- (* y1 y4) (* y0 y5)))
        (t_3 (* y2 (+ (+ (* k t_2) (* x t_1)) (* t (- (* a y5) (* c y4))))))
        (t_4 (- (* k y2) (* j y3)))
        (t_5 (+ (* t_4 t_2) (* y2 (* y5 (* t a))))))
   (if (<= b -1.4e+36)
     (* b (* j (- (* t y4) (* x y0))))
     (if (<= b -2.45e-113)
       (* a (* y2 (- (* t y5) (* x y1))))
       (if (<= b -6.6e-197)
         (* x (* y2 t_1))
         (if (<= b -2.7e-290)
           (*
            y3
            (+
             (* y (- (* c y4) (* a y5)))
             (+ (* j (- (* y0 y5) (* y1 y4))) (* z (- (* a y1) (* c y0))))))
           (if (<= b 2.8e-249)
             t_3
             (if (<= b 1.1e-226)
               (*
                y1
                (+
                 (* i (- (* x j) (* z k)))
                 (+ (* y4 t_4) (* a (- (* z y3) (* x y2))))))
               (if (<= b 3.9e-137)
                 t_5
                 (if (<= b 7.4e-51)
                   t_3
                   (if (<= b 5.4e+109)
                     t_5
                     (* a (* b (- (* x y) (* z t)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (y1 * y4) - (y0 * y5);
	double t_3 = y2 * (((k * t_2) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (t_4 * t_2) + (y2 * (y5 * (t * a)));
	double tmp;
	if (b <= -1.4e+36) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -2.45e-113) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (b <= -6.6e-197) {
		tmp = x * (y2 * t_1);
	} else if (b <= -2.7e-290) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else if (b <= 2.8e-249) {
		tmp = t_3;
	} else if (b <= 1.1e-226) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_4) + (a * ((z * y3) - (x * y2)))));
	} else if (b <= 3.9e-137) {
		tmp = t_5;
	} else if (b <= 7.4e-51) {
		tmp = t_3;
	} else if (b <= 5.4e+109) {
		tmp = t_5;
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (c * y0) - (a * y1)
    t_2 = (y1 * y4) - (y0 * y5)
    t_3 = y2 * (((k * t_2) + (x * t_1)) + (t * ((a * y5) - (c * y4))))
    t_4 = (k * y2) - (j * y3)
    t_5 = (t_4 * t_2) + (y2 * (y5 * (t * a)))
    if (b <= (-1.4d+36)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (b <= (-2.45d-113)) then
        tmp = a * (y2 * ((t * y5) - (x * y1)))
    else if (b <= (-6.6d-197)) then
        tmp = x * (y2 * t_1)
    else if (b <= (-2.7d-290)) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
    else if (b <= 2.8d-249) then
        tmp = t_3
    else if (b <= 1.1d-226) then
        tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_4) + (a * ((z * y3) - (x * y2)))))
    else if (b <= 3.9d-137) then
        tmp = t_5
    else if (b <= 7.4d-51) then
        tmp = t_3
    else if (b <= 5.4d+109) then
        tmp = t_5
    else
        tmp = a * (b * ((x * y) - (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (y1 * y4) - (y0 * y5);
	double t_3 = y2 * (((k * t_2) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (t_4 * t_2) + (y2 * (y5 * (t * a)));
	double tmp;
	if (b <= -1.4e+36) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -2.45e-113) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (b <= -6.6e-197) {
		tmp = x * (y2 * t_1);
	} else if (b <= -2.7e-290) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else if (b <= 2.8e-249) {
		tmp = t_3;
	} else if (b <= 1.1e-226) {
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_4) + (a * ((z * y3) - (x * y2)))));
	} else if (b <= 3.9e-137) {
		tmp = t_5;
	} else if (b <= 7.4e-51) {
		tmp = t_3;
	} else if (b <= 5.4e+109) {
		tmp = t_5;
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * y0) - (a * y1)
	t_2 = (y1 * y4) - (y0 * y5)
	t_3 = y2 * (((k * t_2) + (x * t_1)) + (t * ((a * y5) - (c * y4))))
	t_4 = (k * y2) - (j * y3)
	t_5 = (t_4 * t_2) + (y2 * (y5 * (t * a)))
	tmp = 0
	if b <= -1.4e+36:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif b <= -2.45e-113:
		tmp = a * (y2 * ((t * y5) - (x * y1)))
	elif b <= -6.6e-197:
		tmp = x * (y2 * t_1)
	elif b <= -2.7e-290:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
	elif b <= 2.8e-249:
		tmp = t_3
	elif b <= 1.1e-226:
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_4) + (a * ((z * y3) - (x * y2)))))
	elif b <= 3.9e-137:
		tmp = t_5
	elif b <= 7.4e-51:
		tmp = t_3
	elif b <= 5.4e+109:
		tmp = t_5
	else:
		tmp = a * (b * ((x * y) - (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y0) - Float64(a * y1))
	t_2 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_3 = Float64(y2 * Float64(Float64(Float64(k * t_2) + Float64(x * t_1)) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(Float64(t_4 * t_2) + Float64(y2 * Float64(y5 * Float64(t * a))))
	tmp = 0.0
	if (b <= -1.4e+36)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (b <= -2.45e-113)
		tmp = Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (b <= -6.6e-197)
		tmp = Float64(x * Float64(y2 * t_1));
	elseif (b <= -2.7e-290)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (b <= 2.8e-249)
		tmp = t_3;
	elseif (b <= 1.1e-226)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(y4 * t_4) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2))))));
	elseif (b <= 3.9e-137)
		tmp = t_5;
	elseif (b <= 7.4e-51)
		tmp = t_3;
	elseif (b <= 5.4e+109)
		tmp = t_5;
	else
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (c * y0) - (a * y1);
	t_2 = (y1 * y4) - (y0 * y5);
	t_3 = y2 * (((k * t_2) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	t_4 = (k * y2) - (j * y3);
	t_5 = (t_4 * t_2) + (y2 * (y5 * (t * a)));
	tmp = 0.0;
	if (b <= -1.4e+36)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (b <= -2.45e-113)
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	elseif (b <= -6.6e-197)
		tmp = x * (y2 * t_1);
	elseif (b <= -2.7e-290)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	elseif (b <= 2.8e-249)
		tmp = t_3;
	elseif (b <= 1.1e-226)
		tmp = y1 * ((i * ((x * j) - (z * k))) + ((y4 * t_4) + (a * ((z * y3) - (x * y2)))));
	elseif (b <= 3.9e-137)
		tmp = t_5;
	elseif (b <= 7.4e-51)
		tmp = t_3;
	elseif (b <= 5.4e+109)
		tmp = t_5;
	else
		tmp = a * (b * ((x * y) - (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y2 * N[(N[(N[(k * t$95$2), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$4 * t$95$2), $MachinePrecision] + N[(y2 * N[(y5 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.4e+36], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.45e-113], N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.6e-197], N[(x * N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.7e-290], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $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[b, 2.8e-249], t$95$3, If[LessEqual[b, 1.1e-226], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y4 * t$95$4), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.9e-137], t$95$5, If[LessEqual[b, 7.4e-51], t$95$3, If[LessEqual[b, 5.4e+109], t$95$5, N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if b < -1.4e36

   1. Initial program 27.7%

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

   2. Taylor expanded in j around inf 36.6%

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

      1. +-commutative 36.6%

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

      2. mul-1-neg 36.6%

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

      3. unsub-neg 36.6%

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

      4. *-commutative 36.6%

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

   4. Simplified 36.6%

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

   5. Taylor expanded in b around inf 55.7%

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

   if -1.4e36 < b < -2.4500000000000001e-113

   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 y2 around inf 47.1%

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

      1. sub-neg 47.1%

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

      2. +-commutative 47.1%

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

      3. mul-1-neg 47.1%

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

      4. fma-def 50.7%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 50.7%

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

      6. +-commutative 50.7%

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

      7. sub-neg 50.7%

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

      8. *-commutative 50.7%

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

   4. Simplified 50.7%

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

   5. Taylor expanded in a around -inf 50.9%

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

      1. associate-*r* 50.9%

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

      2. neg-mul-1 50.9%

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

      3. *-commutative 50.9%

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

      4. *-commutative 50.9%

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

   7. Simplified 50.9%

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

   if -2.4500000000000001e-113 < b < -6.5999999999999995e-197

   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 y2 around inf 37.7%

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

      1. sub-neg 37.7%

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

      2. +-commutative 37.7%

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

      3. mul-1-neg 37.7%

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

      4. fma-def 43.0%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 43.0%

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

      6. +-commutative 43.0%

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

      7. sub-neg 43.0%

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

      8. *-commutative 43.0%

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

   4. Simplified 43.0%

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

   5. Taylor expanded in x around inf 63.9%

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

      1. *-commutative 63.9%

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

      2. *-commutative 63.9%

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

   7. Simplified 63.9%

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

   if -6.5999999999999995e-197 < b < -2.69999999999999999e-290

   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 y3 around -inf 69.7%

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

   if -2.69999999999999999e-290 < b < 2.7999999999999999e-249 or 3.8999999999999999e-137 < b < 7.39999999999999946e-51

   1. Initial program 19.6%

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

   2. Taylor expanded in y2 around inf 55.1%

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

   if 2.7999999999999999e-249 < b < 1.1e-226

   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 y1 around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. mul-1-neg 100.0%

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

   4. Simplified 100.0%

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

   if 1.1e-226 < b < 3.8999999999999999e-137 or 7.39999999999999946e-51 < b < 5.40000000000000003e109

   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 a around inf 45.0%

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

      1. sub-neg 45.0%

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

      2. +-commutative 45.0%

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

      3. mul-1-neg 45.0%

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

      4. unsub-neg 45.0%

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

      5. *-commutative 45.0%

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

      6. *-commutative 45.0%

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

      7. mul-1-neg 45.0%

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

      8. remove-double-neg 45.0%

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

      9. *-commutative 45.0%

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

   4. Simplified 45.0%

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

   5. Taylor expanded in y1 around 0 52.6%

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

   6. Taylor expanded in y2 around inf 50.1%

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

      1. *-commutative 50.1%

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

      2. associate-*r* 53.0%

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

      3. associate-*r* 54.3%

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

      4. *-commutative 54.3%

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

      5. associate-*r* 57.1%

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

      6. *-commutative 57.1%

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

   8. Simplified 57.1%

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

   if 5.40000000000000003e109 < b

   1. Initial program 17.5%

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

   2. Taylor expanded in a around inf 45.6%

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

      1. sub-neg 45.6%

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

      2. +-commutative 45.6%

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

      3. mul-1-neg 45.6%

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

      4. unsub-neg 45.6%

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

      5. *-commutative 45.6%

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

      6. *-commutative 45.6%

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

      7. mul-1-neg 45.6%

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

      8. remove-double-neg 45.6%

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

      9. *-commutative 45.6%

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

   4. Simplified 45.6%

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

   5. Taylor expanded in b around inf 66.0%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -2.45 \cdot 10^{-113}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{-197}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-290}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-249}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-226}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-137}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y2 \cdot \left(y5 \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{-51}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{+109}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y2 \cdot \left(y5 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]

Alternative 9: 37.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := y1 \cdot y4 - y0 \cdot y5\\ t_3 := \left(k \cdot y2 - j \cdot y3\right) \cdot t_2 + a \cdot \left(y \cdot \left(x \cdot b\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;y0 \leq -3.5 \cdot 10^{+185}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -2.5 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(y2 \cdot t_1\right)\\ \mathbf{elif}\;y0 \leq -1.55 \cdot 10^{-111}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y0 \leq -3 \cdot 10^{-264}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot t_2 + x \cdot t_1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.4 \cdot 10^{-280}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq 4.5 \cdot 10^{-120}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 7 \cdot 10^{+266}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1)))
        (t_2 (- (* y1 y4) (* y0 y5)))
        (t_3
         (+
          (* (- (* k y2) (* j y3)) t_2)
          (* a (+ (* y (* x b)) (* y5 (- (* t y2) (* y y3))))))))
   (if (<= y0 -3.5e+185)
     (*
      y0
      (+
       (+ (* c (- (* x y2) (* z y3))) (* y5 (- (* j y3) (* k y2))))
       (* b (- (* z k) (* x j)))))
     (if (<= y0 -2.5e+17)
       (* x (* y2 t_1))
       (if (<= y0 -1.55e-111)
         t_3
         (if (<= y0 -3e-264)
           (* y2 (+ (+ (* k t_2) (* x t_1)) (* t (- (* a y5) (* c y4)))))
           (if (<= y0 1.4e-280)
             (* a (* t (- (* y2 y5) (* z b))))
             (if (<= y0 4.5e-120)
               (*
                y3
                (+
                 (* y (- (* c y4) (* a y5)))
                 (+
                  (* j (- (* y0 y5) (* y1 y4)))
                  (* z (- (* a y1) (* c y0))))))
               (if (<= y0 7e+266)
                 t_3
                 (* 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 = (c * y0) - (a * y1);
	double t_2 = (y1 * y4) - (y0 * y5);
	double t_3 = (((k * y2) - (j * y3)) * t_2) + (a * ((y * (x * b)) + (y5 * ((t * y2) - (y * y3)))));
	double tmp;
	if (y0 <= -3.5e+185) {
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	} else if (y0 <= -2.5e+17) {
		tmp = x * (y2 * t_1);
	} else if (y0 <= -1.55e-111) {
		tmp = t_3;
	} else if (y0 <= -3e-264) {
		tmp = y2 * (((k * t_2) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	} else if (y0 <= 1.4e-280) {
		tmp = a * (t * ((y2 * y5) - (z * b)));
	} else if (y0 <= 4.5e-120) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else if (y0 <= 7e+266) {
		tmp = t_3;
	} 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 = (c * y0) - (a * y1)
    t_2 = (y1 * y4) - (y0 * y5)
    t_3 = (((k * y2) - (j * y3)) * t_2) + (a * ((y * (x * b)) + (y5 * ((t * y2) - (y * y3)))))
    if (y0 <= (-3.5d+185)) then
        tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))))
    else if (y0 <= (-2.5d+17)) then
        tmp = x * (y2 * t_1)
    else if (y0 <= (-1.55d-111)) then
        tmp = t_3
    else if (y0 <= (-3d-264)) then
        tmp = y2 * (((k * t_2) + (x * t_1)) + (t * ((a * y5) - (c * y4))))
    else if (y0 <= 1.4d-280) then
        tmp = a * (t * ((y2 * y5) - (z * b)))
    else if (y0 <= 4.5d-120) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
    else if (y0 <= 7d+266) then
        tmp = t_3
    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 = (c * y0) - (a * y1);
	double t_2 = (y1 * y4) - (y0 * y5);
	double t_3 = (((k * y2) - (j * y3)) * t_2) + (a * ((y * (x * b)) + (y5 * ((t * y2) - (y * y3)))));
	double tmp;
	if (y0 <= -3.5e+185) {
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	} else if (y0 <= -2.5e+17) {
		tmp = x * (y2 * t_1);
	} else if (y0 <= -1.55e-111) {
		tmp = t_3;
	} else if (y0 <= -3e-264) {
		tmp = y2 * (((k * t_2) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	} else if (y0 <= 1.4e-280) {
		tmp = a * (t * ((y2 * y5) - (z * b)));
	} else if (y0 <= 4.5e-120) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	} else if (y0 <= 7e+266) {
		tmp = t_3;
	} 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 = (c * y0) - (a * y1)
	t_2 = (y1 * y4) - (y0 * y5)
	t_3 = (((k * y2) - (j * y3)) * t_2) + (a * ((y * (x * b)) + (y5 * ((t * y2) - (y * y3)))))
	tmp = 0
	if y0 <= -3.5e+185:
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))))
	elif y0 <= -2.5e+17:
		tmp = x * (y2 * t_1)
	elif y0 <= -1.55e-111:
		tmp = t_3
	elif y0 <= -3e-264:
		tmp = y2 * (((k * t_2) + (x * t_1)) + (t * ((a * y5) - (c * y4))))
	elif y0 <= 1.4e-280:
		tmp = a * (t * ((y2 * y5) - (z * b)))
	elif y0 <= 4.5e-120:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))))
	elif y0 <= 7e+266:
		tmp = t_3
	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(Float64(c * y0) - Float64(a * y1))
	t_2 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_3 = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * t_2) + Float64(a * Float64(Float64(y * Float64(x * b)) + Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))))
	tmp = 0.0
	if (y0 <= -3.5e+185)
		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)))));
	elseif (y0 <= -2.5e+17)
		tmp = Float64(x * Float64(y2 * t_1));
	elseif (y0 <= -1.55e-111)
		tmp = t_3;
	elseif (y0 <= -3e-264)
		tmp = Float64(y2 * Float64(Float64(Float64(k * t_2) + Float64(x * t_1)) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y0 <= 1.4e-280)
		tmp = Float64(a * Float64(t * Float64(Float64(y2 * y5) - Float64(z * b))));
	elseif (y0 <= 4.5e-120)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (y0 <= 7e+266)
		tmp = t_3;
	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 = (c * y0) - (a * y1);
	t_2 = (y1 * y4) - (y0 * y5);
	t_3 = (((k * y2) - (j * y3)) * t_2) + (a * ((y * (x * b)) + (y5 * ((t * y2) - (y * y3)))));
	tmp = 0.0;
	if (y0 <= -3.5e+185)
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	elseif (y0 <= -2.5e+17)
		tmp = x * (y2 * t_1);
	elseif (y0 <= -1.55e-111)
		tmp = t_3;
	elseif (y0 <= -3e-264)
		tmp = y2 * (((k * t_2) + (x * t_1)) + (t * ((a * y5) - (c * y4))));
	elseif (y0 <= 1.4e-280)
		tmp = a * (t * ((y2 * y5) - (z * b)));
	elseif (y0 <= 4.5e-120)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))));
	elseif (y0 <= 7e+266)
		tmp = t_3;
	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[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] + N[(a * N[(N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -3.5e+185], 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], If[LessEqual[y0, -2.5e+17], N[(x * N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.55e-111], t$95$3, If[LessEqual[y0, -3e-264], N[(y2 * N[(N[(N[(k * t$95$2), $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[y0, 1.4e-280], N[(a * N[(t * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.5e-120], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $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[y0, 7e+266], t$95$3, N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y0 < -3.50000000000000023e185

   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 y0 around inf 70.4%

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

      1. sub-neg 70.4%

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

      2. +-commutative 70.4%

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

      3. mul-1-neg 70.4%

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

      4. +-commutative 70.4%

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

      5. mul-1-neg 70.4%

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

      6. unsub-neg 70.4%

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

      7. *-commutative 70.4%

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

      8. *-commutative 70.4%

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

   4. Simplified 70.4%

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

   if -3.50000000000000023e185 < y0 < -2.5e17

   1. Initial program 11.4%

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

   2. Taylor expanded in y2 around inf 31.8%

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

      1. sub-neg 31.8%

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

      2. +-commutative 31.8%

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

      3. mul-1-neg 31.8%

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

      4. fma-def 31.8%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 31.8%

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

      6. +-commutative 31.8%

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

      7. sub-neg 31.8%

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

      8. *-commutative 31.8%

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

   4. Simplified 31.8%

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

   5. Taylor expanded in x around inf 49.5%

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

      1. *-commutative 49.5%

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

      2. *-commutative 49.5%

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

   7. Simplified 49.5%

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

   if -2.5e17 < y0 < -1.55000000000000007e-111 or 4.5e-120 < y0 < 7.0000000000000005e266

   1. Initial program 35.2%

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

   2. Taylor expanded in a around inf 54.1%

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

      1. sub-neg 54.1%

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

      2. +-commutative 54.1%

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

      3. mul-1-neg 54.1%

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

      4. unsub-neg 54.1%

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

      5. *-commutative 54.1%

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

      6. *-commutative 54.1%

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

      7. mul-1-neg 54.1%

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

      8. remove-double-neg 54.1%

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

      9. *-commutative 54.1%

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

   4. Simplified 54.1%

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

   5. Taylor expanded in y1 around 0 54.5%

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

   6. Taylor expanded in x around inf 52.5%

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

      1. associate-*r* 54.8%

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

   8. Simplified 54.8%

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

   if -1.55000000000000007e-111 < y0 < -3e-264

   1. Initial program 39.0%

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

   2. Taylor expanded in y2 around inf 54.9%

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

   if -3e-264 < y0 < 1.40000000000000009e-280

   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 a around inf 38.8%

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

      1. sub-neg 38.8%

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

      2. +-commutative 38.8%

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

      3. mul-1-neg 38.8%

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

      4. unsub-neg 38.8%

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

      5. *-commutative 38.8%

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

      6. *-commutative 38.8%

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

      7. mul-1-neg 38.8%

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

      8. remove-double-neg 38.8%

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

      9. *-commutative 38.8%

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

   4. Simplified 38.8%

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

   5. Taylor expanded in t around -inf 60.8%

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

      1. mul-1-neg 60.8%

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

      2. distribute-rgt-neg-in 60.8%

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

      3. +-commutative 60.8%

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

      4. mul-1-neg 60.8%

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

      5. unsub-neg 60.8%

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

   7. Simplified 60.8%

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

   if 1.40000000000000009e-280 < y0 < 4.5e-120

   1. Initial program 34.1%

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

   2. Taylor expanded in y3 around -inf 59.0%

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

   if 7.0000000000000005e266 < y0

   1. Initial program 25.0%

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

   2. Taylor expanded in k around -inf 42.0%

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

      1. mul-1-neg 42.0%

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

      2. *-commutative 42.0%

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

      3. distribute-rgt-neg-in 42.0%

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

      4. +-commutative 42.0%

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

      5. mul-1-neg 42.0%

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

      6. unsub-neg 42.0%

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

      7. *-commutative 42.0%

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

   4. Simplified 42.0%

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

   5. Taylor expanded in b around inf 75.5%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -3.5 \cdot 10^{+185}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -2.5 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq -1.55 \cdot 10^{-111}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + a \cdot \left(y \cdot \left(x \cdot b\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -3 \cdot 10^{-264}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.4 \cdot 10^{-280}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq 4.5 \cdot 10^{-120}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 7 \cdot 10^{+266}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + a \cdot \left(y \cdot \left(x \cdot b\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \end{array} \]

Alternative 10: 36.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y2 \cdot \left(y5 \cdot \left(t \cdot a\right)\right)\\ \mathbf{if}\;b \leq -6 \cdot 10^{+35}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-113}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -6.4 \cdot 10^{-199}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-259}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-50}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq 9.7 \cdot 10^{-35} \lor \neg \left(b \leq 1.5 \cdot 10^{+115}\right):\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (+
          (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5)))
          (* y2 (* y5 (* t a))))))
   (if (<= b -6e+35)
     (* b (* j (- (* t y4) (* x y0))))
     (if (<= b -2.8e-113)
       (* a (* y2 (- (* t y5) (* x y1))))
       (if (<= b -6.4e-199)
         (* x (* y2 (- (* c y0) (* a y1))))
         (if (<= b 6.8e-259)
           (* y3 (+ (* y (- (* c y4) (* a y5))) (* j (- (* y0 y5) (* y1 y4)))))
           (if (<= b 2.35e-153)
             t_1
             (if (<= b 1.4e-50)
               (*
                y0
                (+
                 (+ (* c (- (* x y2) (* z y3))) (* y5 (- (* j y3) (* k y2))))
                 (* b (- (* z k) (* x j)))))
               (if (or (<= b 9.7e-35) (not (<= b 1.5e+115)))
                 (* a (* b (- (* x y) (* z t))))
                 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (y2 * (y5 * (t * a)));
	double tmp;
	if (b <= -6e+35) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -2.8e-113) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (b <= -6.4e-199) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (b <= 6.8e-259) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	} else if (b <= 2.35e-153) {
		tmp = t_1;
	} else if (b <= 1.4e-50) {
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	} else if ((b <= 9.7e-35) || !(b <= 1.5e+115)) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (y2 * (y5 * (t * a)))
    if (b <= (-6d+35)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (b <= (-2.8d-113)) then
        tmp = a * (y2 * ((t * y5) - (x * y1)))
    else if (b <= (-6.4d-199)) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (b <= 6.8d-259) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))))
    else if (b <= 2.35d-153) then
        tmp = t_1
    else if (b <= 1.4d-50) then
        tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))))
    else if ((b <= 9.7d-35) .or. (.not. (b <= 1.5d+115))) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (y2 * (y5 * (t * a)));
	double tmp;
	if (b <= -6e+35) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -2.8e-113) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (b <= -6.4e-199) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (b <= 6.8e-259) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	} else if (b <= 2.35e-153) {
		tmp = t_1;
	} else if (b <= 1.4e-50) {
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	} else if ((b <= 9.7e-35) || !(b <= 1.5e+115)) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (y2 * (y5 * (t * a)))
	tmp = 0
	if b <= -6e+35:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif b <= -2.8e-113:
		tmp = a * (y2 * ((t * y5) - (x * y1)))
	elif b <= -6.4e-199:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif b <= 6.8e-259:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))))
	elif b <= 2.35e-153:
		tmp = t_1
	elif b <= 1.4e-50:
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))))
	elif (b <= 9.7e-35) or not (b <= 1.5e+115):
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(y2 * Float64(y5 * Float64(t * a))))
	tmp = 0.0
	if (b <= -6e+35)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (b <= -2.8e-113)
		tmp = Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (b <= -6.4e-199)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (b <= 6.8e-259)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4)))));
	elseif (b <= 2.35e-153)
		tmp = t_1;
	elseif (b <= 1.4e-50)
		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)))));
	elseif ((b <= 9.7e-35) || !(b <= 1.5e+115))
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (y2 * (y5 * (t * a)));
	tmp = 0.0;
	if (b <= -6e+35)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (b <= -2.8e-113)
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	elseif (b <= -6.4e-199)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (b <= 6.8e-259)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	elseif (b <= 2.35e-153)
		tmp = t_1;
	elseif (b <= 1.4e-50)
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * ((z * k) - (x * j))));
	elseif ((b <= 9.7e-35) || ~((b <= 1.5e+115)))
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(y5 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6e+35], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.8e-113], N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.4e-199], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.8e-259], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.35e-153], t$95$1, If[LessEqual[b, 1.4e-50], 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], If[Or[LessEqual[b, 9.7e-35], N[Not[LessEqual[b, 1.5e+115]], $MachinePrecision]], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -5.99999999999999981e35

   1. Initial program 27.7%

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

   2. Taylor expanded in j around inf 36.6%

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

      1. +-commutative 36.6%

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

      2. mul-1-neg 36.6%

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

      3. unsub-neg 36.6%

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

      4. *-commutative 36.6%

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

   4. Simplified 36.6%

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

   5. Taylor expanded in b around inf 55.7%

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

   if -5.99999999999999981e35 < b < -2.8e-113

   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 y2 around inf 47.1%

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

      1. sub-neg 47.1%

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

      2. +-commutative 47.1%

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

      3. mul-1-neg 47.1%

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

      4. fma-def 50.7%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 50.7%

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

      6. +-commutative 50.7%

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

      7. sub-neg 50.7%

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

      8. *-commutative 50.7%

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

   4. Simplified 50.7%

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

   5. Taylor expanded in a around -inf 50.9%

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

      1. associate-*r* 50.9%

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

      2. neg-mul-1 50.9%

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

      3. *-commutative 50.9%

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

      4. *-commutative 50.9%

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

   7. Simplified 50.9%

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

   if -2.8e-113 < b < -6.3999999999999999e-199

   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 y2 around inf 37.7%

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

      1. sub-neg 37.7%

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

      2. +-commutative 37.7%

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

      3. mul-1-neg 37.7%

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

      4. fma-def 43.0%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 43.0%

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

      6. +-commutative 43.0%

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

      7. sub-neg 43.0%

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

      8. *-commutative 43.0%

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

   4. Simplified 43.0%

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

   5. Taylor expanded in x around inf 63.9%

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

      1. *-commutative 63.9%

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

      2. *-commutative 63.9%

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

   7. Simplified 63.9%

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

   if -6.3999999999999999e-199 < b < 6.80000000000000024e-259

   1. Initial program 46.2%

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

   2. Taylor expanded in j around inf 52.6%

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

      1. mul-1-neg 52.6%

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

      2. associate-*r* 56.1%

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

   4. Simplified 56.1%

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

   5. Taylor expanded in y3 around inf 53.7%

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

      1. distribute-lft-out-- 53.7%

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

      2. *-commutative 53.7%

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

      3. *-commutative 53.7%

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

      4. *-commutative 53.7%

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

      5. *-commutative 53.7%

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

   7. Simplified 53.7%

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

   if 6.80000000000000024e-259 < b < 2.35e-153 or 9.70000000000000073e-35 < b < 1.5e115

   1. Initial program 34.3%

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

   2. Taylor expanded in a around inf 40.7%

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

      1. sub-neg 40.7%

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

      2. +-commutative 40.7%

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

      3. mul-1-neg 40.7%

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

      4. unsub-neg 40.7%

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

      5. *-commutative 40.7%

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

      6. *-commutative 40.7%

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

      7. mul-1-neg 40.7%

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

      8. remove-double-neg 40.7%

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

      9. *-commutative 40.7%

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

   4. Simplified 40.7%

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

   5. Taylor expanded in y1 around 0 48.9%

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

   6. Taylor expanded in y2 around inf 49.4%

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

      1. *-commutative 49.4%

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

      2. associate-*r* 54.0%

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

      3. associate-*r* 55.3%

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

      4. *-commutative 55.3%

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

      5. associate-*r* 58.4%

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

      6. *-commutative 58.4%

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

   8. Simplified 58.4%

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

   if 2.35e-153 < b < 1.3999999999999999e-50

   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 y0 around inf 42.0%

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

      1. sub-neg 42.0%

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

      2. +-commutative 42.0%

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

      3. mul-1-neg 42.0%

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

      4. +-commutative 42.0%

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

      5. mul-1-neg 42.0%

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

      6. unsub-neg 42.0%

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

      7. *-commutative 42.0%

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

      8. *-commutative 42.0%

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

   4. Simplified 42.0%

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

   if 1.3999999999999999e-50 < b < 9.70000000000000073e-35 or 1.5e115 < b

   1. Initial program 14.1%

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

   2. Taylor expanded in a around inf 50.6%

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

      1. sub-neg 50.6%

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

      2. +-commutative 50.6%

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

      3. mul-1-neg 50.6%

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

      4. unsub-neg 50.6%

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

      5. *-commutative 50.6%

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

      6. *-commutative 50.6%

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

      7. mul-1-neg 50.6%

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

      8. remove-double-neg 50.6%

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

      9. *-commutative 50.6%

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

   4. Simplified 50.6%

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

   5. Taylor expanded in b around inf 69.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+35}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-113}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -6.4 \cdot 10^{-199}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-259}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{-153}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y2 \cdot \left(y5 \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-50}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq 9.7 \cdot 10^{-35} \lor \neg \left(b \leq 1.5 \cdot 10^{+115}\right):\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y2 \cdot \left(y5 \cdot \left(t \cdot a\right)\right)\\ \end{array} \]

Alternative 11: 36.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot y4 - y0 \cdot y5\\ t_2 := \left(k \cdot y2 - j \cdot y3\right) \cdot t_1 + y2 \cdot \left(y5 \cdot \left(t \cdot a\right)\right)\\ t_3 := c \cdot y0 - a \cdot y1\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -3.75 \cdot 10^{-113}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-199}:\\ \;\;\;\;x \cdot \left(y2 \cdot t_3\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-259}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-137}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-50}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot t_1 + x \cdot t_3\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+112}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y1 y4) (* y0 y5)))
        (t_2 (+ (* (- (* k y2) (* j y3)) t_1) (* y2 (* y5 (* t a)))))
        (t_3 (- (* c y0) (* a y1))))
   (if (<= b -1.3e+36)
     (* b (* j (- (* t y4) (* x y0))))
     (if (<= b -3.75e-113)
       (* a (* y2 (- (* t y5) (* x y1))))
       (if (<= b -3.2e-199)
         (* x (* y2 t_3))
         (if (<= b 2.3e-259)
           (* y3 (+ (* y (- (* c y4) (* a y5))) (* j (- (* y0 y5) (* y1 y4)))))
           (if (<= b 4e-137)
             t_2
             (if (<= b 1.7e-50)
               (* y2 (+ (+ (* k t_1) (* x t_3)) (* t (- (* a y5) (* c y4)))))
               (if (<= b 3.5e+112) t_2 (* a (* b (- (* x y) (* z t)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double t_2 = (((k * y2) - (j * y3)) * t_1) + (y2 * (y5 * (t * a)));
	double t_3 = (c * y0) - (a * y1);
	double tmp;
	if (b <= -1.3e+36) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -3.75e-113) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (b <= -3.2e-199) {
		tmp = x * (y2 * t_3);
	} else if (b <= 2.3e-259) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	} else if (b <= 4e-137) {
		tmp = t_2;
	} else if (b <= 1.7e-50) {
		tmp = y2 * (((k * t_1) + (x * t_3)) + (t * ((a * y5) - (c * y4))));
	} else if (b <= 3.5e+112) {
		tmp = t_2;
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y1 * y4) - (y0 * y5)
    t_2 = (((k * y2) - (j * y3)) * t_1) + (y2 * (y5 * (t * a)))
    t_3 = (c * y0) - (a * y1)
    if (b <= (-1.3d+36)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (b <= (-3.75d-113)) then
        tmp = a * (y2 * ((t * y5) - (x * y1)))
    else if (b <= (-3.2d-199)) then
        tmp = x * (y2 * t_3)
    else if (b <= 2.3d-259) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))))
    else if (b <= 4d-137) then
        tmp = t_2
    else if (b <= 1.7d-50) then
        tmp = y2 * (((k * t_1) + (x * t_3)) + (t * ((a * y5) - (c * y4))))
    else if (b <= 3.5d+112) then
        tmp = t_2
    else
        tmp = a * (b * ((x * y) - (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double t_2 = (((k * y2) - (j * y3)) * t_1) + (y2 * (y5 * (t * a)));
	double t_3 = (c * y0) - (a * y1);
	double tmp;
	if (b <= -1.3e+36) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -3.75e-113) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (b <= -3.2e-199) {
		tmp = x * (y2 * t_3);
	} else if (b <= 2.3e-259) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	} else if (b <= 4e-137) {
		tmp = t_2;
	} else if (b <= 1.7e-50) {
		tmp = y2 * (((k * t_1) + (x * t_3)) + (t * ((a * y5) - (c * y4))));
	} else if (b <= 3.5e+112) {
		tmp = t_2;
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y1 * y4) - (y0 * y5)
	t_2 = (((k * y2) - (j * y3)) * t_1) + (y2 * (y5 * (t * a)))
	t_3 = (c * y0) - (a * y1)
	tmp = 0
	if b <= -1.3e+36:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif b <= -3.75e-113:
		tmp = a * (y2 * ((t * y5) - (x * y1)))
	elif b <= -3.2e-199:
		tmp = x * (y2 * t_3)
	elif b <= 2.3e-259:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))))
	elif b <= 4e-137:
		tmp = t_2
	elif b <= 1.7e-50:
		tmp = y2 * (((k * t_1) + (x * t_3)) + (t * ((a * y5) - (c * y4))))
	elif b <= 3.5e+112:
		tmp = t_2
	else:
		tmp = a * (b * ((x * y) - (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_2 = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * t_1) + Float64(y2 * Float64(y5 * Float64(t * a))))
	t_3 = Float64(Float64(c * y0) - Float64(a * y1))
	tmp = 0.0
	if (b <= -1.3e+36)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (b <= -3.75e-113)
		tmp = Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (b <= -3.2e-199)
		tmp = Float64(x * Float64(y2 * t_3));
	elseif (b <= 2.3e-259)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4)))));
	elseif (b <= 4e-137)
		tmp = t_2;
	elseif (b <= 1.7e-50)
		tmp = Float64(y2 * Float64(Float64(Float64(k * t_1) + Float64(x * t_3)) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (b <= 3.5e+112)
		tmp = t_2;
	else
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y1 * y4) - (y0 * y5);
	t_2 = (((k * y2) - (j * y3)) * t_1) + (y2 * (y5 * (t * a)));
	t_3 = (c * y0) - (a * y1);
	tmp = 0.0;
	if (b <= -1.3e+36)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (b <= -3.75e-113)
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	elseif (b <= -3.2e-199)
		tmp = x * (y2 * t_3);
	elseif (b <= 2.3e-259)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	elseif (b <= 4e-137)
		tmp = t_2;
	elseif (b <= 1.7e-50)
		tmp = y2 * (((k * t_1) + (x * t_3)) + (t * ((a * y5) - (c * y4))));
	elseif (b <= 3.5e+112)
		tmp = t_2;
	else
		tmp = a * (b * ((x * y) - (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(y2 * N[(y5 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.3e+36], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.75e-113], N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.2e-199], N[(x * N[(y2 * t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e-259], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e-137], t$95$2, If[LessEqual[b, 1.7e-50], N[(y2 * N[(N[(N[(k * t$95$1), $MachinePrecision] + N[(x * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.5e+112], t$95$2, N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -1.3000000000000001e36

   1. Initial program 27.7%

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

   2. Taylor expanded in j around inf 36.6%

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

      1. +-commutative 36.6%

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

      2. mul-1-neg 36.6%

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

      3. unsub-neg 36.6%

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

      4. *-commutative 36.6%

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

   4. Simplified 36.6%

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

   5. Taylor expanded in b around inf 55.7%

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

   if -1.3000000000000001e36 < b < -3.7500000000000001e-113

   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 y2 around inf 47.1%

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

      1. sub-neg 47.1%

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

      2. +-commutative 47.1%

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

      3. mul-1-neg 47.1%

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

      4. fma-def 50.7%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 50.7%

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

      6. +-commutative 50.7%

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

      7. sub-neg 50.7%

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

      8. *-commutative 50.7%

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

   4. Simplified 50.7%

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

   5. Taylor expanded in a around -inf 50.9%

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

      1. associate-*r* 50.9%

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

      2. neg-mul-1 50.9%

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

      3. *-commutative 50.9%

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

      4. *-commutative 50.9%

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

   7. Simplified 50.9%

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

   if -3.7500000000000001e-113 < b < -3.1999999999999999e-199

   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 y2 around inf 37.7%

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

      1. sub-neg 37.7%

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

      2. +-commutative 37.7%

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

      3. mul-1-neg 37.7%

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

      4. fma-def 43.0%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 43.0%

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

      6. +-commutative 43.0%

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

      7. sub-neg 43.0%

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

      8. *-commutative 43.0%

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

   4. Simplified 43.0%

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

   5. Taylor expanded in x around inf 63.9%

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

      1. *-commutative 63.9%

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

      2. *-commutative 63.9%

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

   7. Simplified 63.9%

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

   if -3.1999999999999999e-199 < b < 2.2999999999999999e-259

   1. Initial program 46.2%

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

   2. Taylor expanded in j around inf 52.6%

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

      1. mul-1-neg 52.6%

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

      2. associate-*r* 56.1%

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

   4. Simplified 56.1%

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

   5. Taylor expanded in y3 around inf 53.7%

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

      1. distribute-lft-out-- 53.7%

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

      2. *-commutative 53.7%

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

      3. *-commutative 53.7%

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

      4. *-commutative 53.7%

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

      5. *-commutative 53.7%

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

   7. Simplified 53.7%

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

   if 2.2999999999999999e-259 < b < 3.99999999999999991e-137 or 1.70000000000000007e-50 < b < 3.49999999999999997e112

   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 a around inf 43.5%

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

      1. sub-neg 43.5%

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

      2. +-commutative 43.5%

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

      3. mul-1-neg 43.5%

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

      4. unsub-neg 43.5%

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

      5. *-commutative 43.5%

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

      6. *-commutative 43.5%

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

      7. mul-1-neg 43.5%

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

      8. remove-double-neg 43.5%

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

      9. *-commutative 43.5%

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

   4. Simplified 43.5%

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

   5. Taylor expanded in y1 around 0 50.4%

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

   6. Taylor expanded in y2 around inf 49.5%

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

      1. *-commutative 49.5%

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

      2. associate-*r* 53.4%

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

      3. associate-*r* 54.5%

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

      4. *-commutative 54.5%

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

      5. associate-*r* 57.1%

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

      6. *-commutative 57.1%

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

   8. Simplified 57.1%

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

   if 3.99999999999999991e-137 < b < 1.70000000000000007e-50

   1. Initial program 10.5%

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

   2. Taylor expanded in y2 around inf 52.9%

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

   if 3.49999999999999997e112 < b

   1. Initial program 17.5%

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

   2. Taylor expanded in a around inf 45.6%

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

      1. sub-neg 45.6%

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

      2. +-commutative 45.6%

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

      3. mul-1-neg 45.6%

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

      4. unsub-neg 45.6%

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

      5. *-commutative 45.6%

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

      6. *-commutative 45.6%

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

      7. mul-1-neg 45.6%

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

      8. remove-double-neg 45.6%

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

      9. *-commutative 45.6%

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

   4. Simplified 45.6%

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

   5. Taylor expanded in b around inf 66.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -3.75 \cdot 10^{-113}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-199}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-259}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-137}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y2 \cdot \left(y5 \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-50}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+112}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y2 \cdot \left(y5 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]

Alternative 12: 33.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y2 \cdot \left(y5 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ t_2 := y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{+37}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-113}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-197}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-257}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{-44}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 1550:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+91}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y2 (* y5 (- (* t a) (* k y0)))))
        (t_2
         (* y3 (+ (* y (- (* c y4) (* a y5))) (* j (- (* y0 y5) (* y1 y4)))))))
   (if (<= b -1.3e+37)
     (* b (* j (- (* t y4) (* x y0))))
     (if (<= b -8.2e-113)
       (* a (* y2 (- (* t y5) (* x y1))))
       (if (<= b -5.2e-197)
         (* x (* y2 (- (* c y0) (* a y1))))
         (if (<= b 9.5e-257)
           t_2
           (if (<= b 4.3e-148)
             t_1
             (if (<= b 5.4e-44)
               (* j (* y1 (- (* x i) (* y3 y4))))
               (if (<= b 1550.0)
                 t_1
                 (if (<= b 4.6e+91)
                   t_2
                   (* a (* b (- (* x y) (* z t))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (y5 * ((t * a) - (k * y0)));
	double t_2 = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	double tmp;
	if (b <= -1.3e+37) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -8.2e-113) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (b <= -5.2e-197) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (b <= 9.5e-257) {
		tmp = t_2;
	} else if (b <= 4.3e-148) {
		tmp = t_1;
	} else if (b <= 5.4e-44) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (b <= 1550.0) {
		tmp = t_1;
	} else if (b <= 4.6e+91) {
		tmp = t_2;
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y2 * (y5 * ((t * a) - (k * y0)))
    t_2 = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))))
    if (b <= (-1.3d+37)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (b <= (-8.2d-113)) then
        tmp = a * (y2 * ((t * y5) - (x * y1)))
    else if (b <= (-5.2d-197)) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (b <= 9.5d-257) then
        tmp = t_2
    else if (b <= 4.3d-148) then
        tmp = t_1
    else if (b <= 5.4d-44) then
        tmp = j * (y1 * ((x * i) - (y3 * y4)))
    else if (b <= 1550.0d0) then
        tmp = t_1
    else if (b <= 4.6d+91) then
        tmp = t_2
    else
        tmp = a * (b * ((x * y) - (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (y5 * ((t * a) - (k * y0)));
	double t_2 = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	double tmp;
	if (b <= -1.3e+37) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -8.2e-113) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (b <= -5.2e-197) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (b <= 9.5e-257) {
		tmp = t_2;
	} else if (b <= 4.3e-148) {
		tmp = t_1;
	} else if (b <= 5.4e-44) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (b <= 1550.0) {
		tmp = t_1;
	} else if (b <= 4.6e+91) {
		tmp = t_2;
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y2 * (y5 * ((t * a) - (k * y0)))
	t_2 = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))))
	tmp = 0
	if b <= -1.3e+37:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif b <= -8.2e-113:
		tmp = a * (y2 * ((t * y5) - (x * y1)))
	elif b <= -5.2e-197:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif b <= 9.5e-257:
		tmp = t_2
	elif b <= 4.3e-148:
		tmp = t_1
	elif b <= 5.4e-44:
		tmp = j * (y1 * ((x * i) - (y3 * y4)))
	elif b <= 1550.0:
		tmp = t_1
	elif b <= 4.6e+91:
		tmp = t_2
	else:
		tmp = a * (b * ((x * y) - (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y2 * Float64(y5 * Float64(Float64(t * a) - Float64(k * y0))))
	t_2 = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4)))))
	tmp = 0.0
	if (b <= -1.3e+37)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (b <= -8.2e-113)
		tmp = Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (b <= -5.2e-197)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (b <= 9.5e-257)
		tmp = t_2;
	elseif (b <= 4.3e-148)
		tmp = t_1;
	elseif (b <= 5.4e-44)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (b <= 1550.0)
		tmp = t_1;
	elseif (b <= 4.6e+91)
		tmp = t_2;
	else
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y2 * (y5 * ((t * a) - (k * y0)));
	t_2 = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	tmp = 0.0;
	if (b <= -1.3e+37)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (b <= -8.2e-113)
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	elseif (b <= -5.2e-197)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (b <= 9.5e-257)
		tmp = t_2;
	elseif (b <= 4.3e-148)
		tmp = t_1;
	elseif (b <= 5.4e-44)
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	elseif (b <= 1550.0)
		tmp = t_1;
	elseif (b <= 4.6e+91)
		tmp = t_2;
	else
		tmp = a * (b * ((x * y) - (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y2 * N[(y5 * N[(N[(t * a), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.3e+37], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8.2e-113], N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.2e-197], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e-257], t$95$2, If[LessEqual[b, 4.3e-148], t$95$1, If[LessEqual[b, 5.4e-44], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1550.0], t$95$1, If[LessEqual[b, 4.6e+91], t$95$2, N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -1.3e37

   1. Initial program 27.7%

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

   2. Taylor expanded in j around inf 36.6%

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

      1. +-commutative 36.6%

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

      2. mul-1-neg 36.6%

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

      3. unsub-neg 36.6%

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

      4. *-commutative 36.6%

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

   4. Simplified 36.6%

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

   5. Taylor expanded in b around inf 55.7%

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

   if -1.3e37 < b < -8.1999999999999999e-113

   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 y2 around inf 47.1%

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

      1. sub-neg 47.1%

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

      2. +-commutative 47.1%

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

      3. mul-1-neg 47.1%

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

      4. fma-def 50.7%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 50.7%

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

      6. +-commutative 50.7%

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

      7. sub-neg 50.7%

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

      8. *-commutative 50.7%

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

   4. Simplified 50.7%

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

   5. Taylor expanded in a around -inf 50.9%

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

      1. associate-*r* 50.9%

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

      2. neg-mul-1 50.9%

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

      3. *-commutative 50.9%

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

      4. *-commutative 50.9%

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

   7. Simplified 50.9%

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

   if -8.1999999999999999e-113 < b < -5.2000000000000003e-197

   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 y2 around inf 37.7%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 37.7%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 37.7%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 37.7%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 43.0%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 43.0%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 43.0%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 43.0%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 43.0%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 43.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in x around inf 63.9%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 63.9%

         \[\leadsto x \cdot \left(y2 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right)\right) \]

      2. *-commutative 63.9%

         \[\leadsto x \cdot \left(y2 \cdot \left(y0 \cdot c - \color{blue}{y1 \cdot a}\right)\right) \]

   7. Simplified 63.9%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(y0 \cdot c - y1 \cdot a\right)\right)} \]

   if -5.2000000000000003e-197 < b < 9.49999999999999941e-257 or 1550 < b < 4.59999999999999982e91

   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 50.4%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 50.4%

         \[\leadsto \left(\left(\color{blue}{\left(-j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 52.4%

         \[\leadsto \left(\left(\left(-\color{blue}{\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 52.4%

      \[\leadsto \left(\left(\color{blue}{\left(-\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y3 around inf 55.4%

      \[\leadsto \color{blue}{y3 \cdot \left(-1 \cdot \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 55.4%

         \[\leadsto y3 \cdot \color{blue}{\left(-1 \cdot \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      2. *-commutative 55.4%

         \[\leadsto y3 \cdot \left(-1 \cdot \left(\color{blue}{\left(y1 \cdot y4 - y0 \cdot y5\right) \cdot j} - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      3. *-commutative 55.4%

         \[\leadsto y3 \cdot \left(-1 \cdot \left(\left(y1 \cdot y4 - y0 \cdot y5\right) \cdot j - \color{blue}{\left(c \cdot y4 - a \cdot y5\right) \cdot y}\right)\right) \]

      4. *-commutative 55.4%

         \[\leadsto y3 \cdot \left(-1 \cdot \left(\left(y1 \cdot y4 - y0 \cdot y5\right) \cdot j - \left(\color{blue}{y4 \cdot c} - a \cdot y5\right) \cdot y\right)\right) \]

      5. *-commutative 55.4%

         \[\leadsto y3 \cdot \left(-1 \cdot \left(\left(y1 \cdot y4 - y0 \cdot y5\right) \cdot j - \left(y4 \cdot c - \color{blue}{y5 \cdot a}\right) \cdot y\right)\right) \]

   7. Simplified 55.4%

      \[\leadsto \color{blue}{y3 \cdot \left(-1 \cdot \left(\left(y1 \cdot y4 - y0 \cdot y5\right) \cdot j - \left(y4 \cdot c - y5 \cdot a\right) \cdot y\right)\right)} \]

   if 9.49999999999999941e-257 < b < 4.2999999999999998e-148 or 5.3999999999999998e-44 < b < 1550

   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 y2 around inf 39.9%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 39.9%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 39.9%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 39.9%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 42.3%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 42.3%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 42.3%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 42.3%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 42.3%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 42.3%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in y5 around -inf 56.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y2 \cdot \left(y5 \cdot \left(k \cdot y0 - a \cdot t\right)\right)\right)} \]

   if 4.2999999999999998e-148 < b < 5.3999999999999998e-44

   1. Initial program 12.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 29.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 29.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 29.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 29.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 29.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 29.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y1 around -inf 41.7%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 41.7%

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 41.7%

         \[\leadsto j \cdot \left(y1 \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 41.7%

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 41.7%

         \[\leadsto j \cdot \left(y1 \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 41.7%

         \[\leadsto j \cdot \left(y1 \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 41.7%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   if 4.59999999999999982e91 < b

   1. Initial program 20.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around inf 46.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. sub-neg 46.3%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. +-commutative 46.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. mul-1-neg 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. unsub-neg 46.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. mul-1-neg 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(-\color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. remove-double-neg 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \color{blue}{y5 \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. *-commutative 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 46.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in b around inf 63.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+37}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-113}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-197}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-257}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{-148}:\\ \;\;\;\;y2 \cdot \left(y5 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{-44}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 1550:\\ \;\;\;\;y2 \cdot \left(y5 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+91}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]

Alternative 13: 36.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{-113}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-200}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-257}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+116}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y2 \cdot \left(y5 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -6.5e+36)
   (* b (* j (- (* t y4) (* x y0))))
   (if (<= b -7.2e-113)
     (* a (* y2 (- (* t y5) (* x y1))))
     (if (<= b -2e-200)
       (* x (* y2 (- (* c y0) (* a y1))))
       (if (<= b 3.2e-257)
         (* y3 (+ (* y (- (* c y4) (* a y5))) (* j (- (* y0 y5) (* y1 y4)))))
         (if (<= b 5e+116)
           (+
            (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5)))
            (* y2 (* y5 (* t a))))
           (* a (* b (- (* x y) (* z t))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -6.5e+36) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -7.2e-113) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (b <= -2e-200) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (b <= 3.2e-257) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	} else if (b <= 5e+116) {
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (y2 * (y5 * (t * a)));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (b <= (-6.5d+36)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (b <= (-7.2d-113)) then
        tmp = a * (y2 * ((t * y5) - (x * y1)))
    else if (b <= (-2d-200)) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (b <= 3.2d-257) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))))
    else if (b <= 5d+116) then
        tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (y2 * (y5 * (t * a)))
    else
        tmp = a * (b * ((x * y) - (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -6.5e+36) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -7.2e-113) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (b <= -2e-200) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (b <= 3.2e-257) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	} else if (b <= 5e+116) {
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (y2 * (y5 * (t * a)));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -6.5e+36:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif b <= -7.2e-113:
		tmp = a * (y2 * ((t * y5) - (x * y1)))
	elif b <= -2e-200:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif b <= 3.2e-257:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))))
	elif b <= 5e+116:
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (y2 * (y5 * (t * a)))
	else:
		tmp = a * (b * ((x * y) - (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (b <= -6.5e+36)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (b <= -7.2e-113)
		tmp = Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (b <= -2e-200)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (b <= 3.2e-257)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4)))));
	elseif (b <= 5e+116)
		tmp = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(y2 * Float64(y5 * Float64(t * a))));
	else
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (b <= -6.5e+36)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (b <= -7.2e-113)
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	elseif (b <= -2e-200)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (b <= 3.2e-257)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	elseif (b <= 5e+116)
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (y2 * (y5 * (t * a)));
	else
		tmp = a * (b * ((x * y) - (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[b, -6.5e+36], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7.2e-113], N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2e-200], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e-257], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5e+116], N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(y5 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -6.4999999999999998e36

   1. Initial program 27.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 36.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 36.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 36.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 36.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 36.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 36.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in b around inf 55.7%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -6.4999999999999998e36 < b < -7.1999999999999995e-113

   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 y2 around inf 47.1%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 47.1%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 47.1%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 47.1%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 50.7%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 50.7%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 50.7%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 50.7%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 50.7%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 50.7%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in a around -inf 50.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y2 \cdot \left(x \cdot y1 - t \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 50.9%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y2 \cdot \left(x \cdot y1 - t \cdot y5\right)\right)} \]

      2. neg-mul-1 50.9%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y2 \cdot \left(x \cdot y1 - t \cdot y5\right)\right) \]

      3. *-commutative 50.9%

         \[\leadsto \left(-a\right) \cdot \left(y2 \cdot \left(\color{blue}{y1 \cdot x} - t \cdot y5\right)\right) \]

      4. *-commutative 50.9%

         \[\leadsto \left(-a\right) \cdot \left(y2 \cdot \left(y1 \cdot x - \color{blue}{y5 \cdot t}\right)\right) \]

   7. Simplified 50.9%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y2 \cdot \left(y1 \cdot x - y5 \cdot t\right)\right)} \]

   if -7.1999999999999995e-113 < b < -2e-200

   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 y2 around inf 37.7%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 37.7%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 37.7%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 37.7%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 43.0%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 43.0%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 43.0%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 43.0%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 43.0%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 43.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in x around inf 63.9%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 63.9%

         \[\leadsto x \cdot \left(y2 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right)\right) \]

      2. *-commutative 63.9%

         \[\leadsto x \cdot \left(y2 \cdot \left(y0 \cdot c - \color{blue}{y1 \cdot a}\right)\right) \]

   7. Simplified 63.9%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(y0 \cdot c - y1 \cdot a\right)\right)} \]

   if -2e-200 < b < 3.19999999999999985e-257

   1. Initial program 46.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 52.6%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 52.6%

         \[\leadsto \left(\left(\color{blue}{\left(-j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 56.1%

         \[\leadsto \left(\left(\left(-\color{blue}{\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 56.1%

      \[\leadsto \left(\left(\color{blue}{\left(-\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y3 around inf 53.7%

      \[\leadsto \color{blue}{y3 \cdot \left(-1 \cdot \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 53.7%

         \[\leadsto y3 \cdot \color{blue}{\left(-1 \cdot \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      2. *-commutative 53.7%

         \[\leadsto y3 \cdot \left(-1 \cdot \left(\color{blue}{\left(y1 \cdot y4 - y0 \cdot y5\right) \cdot j} - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      3. *-commutative 53.7%

         \[\leadsto y3 \cdot \left(-1 \cdot \left(\left(y1 \cdot y4 - y0 \cdot y5\right) \cdot j - \color{blue}{\left(c \cdot y4 - a \cdot y5\right) \cdot y}\right)\right) \]

      4. *-commutative 53.7%

         \[\leadsto y3 \cdot \left(-1 \cdot \left(\left(y1 \cdot y4 - y0 \cdot y5\right) \cdot j - \left(\color{blue}{y4 \cdot c} - a \cdot y5\right) \cdot y\right)\right) \]

      5. *-commutative 53.7%

         \[\leadsto y3 \cdot \left(-1 \cdot \left(\left(y1 \cdot y4 - y0 \cdot y5\right) \cdot j - \left(y4 \cdot c - \color{blue}{y5 \cdot a}\right) \cdot y\right)\right) \]

   7. Simplified 53.7%

      \[\leadsto \color{blue}{y3 \cdot \left(-1 \cdot \left(\left(y1 \cdot y4 - y0 \cdot y5\right) \cdot j - \left(y4 \cdot c - y5 \cdot a\right) \cdot y\right)\right)} \]

   if 3.19999999999999985e-257 < b < 5.00000000000000025e116

   1. Initial program 26.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around inf 41.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. sub-neg 41.2%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. +-commutative 41.2%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. mul-1-neg 41.2%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. unsub-neg 41.2%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 41.2%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 41.2%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. mul-1-neg 41.2%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(-\color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. remove-double-neg 41.2%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \color{blue}{y5 \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. *-commutative 41.2%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 41.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y1 around 0 46.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in y2 around inf 46.2%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   7. Step-by-step derivation

      1. *-commutative 46.2%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 49.3%

         \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot y5\right) \cdot y2\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. associate-*r* 49.2%

         \[\leadsto \color{blue}{\left(a \cdot \left(t \cdot y5\right)\right) \cdot y2} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. *-commutative 49.2%

         \[\leadsto \color{blue}{y2 \cdot \left(a \cdot \left(t \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. associate-*r* 51.2%

         \[\leadsto y2 \cdot \color{blue}{\left(\left(a \cdot t\right) \cdot y5\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 51.2%

         \[\leadsto y2 \cdot \color{blue}{\left(y5 \cdot \left(a \cdot t\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   8. Simplified 51.2%

      \[\leadsto \color{blue}{y2 \cdot \left(y5 \cdot \left(a \cdot t\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   if 5.00000000000000025e116 < b

   1. Initial program 17.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around inf 45.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. sub-neg 45.6%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. +-commutative 45.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. mul-1-neg 45.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. unsub-neg 45.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 45.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 45.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. mul-1-neg 45.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(-\color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. remove-double-neg 45.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \color{blue}{y5 \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. *-commutative 45.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 45.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in b around inf 66.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{-113}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-200}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-257}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+116}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y2 \cdot \left(y5 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]

Alternative 14: 32.0% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.06 \cdot 10^{+35}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-113}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{-230}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{-140}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-91}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 9.7 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+70}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{+108}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+133}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+137}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -1.06e+35)
   (* b (* j (- (* t y4) (* x y0))))
   (if (<= b -5.8e-113)
     (* a (* y2 (- (* t y5) (* x y1))))
     (if (<= b 1.85e-230)
       (* x (* y2 (- (* c y0) (* a y1))))
       (if (<= b 7.8e-140)
         (* t (* y2 (- (* a y5) (* c y4))))
         (if (<= b 1.9e-91)
           (* j (* y1 (- (* x i) (* y3 y4))))
           (if (<= b 9.7e-35)
             (* a (* t (- (* y2 y5) (* z b))))
             (if (<= b 7e+70)
               (* j (* y0 (- (* y3 y5) (* x b))))
               (if (<= b 4.7e+108)
                 (* j (* t (- (* b y4) (* i y5))))
                 (if (<= b 1.25e+133)
                   (* a (* y5 (- (* t y2) (* y y3))))
                   (if (<= b 9.5e+137)
                     (* (* z y0) (* b k))
                     (* a (* b (- (* x y) (* z t)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -1.06e+35) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -5.8e-113) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (b <= 1.85e-230) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (b <= 7.8e-140) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (b <= 1.9e-91) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (b <= 9.7e-35) {
		tmp = a * (t * ((y2 * y5) - (z * b)));
	} else if (b <= 7e+70) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (b <= 4.7e+108) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (b <= 1.25e+133) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (b <= 9.5e+137) {
		tmp = (z * y0) * (b * k);
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (b <= (-1.06d+35)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (b <= (-5.8d-113)) then
        tmp = a * (y2 * ((t * y5) - (x * y1)))
    else if (b <= 1.85d-230) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (b <= 7.8d-140) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (b <= 1.9d-91) then
        tmp = j * (y1 * ((x * i) - (y3 * y4)))
    else if (b <= 9.7d-35) then
        tmp = a * (t * ((y2 * y5) - (z * b)))
    else if (b <= 7d+70) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else if (b <= 4.7d+108) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (b <= 1.25d+133) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (b <= 9.5d+137) then
        tmp = (z * y0) * (b * k)
    else
        tmp = a * (b * ((x * y) - (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -1.06e+35) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -5.8e-113) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (b <= 1.85e-230) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (b <= 7.8e-140) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (b <= 1.9e-91) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (b <= 9.7e-35) {
		tmp = a * (t * ((y2 * y5) - (z * b)));
	} else if (b <= 7e+70) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (b <= 4.7e+108) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (b <= 1.25e+133) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (b <= 9.5e+137) {
		tmp = (z * y0) * (b * k);
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -1.06e+35:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif b <= -5.8e-113:
		tmp = a * (y2 * ((t * y5) - (x * y1)))
	elif b <= 1.85e-230:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif b <= 7.8e-140:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif b <= 1.9e-91:
		tmp = j * (y1 * ((x * i) - (y3 * y4)))
	elif b <= 9.7e-35:
		tmp = a * (t * ((y2 * y5) - (z * b)))
	elif b <= 7e+70:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	elif b <= 4.7e+108:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif b <= 1.25e+133:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif b <= 9.5e+137:
		tmp = (z * y0) * (b * k)
	else:
		tmp = a * (b * ((x * y) - (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (b <= -1.06e+35)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (b <= -5.8e-113)
		tmp = Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (b <= 1.85e-230)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (b <= 7.8e-140)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (b <= 1.9e-91)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (b <= 9.7e-35)
		tmp = Float64(a * Float64(t * Float64(Float64(y2 * y5) - Float64(z * b))));
	elseif (b <= 7e+70)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (b <= 4.7e+108)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (b <= 1.25e+133)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (b <= 9.5e+137)
		tmp = Float64(Float64(z * y0) * Float64(b * k));
	else
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (b <= -1.06e+35)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (b <= -5.8e-113)
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	elseif (b <= 1.85e-230)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (b <= 7.8e-140)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (b <= 1.9e-91)
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	elseif (b <= 9.7e-35)
		tmp = a * (t * ((y2 * y5) - (z * b)));
	elseif (b <= 7e+70)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	elseif (b <= 4.7e+108)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (b <= 1.25e+133)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (b <= 9.5e+137)
		tmp = (z * y0) * (b * k);
	else
		tmp = a * (b * ((x * y) - (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[b, -1.06e+35], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.8e-113], N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.85e-230], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.8e-140], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.9e-91], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.7e-35], N[(a * N[(t * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e+70], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.7e+108], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.25e+133], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e+137], N[(N[(z * y0), $MachinePrecision] * N[(b * k), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if b < -1.0600000000000001e35

   1. Initial program 27.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 36.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 36.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 36.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 36.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 36.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 36.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in b around inf 55.7%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -1.0600000000000001e35 < b < -5.80000000000000008e-113

   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 y2 around inf 47.1%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 47.1%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 47.1%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 47.1%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 50.7%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 50.7%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 50.7%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 50.7%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 50.7%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 50.7%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in a around -inf 50.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y2 \cdot \left(x \cdot y1 - t \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 50.9%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y2 \cdot \left(x \cdot y1 - t \cdot y5\right)\right)} \]

      2. neg-mul-1 50.9%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y2 \cdot \left(x \cdot y1 - t \cdot y5\right)\right) \]

      3. *-commutative 50.9%

         \[\leadsto \left(-a\right) \cdot \left(y2 \cdot \left(\color{blue}{y1 \cdot x} - t \cdot y5\right)\right) \]

      4. *-commutative 50.9%

         \[\leadsto \left(-a\right) \cdot \left(y2 \cdot \left(y1 \cdot x - \color{blue}{y5 \cdot t}\right)\right) \]

   7. Simplified 50.9%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y2 \cdot \left(y1 \cdot x - y5 \cdot t\right)\right)} \]

   if -5.80000000000000008e-113 < b < 1.84999999999999991e-230

   1. Initial program 40.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 44.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 44.0%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 44.0%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 44.0%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 45.9%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 45.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 45.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 45.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 45.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 45.9%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in x around inf 48.2%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 48.2%

         \[\leadsto x \cdot \left(y2 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right)\right) \]

      2. *-commutative 48.2%

         \[\leadsto x \cdot \left(y2 \cdot \left(y0 \cdot c - \color{blue}{y1 \cdot a}\right)\right) \]

   7. Simplified 48.2%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(y0 \cdot c - y1 \cdot a\right)\right)} \]

   if 1.84999999999999991e-230 < b < 7.80000000000000038e-140

   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 y2 around inf 29.6%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 29.6%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 29.6%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 29.6%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 33.8%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 33.8%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 33.8%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 33.8%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 33.8%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 33.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in t around inf 50.9%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   if 7.80000000000000038e-140 < b < 1.89999999999999989e-91

   1. Initial program 7.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 38.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 38.9%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 38.9%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 38.9%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 38.9%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 38.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y1 around -inf 54.8%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 54.8%

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 54.8%

         \[\leadsto j \cdot \left(y1 \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 54.8%

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 54.8%

         \[\leadsto j \cdot \left(y1 \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 54.8%

         \[\leadsto j \cdot \left(y1 \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 54.8%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   if 1.89999999999999989e-91 < b < 9.70000000000000073e-35

   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 a around inf 67.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. sub-neg 67.3%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. +-commutative 67.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. mul-1-neg 67.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. unsub-neg 67.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 67.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 67.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. mul-1-neg 67.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(-\color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. remove-double-neg 67.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \color{blue}{y5 \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. *-commutative 67.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 67.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in t around -inf 55.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot \left(-1 \cdot \left(y2 \cdot y5\right) + b \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 55.3%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot \left(-1 \cdot \left(y2 \cdot y5\right) + b \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 55.3%

         \[\leadsto \color{blue}{a \cdot \left(-t \cdot \left(-1 \cdot \left(y2 \cdot y5\right) + b \cdot z\right)\right)} \]

      3. +-commutative 55.3%

         \[\leadsto a \cdot \left(-t \cdot \color{blue}{\left(b \cdot z + -1 \cdot \left(y2 \cdot y5\right)\right)}\right) \]

      4. mul-1-neg 55.3%

         \[\leadsto a \cdot \left(-t \cdot \left(b \cdot z + \color{blue}{\left(-y2 \cdot y5\right)}\right)\right) \]

      5. unsub-neg 55.3%

         \[\leadsto a \cdot \left(-t \cdot \color{blue}{\left(b \cdot z - y2 \cdot y5\right)}\right) \]

   7. Simplified 55.3%

      \[\leadsto \color{blue}{a \cdot \left(-t \cdot \left(b \cdot z - y2 \cdot y5\right)\right)} \]

   if 9.70000000000000073e-35 < b < 7.00000000000000005e70

   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 j around inf 38.4%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 38.4%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 38.4%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 38.4%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 38.4%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 38.4%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y0 around -inf 52.7%

      \[\leadsto j \cdot \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 52.7%

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      2. mul-1-neg 52.7%

         \[\leadsto j \cdot \left(y0 \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      3. unsub-neg 52.7%

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

      4. *-commutative 52.7%

         \[\leadsto j \cdot \left(y0 \cdot \left(\color{blue}{y5 \cdot y3} - b \cdot x\right)\right) \]

      5. *-commutative 52.7%

         \[\leadsto j \cdot \left(y0 \cdot \left(y5 \cdot y3 - \color{blue}{x \cdot b}\right)\right) \]

   7. Simplified 52.7%

      \[\leadsto j \cdot \color{blue}{\left(y0 \cdot \left(y5 \cdot y3 - x \cdot b\right)\right)} \]

   if 7.00000000000000005e70 < b < 4.6999999999999996e108

   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 j around inf 57.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 57.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 57.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 57.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 57.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 57.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in t around inf 57.3%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 57.3%

         \[\leadsto j \cdot \left(t \cdot \left(\color{blue}{y4 \cdot b} - i \cdot y5\right)\right) \]

      2. *-commutative 57.3%

         \[\leadsto j \cdot \left(t \cdot \left(y4 \cdot b - \color{blue}{y5 \cdot i}\right)\right) \]

   7. Simplified 57.3%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(y4 \cdot b - y5 \cdot i\right)\right)} \]

   if 4.6999999999999996e108 < b < 1.2499999999999999e133

   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 j around inf 40.0%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 40.0%

         \[\leadsto \left(\left(\color{blue}{\left(-j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 40.0%

         \[\leadsto \left(\left(\left(-\color{blue}{\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 40.0%

      \[\leadsto \left(\left(\color{blue}{\left(-\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 80.2%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 80.2%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 80.2%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 80.2%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   if 1.2499999999999999e133 < b < 9.50000000000000031e137

   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 k around -inf 50.0%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 50.0%

         \[\leadsto \color{blue}{-k \cdot \left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. *-commutative 50.0%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot k} \]

      3. distribute-rgt-neg-in 50.0%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right)} \]

      4. +-commutative 50.0%

         \[\leadsto \left(\color{blue}{\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      5. mul-1-neg 50.0%

         \[\leadsto \left(\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      6. unsub-neg 50.0%

         \[\leadsto \left(\color{blue}{\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      7. *-commutative 50.0%

         \[\leadsto \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y} - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

   4. Simplified 50.0%

      \[\leadsto \color{blue}{\left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot y - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right)} \]

   5. Taylor expanded in y0 around -inf 52.4%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \cdot \left(-k\right) \]
   6. Step-by-step derivation

      1. +-commutative 52.4%

         \[\leadsto \left(y0 \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \cdot \left(-k\right) \]

      2. mul-1-neg 52.4%

         \[\leadsto \left(y0 \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \cdot \left(-k\right) \]

      3. unsub-neg 52.4%

         \[\leadsto \left(y0 \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \cdot \left(-k\right) \]

   7. Simplified 52.4%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \cdot \left(-k\right) \]

   8. Taylor expanded in y2 around 0 52.4%

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(b \cdot k\right) \cdot \left(y0 \cdot z\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \color{blue}{\left(k \cdot b\right)} \cdot \left(y0 \cdot z\right) \]

   10. Simplified 100.0%

       \[\leadsto \color{blue}{\left(k \cdot b\right) \cdot \left(y0 \cdot z\right)} \]

   if 9.50000000000000031e137 < b

   1. Initial program 12.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around inf 42.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. sub-neg 42.5%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. +-commutative 42.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. mul-1-neg 42.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. unsub-neg 42.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 42.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 42.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. mul-1-neg 42.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(-\color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. remove-double-neg 42.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \color{blue}{y5 \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. *-commutative 42.5%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 42.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in b around inf 71.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 11 regimes into one program.

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.06 \cdot 10^{+35}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-113}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{-230}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{-140}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-91}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 9.7 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+70}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{+108}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+133}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+137}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]

Alternative 15: 32.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y2 \cdot \left(y5 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{if}\;b \leq -3.3 \cdot 10^{+35}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-113}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-257}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-45}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 90000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+76}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 3.15 \cdot 10^{+96}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y2 (* y5 (- (* t a) (* k y0))))))
   (if (<= b -3.3e+35)
     (* b (* j (- (* t y4) (* x y0))))
     (if (<= b -2.3e-113)
       (* a (* y2 (- (* t y5) (* x y1))))
       (if (<= b 8e-257)
         (* x (* y2 (- (* c y0) (* a y1))))
         (if (<= b 2.4e-148)
           t_1
           (if (<= b 1.2e-45)
             (* j (* y1 (- (* x i) (* y3 y4))))
             (if (<= b 90000000.0)
               t_1
               (if (<= b 1.15e+76)
                 (* j (* y0 (- (* y3 y5) (* x b))))
                 (if (<= b 3.15e+96)
                   (* j (* t (- (* b y4) (* i y5))))
                   (* a (* b (- (* x y) (* z t))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (y5 * ((t * a) - (k * y0)));
	double tmp;
	if (b <= -3.3e+35) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -2.3e-113) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (b <= 8e-257) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (b <= 2.4e-148) {
		tmp = t_1;
	} else if (b <= 1.2e-45) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (b <= 90000000.0) {
		tmp = t_1;
	} else if (b <= 1.15e+76) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (b <= 3.15e+96) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y2 * (y5 * ((t * a) - (k * y0)))
    if (b <= (-3.3d+35)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (b <= (-2.3d-113)) then
        tmp = a * (y2 * ((t * y5) - (x * y1)))
    else if (b <= 8d-257) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (b <= 2.4d-148) then
        tmp = t_1
    else if (b <= 1.2d-45) then
        tmp = j * (y1 * ((x * i) - (y3 * y4)))
    else if (b <= 90000000.0d0) then
        tmp = t_1
    else if (b <= 1.15d+76) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else if (b <= 3.15d+96) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else
        tmp = a * (b * ((x * y) - (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (y5 * ((t * a) - (k * y0)));
	double tmp;
	if (b <= -3.3e+35) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -2.3e-113) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (b <= 8e-257) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (b <= 2.4e-148) {
		tmp = t_1;
	} else if (b <= 1.2e-45) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (b <= 90000000.0) {
		tmp = t_1;
	} else if (b <= 1.15e+76) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (b <= 3.15e+96) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y2 * (y5 * ((t * a) - (k * y0)))
	tmp = 0
	if b <= -3.3e+35:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif b <= -2.3e-113:
		tmp = a * (y2 * ((t * y5) - (x * y1)))
	elif b <= 8e-257:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif b <= 2.4e-148:
		tmp = t_1
	elif b <= 1.2e-45:
		tmp = j * (y1 * ((x * i) - (y3 * y4)))
	elif b <= 90000000.0:
		tmp = t_1
	elif b <= 1.15e+76:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	elif b <= 3.15e+96:
		tmp = j * (t * ((b * y4) - (i * y5)))
	else:
		tmp = a * (b * ((x * y) - (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y2 * Float64(y5 * Float64(Float64(t * a) - Float64(k * y0))))
	tmp = 0.0
	if (b <= -3.3e+35)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (b <= -2.3e-113)
		tmp = Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (b <= 8e-257)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (b <= 2.4e-148)
		tmp = t_1;
	elseif (b <= 1.2e-45)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (b <= 90000000.0)
		tmp = t_1;
	elseif (b <= 1.15e+76)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (b <= 3.15e+96)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	else
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y2 * (y5 * ((t * a) - (k * y0)));
	tmp = 0.0;
	if (b <= -3.3e+35)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (b <= -2.3e-113)
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	elseif (b <= 8e-257)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (b <= 2.4e-148)
		tmp = t_1;
	elseif (b <= 1.2e-45)
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	elseif (b <= 90000000.0)
		tmp = t_1;
	elseif (b <= 1.15e+76)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	elseif (b <= 3.15e+96)
		tmp = j * (t * ((b * y4) - (i * y5)));
	else
		tmp = a * (b * ((x * y) - (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y2 * N[(y5 * N[(N[(t * a), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.3e+35], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.3e-113], N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8e-257], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e-148], t$95$1, If[LessEqual[b, 1.2e-45], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 90000000.0], t$95$1, If[LessEqual[b, 1.15e+76], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.15e+96], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if b < -3.3000000000000002e35

   1. Initial program 27.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 36.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 36.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 36.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 36.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 36.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 36.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in b around inf 55.7%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -3.3000000000000002e35 < b < -2.30000000000000008e-113

   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 y2 around inf 47.1%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 47.1%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 47.1%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 47.1%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 50.7%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 50.7%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 50.7%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 50.7%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 50.7%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 50.7%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in a around -inf 50.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y2 \cdot \left(x \cdot y1 - t \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 50.9%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y2 \cdot \left(x \cdot y1 - t \cdot y5\right)\right)} \]

      2. neg-mul-1 50.9%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y2 \cdot \left(x \cdot y1 - t \cdot y5\right)\right) \]

      3. *-commutative 50.9%

         \[\leadsto \left(-a\right) \cdot \left(y2 \cdot \left(\color{blue}{y1 \cdot x} - t \cdot y5\right)\right) \]

      4. *-commutative 50.9%

         \[\leadsto \left(-a\right) \cdot \left(y2 \cdot \left(y1 \cdot x - \color{blue}{y5 \cdot t}\right)\right) \]

   7. Simplified 50.9%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y2 \cdot \left(y1 \cdot x - y5 \cdot t\right)\right)} \]

   if -2.30000000000000008e-113 < b < 7.9999999999999998e-257

   1. Initial program 44.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 42.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 42.2%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 42.2%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 42.2%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 44.4%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 44.4%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 44.4%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 44.4%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 44.4%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 44.4%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in x around inf 49.0%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 49.0%

         \[\leadsto x \cdot \left(y2 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right)\right) \]

      2. *-commutative 49.0%

         \[\leadsto x \cdot \left(y2 \cdot \left(y0 \cdot c - \color{blue}{y1 \cdot a}\right)\right) \]

   7. Simplified 49.0%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(y0 \cdot c - y1 \cdot a\right)\right)} \]

   if 7.9999999999999998e-257 < b < 2.4000000000000001e-148 or 1.19999999999999995e-45 < b < 9e7

   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 y2 around inf 39.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 39.0%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 39.0%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 39.0%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 41.3%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 41.3%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 41.3%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 41.3%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 41.3%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 41.3%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in y5 around -inf 57.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y2 \cdot \left(y5 \cdot \left(k \cdot y0 - a \cdot t\right)\right)\right)} \]

   if 2.4000000000000001e-148 < b < 1.19999999999999995e-45

   1. Initial program 12.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 29.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 29.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 29.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 29.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 29.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 29.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y1 around -inf 41.7%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 41.7%

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 41.7%

         \[\leadsto j \cdot \left(y1 \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 41.7%

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 41.7%

         \[\leadsto j \cdot \left(y1 \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 41.7%

         \[\leadsto j \cdot \left(y1 \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 41.7%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   if 9e7 < b < 1.15000000000000001e76

   1. Initial program 29.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 47.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 47.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 47.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 47.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 47.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 47.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y0 around -inf 59.9%

      \[\leadsto j \cdot \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 59.9%

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      2. mul-1-neg 59.9%

         \[\leadsto j \cdot \left(y0 \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      3. unsub-neg 59.9%

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

      4. *-commutative 59.9%

         \[\leadsto j \cdot \left(y0 \cdot \left(\color{blue}{y5 \cdot y3} - b \cdot x\right)\right) \]

      5. *-commutative 59.9%

         \[\leadsto j \cdot \left(y0 \cdot \left(y5 \cdot y3 - \color{blue}{x \cdot b}\right)\right) \]

   7. Simplified 59.9%

      \[\leadsto j \cdot \color{blue}{\left(y0 \cdot \left(y5 \cdot y3 - x \cdot b\right)\right)} \]

   if 1.15000000000000001e76 < b < 3.1500000000000002e96

   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 100.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 100.0%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 100.0%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 100.0%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 100.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in t around inf 100.0%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto j \cdot \left(t \cdot \left(\color{blue}{y4 \cdot b} - i \cdot y5\right)\right) \]

      2. *-commutative 100.0%

         \[\leadsto j \cdot \left(t \cdot \left(y4 \cdot b - \color{blue}{y5 \cdot i}\right)\right) \]

   7. Simplified 100.0%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(y4 \cdot b - y5 \cdot i\right)\right)} \]

   if 3.1500000000000002e96 < b

   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 a around inf 47.7%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. sub-neg 47.7%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. +-commutative 47.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. mul-1-neg 47.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. unsub-neg 47.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 47.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 47.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. mul-1-neg 47.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(-\color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. remove-double-neg 47.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \color{blue}{y5 \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. *-commutative 47.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 47.7%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in b around inf 65.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+35}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-113}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-257}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-148}:\\ \;\;\;\;y2 \cdot \left(y5 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-45}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 90000000:\\ \;\;\;\;y2 \cdot \left(y5 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+76}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 3.15 \cdot 10^{+96}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]

Alternative 16: 22.2% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-b\right) \cdot \left(k \cdot \left(y \cdot y4\right)\right)\\ \mathbf{if}\;y4 \leq -3.6 \cdot 10^{+186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq -8.2 \cdot 10^{+160}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(x \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -3 \cdot 10^{-63}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq -6.8 \cdot 10^{-83}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -8.5 \cdot 10^{-146}:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;y4 \leq -3.4 \cdot 10^{-229}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y0 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 2.5 \cdot 10^{-218}:\\ \;\;\;\;a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 3100000000:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(y0 \cdot \left(-k\right)\right)\\ \mathbf{elif}\;y4 \leq 4.1 \cdot 10^{+249}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(y4 \cdot \left(-c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (- b) (* k (* y y4)))))
   (if (<= y4 -3.6e+186)
     t_1
     (if (<= y4 -8.2e+160)
       (* y0 (* b (* x (- j))))
       (if (<= y4 -3e-63)
         (* j (* y0 (* y3 y5)))
         (if (<= y4 -6.8e-83)
           (* b (* k (* z y0)))
           (if (<= y4 -8.5e-146)
             (* (* y2 y5) (* t a))
             (if (<= y4 -3.4e-229)
               (* k (* y2 (* y0 (- y5))))
               (if (<= y4 2.5e-218)
                 (* a (* y (* y3 (- y5))))
                 (if (<= y4 3100000000.0)
                   (* (* y2 y5) (* y0 (- k)))
                   (if (<= y4 4.1e+249)
                     t_1
                     (* y2 (* t (* y4 (- c)))))))))))))))

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 * (k * (y * y4));
	double tmp;
	if (y4 <= -3.6e+186) {
		tmp = t_1;
	} else if (y4 <= -8.2e+160) {
		tmp = y0 * (b * (x * -j));
	} else if (y4 <= -3e-63) {
		tmp = j * (y0 * (y3 * y5));
	} else if (y4 <= -6.8e-83) {
		tmp = b * (k * (z * y0));
	} else if (y4 <= -8.5e-146) {
		tmp = (y2 * y5) * (t * a);
	} else if (y4 <= -3.4e-229) {
		tmp = k * (y2 * (y0 * -y5));
	} else if (y4 <= 2.5e-218) {
		tmp = a * (y * (y3 * -y5));
	} else if (y4 <= 3100000000.0) {
		tmp = (y2 * y5) * (y0 * -k);
	} else if (y4 <= 4.1e+249) {
		tmp = t_1;
	} else {
		tmp = y2 * (t * (y4 * -c));
	}
	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 * (k * (y * y4))
    if (y4 <= (-3.6d+186)) then
        tmp = t_1
    else if (y4 <= (-8.2d+160)) then
        tmp = y0 * (b * (x * -j))
    else if (y4 <= (-3d-63)) then
        tmp = j * (y0 * (y3 * y5))
    else if (y4 <= (-6.8d-83)) then
        tmp = b * (k * (z * y0))
    else if (y4 <= (-8.5d-146)) then
        tmp = (y2 * y5) * (t * a)
    else if (y4 <= (-3.4d-229)) then
        tmp = k * (y2 * (y0 * -y5))
    else if (y4 <= 2.5d-218) then
        tmp = a * (y * (y3 * -y5))
    else if (y4 <= 3100000000.0d0) then
        tmp = (y2 * y5) * (y0 * -k)
    else if (y4 <= 4.1d+249) then
        tmp = t_1
    else
        tmp = y2 * (t * (y4 * -c))
    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 * (k * (y * y4));
	double tmp;
	if (y4 <= -3.6e+186) {
		tmp = t_1;
	} else if (y4 <= -8.2e+160) {
		tmp = y0 * (b * (x * -j));
	} else if (y4 <= -3e-63) {
		tmp = j * (y0 * (y3 * y5));
	} else if (y4 <= -6.8e-83) {
		tmp = b * (k * (z * y0));
	} else if (y4 <= -8.5e-146) {
		tmp = (y2 * y5) * (t * a);
	} else if (y4 <= -3.4e-229) {
		tmp = k * (y2 * (y0 * -y5));
	} else if (y4 <= 2.5e-218) {
		tmp = a * (y * (y3 * -y5));
	} else if (y4 <= 3100000000.0) {
		tmp = (y2 * y5) * (y0 * -k);
	} else if (y4 <= 4.1e+249) {
		tmp = t_1;
	} else {
		tmp = y2 * (t * (y4 * -c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = -b * (k * (y * y4))
	tmp = 0
	if y4 <= -3.6e+186:
		tmp = t_1
	elif y4 <= -8.2e+160:
		tmp = y0 * (b * (x * -j))
	elif y4 <= -3e-63:
		tmp = j * (y0 * (y3 * y5))
	elif y4 <= -6.8e-83:
		tmp = b * (k * (z * y0))
	elif y4 <= -8.5e-146:
		tmp = (y2 * y5) * (t * a)
	elif y4 <= -3.4e-229:
		tmp = k * (y2 * (y0 * -y5))
	elif y4 <= 2.5e-218:
		tmp = a * (y * (y3 * -y5))
	elif y4 <= 3100000000.0:
		tmp = (y2 * y5) * (y0 * -k)
	elif y4 <= 4.1e+249:
		tmp = t_1
	else:
		tmp = y2 * (t * (y4 * -c))
	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) * Float64(k * Float64(y * y4)))
	tmp = 0.0
	if (y4 <= -3.6e+186)
		tmp = t_1;
	elseif (y4 <= -8.2e+160)
		tmp = Float64(y0 * Float64(b * Float64(x * Float64(-j))));
	elseif (y4 <= -3e-63)
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	elseif (y4 <= -6.8e-83)
		tmp = Float64(b * Float64(k * Float64(z * y0)));
	elseif (y4 <= -8.5e-146)
		tmp = Float64(Float64(y2 * y5) * Float64(t * a));
	elseif (y4 <= -3.4e-229)
		tmp = Float64(k * Float64(y2 * Float64(y0 * Float64(-y5))));
	elseif (y4 <= 2.5e-218)
		tmp = Float64(a * Float64(y * Float64(y3 * Float64(-y5))));
	elseif (y4 <= 3100000000.0)
		tmp = Float64(Float64(y2 * y5) * Float64(y0 * Float64(-k)));
	elseif (y4 <= 4.1e+249)
		tmp = t_1;
	else
		tmp = Float64(y2 * Float64(t * Float64(y4 * Float64(-c))));
	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 * (k * (y * y4));
	tmp = 0.0;
	if (y4 <= -3.6e+186)
		tmp = t_1;
	elseif (y4 <= -8.2e+160)
		tmp = y0 * (b * (x * -j));
	elseif (y4 <= -3e-63)
		tmp = j * (y0 * (y3 * y5));
	elseif (y4 <= -6.8e-83)
		tmp = b * (k * (z * y0));
	elseif (y4 <= -8.5e-146)
		tmp = (y2 * y5) * (t * a);
	elseif (y4 <= -3.4e-229)
		tmp = k * (y2 * (y0 * -y5));
	elseif (y4 <= 2.5e-218)
		tmp = a * (y * (y3 * -y5));
	elseif (y4 <= 3100000000.0)
		tmp = (y2 * y5) * (y0 * -k);
	elseif (y4 <= 4.1e+249)
		tmp = t_1;
	else
		tmp = y2 * (t * (y4 * -c));
	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[(k * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -3.6e+186], t$95$1, If[LessEqual[y4, -8.2e+160], N[(y0 * N[(b * N[(x * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -3e-63], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -6.8e-83], N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -8.5e-146], N[(N[(y2 * y5), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -3.4e-229], N[(k * N[(y2 * N[(y0 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2.5e-218], N[(a * N[(y * N[(y3 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 3100000000.0], N[(N[(y2 * y5), $MachinePrecision] * N[(y0 * (-k)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 4.1e+249], t$95$1, N[(y2 * N[(t * N[(y4 * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y4 < -3.6000000000000002e186 or 3.1e9 < y4 < 4.0999999999999997e249

   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 y4 around inf 39.4%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in k around inf 44.2%

      \[\leadsto \color{blue}{k \cdot \left(-1 \cdot \left(b \cdot \left(y \cdot y4\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 44.2%

         \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(b \cdot \left(y \cdot y4\right)\right)\right)} \]

      2. mul-1-neg 44.2%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-b \cdot \left(y \cdot y4\right)\right)}\right) \]

      3. unsub-neg 44.2%

         \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \left(y \cdot y4\right)\right)} \]

      4. *-commutative 44.2%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \color{blue}{\left(y4 \cdot y\right)}\right) \]

   5. Simplified 44.2%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \left(y4 \cdot y\right)\right)} \]

   6. Taylor expanded in y2 around 0 44.6%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(k \cdot \left(y \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 44.6%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(k \cdot \left(y \cdot y4\right)\right)} \]

      2. neg-mul-1 44.6%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(k \cdot \left(y \cdot y4\right)\right) \]

      3. *-commutative 44.6%

         \[\leadsto \left(-b\right) \cdot \left(k \cdot \color{blue}{\left(y4 \cdot y\right)}\right) \]

   8. Simplified 44.6%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(k \cdot \left(y4 \cdot y\right)\right)} \]

   if -3.6000000000000002e186 < y4 < -8.19999999999999996e160

   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 y0 around inf 33.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 33.5%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \color{blue}{\left(j \cdot x + \left(-k \cdot z\right)\right)}\right) \]

      2. +-commutative 33.5%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \color{blue}{\left(\left(-k \cdot z\right) + j \cdot x\right)}\right) \]

      3. mul-1-neg 33.5%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(\color{blue}{-1 \cdot \left(k \cdot z\right)} + j \cdot x\right)\right) \]

      4. +-commutative 33.5%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      5. mul-1-neg 33.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      6. unsub-neg 33.5%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      7. *-commutative 33.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      8. *-commutative 33.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

   4. Simplified 33.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   5. Taylor expanded in j around -inf 45.3%

      \[\leadsto y0 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 45.3%

         \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      2. mul-1-neg 45.3%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      3. unsub-neg 45.3%

         \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   7. Simplified 45.3%

      \[\leadsto y0 \cdot \color{blue}{\left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   8. Taylor expanded in y3 around 0 67.3%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot \left(x \cdot y0\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 67.3%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(j \cdot \left(x \cdot y0\right)\right)} \]

      2. neg-mul-1 67.3%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(j \cdot \left(x \cdot y0\right)\right) \]

      3. associate-*r* 78.1%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(\left(j \cdot x\right) \cdot y0\right)} \]

      4. associate-*r* 67.4%

         \[\leadsto \color{blue}{\left(\left(-b\right) \cdot \left(j \cdot x\right)\right) \cdot y0} \]

      5. distribute-lft-neg-in 67.4%

         \[\leadsto \color{blue}{\left(-b \cdot \left(j \cdot x\right)\right)} \cdot y0 \]

      6. distribute-rgt-neg-in 67.4%

         \[\leadsto \color{blue}{\left(b \cdot \left(-j \cdot x\right)\right)} \cdot y0 \]

   10. Simplified 67.4%

       \[\leadsto \color{blue}{\left(b \cdot \left(-j \cdot x\right)\right) \cdot y0} \]

   if -8.19999999999999996e160 < y4 < -2.99999999999999979e-63

   1. Initial program 23.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y0 around inf 36.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 36.1%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \color{blue}{\left(j \cdot x + \left(-k \cdot z\right)\right)}\right) \]

      2. +-commutative 36.1%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \color{blue}{\left(\left(-k \cdot z\right) + j \cdot x\right)}\right) \]

      3. mul-1-neg 36.1%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(\color{blue}{-1 \cdot \left(k \cdot z\right)} + j \cdot x\right)\right) \]

      4. +-commutative 36.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      5. mul-1-neg 36.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      6. unsub-neg 36.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      7. *-commutative 36.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      8. *-commutative 36.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

   4. Simplified 36.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   5. Taylor expanded in j around -inf 36.3%

      \[\leadsto y0 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 36.3%

         \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      2. mul-1-neg 36.3%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      3. unsub-neg 36.3%

         \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   7. Simplified 36.3%

      \[\leadsto y0 \cdot \color{blue}{\left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   8. Taylor expanded in y3 around inf 32.3%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]

   if -2.99999999999999979e-63 < y4 < -6.7999999999999995e-83

   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 k around -inf 62.9%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 62.9%

         \[\leadsto \color{blue}{-k \cdot \left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. *-commutative 62.9%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot k} \]

      3. distribute-rgt-neg-in 62.9%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right)} \]

      4. +-commutative 62.9%

         \[\leadsto \left(\color{blue}{\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      5. mul-1-neg 62.9%

         \[\leadsto \left(\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      6. unsub-neg 62.9%

         \[\leadsto \left(\color{blue}{\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      7. *-commutative 62.9%

         \[\leadsto \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y} - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

   4. Simplified 62.9%

      \[\leadsto \color{blue}{\left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot y - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right)} \]

   5. Taylor expanded in y0 around -inf 75.6%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \cdot \left(-k\right) \]
   6. Step-by-step derivation

      1. +-commutative 75.6%

         \[\leadsto \left(y0 \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \cdot \left(-k\right) \]

      2. mul-1-neg 75.6%

         \[\leadsto \left(y0 \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \cdot \left(-k\right) \]

      3. unsub-neg 75.6%

         \[\leadsto \left(y0 \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \cdot \left(-k\right) \]

   7. Simplified 75.6%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \cdot \left(-k\right) \]

   8. Taylor expanded in y2 around 0 63.4%

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]

   if -6.7999999999999995e-83 < y4 < -8.4999999999999997e-146

   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 j around inf 31.6%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 31.6%

         \[\leadsto \left(\left(\color{blue}{\left(-j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 31.6%

         \[\leadsto \left(\left(\left(-\color{blue}{\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 31.6%

      \[\leadsto \left(\left(\color{blue}{\left(-\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 57.2%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 57.2%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 57.2%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 57.2%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y2 around inf 44.5%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 44.5%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \left(y2 \cdot y5\right)} \]

   10. Simplified 44.5%

       \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \left(y2 \cdot y5\right)} \]

   if -8.4999999999999997e-146 < y4 < -3.3999999999999999e-229

   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 y4 around inf 23.6%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in k around inf 46.0%

      \[\leadsto \color{blue}{k \cdot \left(-1 \cdot \left(b \cdot \left(y \cdot y4\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 46.0%

         \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(b \cdot \left(y \cdot y4\right)\right)\right)} \]

      2. mul-1-neg 46.0%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-b \cdot \left(y \cdot y4\right)\right)}\right) \]

      3. unsub-neg 46.0%

         \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \left(y \cdot y4\right)\right)} \]

      4. *-commutative 46.0%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \color{blue}{\left(y4 \cdot y\right)}\right) \]

   5. Simplified 46.0%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \left(y4 \cdot y\right)\right)} \]

   6. Taylor expanded in y4 around 0 40.2%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 40.2%

         \[\leadsto \color{blue}{-k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)} \]

      2. *-commutative 40.2%

         \[\leadsto -\color{blue}{\left(y0 \cdot \left(y2 \cdot y5\right)\right) \cdot k} \]

      3. distribute-rgt-neg-in 40.2%

         \[\leadsto \color{blue}{\left(y0 \cdot \left(y2 \cdot y5\right)\right) \cdot \left(-k\right)} \]

      4. *-commutative 40.2%

         \[\leadsto \color{blue}{\left(\left(y2 \cdot y5\right) \cdot y0\right)} \cdot \left(-k\right) \]

      5. associate-*l* 45.6%

         \[\leadsto \color{blue}{\left(y2 \cdot \left(y5 \cdot y0\right)\right)} \cdot \left(-k\right) \]

      6. *-commutative 45.6%

         \[\leadsto \left(y2 \cdot \color{blue}{\left(y0 \cdot y5\right)}\right) \cdot \left(-k\right) \]

   8. Simplified 45.6%

      \[\leadsto \color{blue}{\left(y2 \cdot \left(y0 \cdot y5\right)\right) \cdot \left(-k\right)} \]

   if -3.3999999999999999e-229 < y4 < 2.50000000000000021e-218

   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 j around inf 32.6%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 32.6%

         \[\leadsto \left(\left(\color{blue}{\left(-j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 32.6%

         \[\leadsto \left(\left(\left(-\color{blue}{\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 32.6%

      \[\leadsto \left(\left(\color{blue}{\left(-\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 51.2%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 51.2%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 51.2%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 51.2%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y2 around 0 40.5%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 40.5%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot y\right) \cdot \left(y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 40.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y\right)} \cdot \left(y3 \cdot y5\right)\right) \]

   10. Simplified 40.5%

       \[\leadsto a \cdot \color{blue}{\left(\left(-y\right) \cdot \left(y3 \cdot y5\right)\right)} \]

   if 2.50000000000000021e-218 < y4 < 3.1e9

   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 y4 around inf 42.6%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in k around inf 33.8%

      \[\leadsto \color{blue}{k \cdot \left(-1 \cdot \left(b \cdot \left(y \cdot y4\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 33.8%

         \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(b \cdot \left(y \cdot y4\right)\right)\right)} \]

      2. mul-1-neg 33.8%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-b \cdot \left(y \cdot y4\right)\right)}\right) \]

      3. unsub-neg 33.8%

         \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \left(y \cdot y4\right)\right)} \]

      4. *-commutative 33.8%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \color{blue}{\left(y4 \cdot y\right)}\right) \]

   5. Simplified 33.8%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \left(y4 \cdot y\right)\right)} \]

   6. Taylor expanded in y4 around 0 29.2%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 29.2%

         \[\leadsto \color{blue}{-k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)} \]

      2. associate-*r* 31.4%

         \[\leadsto -\color{blue}{\left(k \cdot y0\right) \cdot \left(y2 \cdot y5\right)} \]

   8. Simplified 31.4%

      \[\leadsto \color{blue}{-\left(k \cdot y0\right) \cdot \left(y2 \cdot y5\right)} \]

   if 4.0999999999999997e249 < y4

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 33.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 33.8%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 33.8%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 33.8%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 33.8%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 33.8%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 33.8%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 33.8%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 33.8%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 33.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in t around inf 67.9%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   6. Taylor expanded in a around 0 47.0%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 47.0%

         \[\leadsto t \cdot \color{blue}{\left(-c \cdot \left(y2 \cdot y4\right)\right)} \]

      2. *-commutative 47.0%

         \[\leadsto t \cdot \left(-\color{blue}{\left(y2 \cdot y4\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in 47.0%

         \[\leadsto t \cdot \color{blue}{\left(\left(y2 \cdot y4\right) \cdot \left(-c\right)\right)} \]

   8. Simplified 47.0%

      \[\leadsto t \cdot \color{blue}{\left(\left(y2 \cdot y4\right) \cdot \left(-c\right)\right)} \]

   9. Taylor expanded in t around 0 46.8%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 46.8%

          \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

       2. distribute-lft-neg-in 46.8%

          \[\leadsto \color{blue}{\left(-c\right) \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

       3. *-commutative 46.8%

          \[\leadsto \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right) \cdot \left(-c\right)} \]

       4. associate-*r* 46.4%

          \[\leadsto \color{blue}{\left(\left(t \cdot y2\right) \cdot y4\right)} \cdot \left(-c\right) \]

       5. associate-*r* 56.8%

          \[\leadsto \color{blue}{\left(t \cdot y2\right) \cdot \left(y4 \cdot \left(-c\right)\right)} \]

       6. *-commutative 56.8%

          \[\leadsto \color{blue}{\left(y2 \cdot t\right)} \cdot \left(y4 \cdot \left(-c\right)\right) \]

       7. associate-*l* 78.2%

          \[\leadsto \color{blue}{y2 \cdot \left(t \cdot \left(y4 \cdot \left(-c\right)\right)\right)} \]

   11. Simplified 78.2%

       \[\leadsto \color{blue}{y2 \cdot \left(t \cdot \left(y4 \cdot \left(-c\right)\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -3.6 \cdot 10^{+186}:\\ \;\;\;\;\left(-b\right) \cdot \left(k \cdot \left(y \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -8.2 \cdot 10^{+160}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(x \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -3 \cdot 10^{-63}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq -6.8 \cdot 10^{-83}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -8.5 \cdot 10^{-146}:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;y4 \leq -3.4 \cdot 10^{-229}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y0 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 2.5 \cdot 10^{-218}:\\ \;\;\;\;a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 3100000000:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(y0 \cdot \left(-k\right)\right)\\ \mathbf{elif}\;y4 \leq 4.1 \cdot 10^{+249}:\\ \;\;\;\;\left(-b\right) \cdot \left(k \cdot \left(y \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(y4 \cdot \left(-c\right)\right)\right)\\ \end{array} \]

Alternative 17: 21.7% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-b\right) \cdot \left(k \cdot \left(y \cdot y4\right)\right)\\ \mathbf{if}\;y4 \leq -1.2 \cdot 10^{+219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq -6.8 \cdot 10^{+161}:\\ \;\;\;\;b \cdot \left(j \cdot \left(y0 \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -9.5 \cdot 10^{-63}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq -2.6 \cdot 10^{-82}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -8 \cdot 10^{-146}:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;y4 \leq -2.1 \cdot 10^{-223}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y0 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 2.9 \cdot 10^{-214}:\\ \;\;\;\;a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 32000000000:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(y0 \cdot \left(-k\right)\right)\\ \mathbf{elif}\;y4 \leq 1.05 \cdot 10^{+250}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(y4 \cdot \left(-c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (- b) (* k (* y y4)))))
   (if (<= y4 -1.2e+219)
     t_1
     (if (<= y4 -6.8e+161)
       (* b (* j (* y0 (- x))))
       (if (<= y4 -9.5e-63)
         (* j (* y0 (* y3 y5)))
         (if (<= y4 -2.6e-82)
           (* b (* k (* z y0)))
           (if (<= y4 -8e-146)
             (* (* y2 y5) (* t a))
             (if (<= y4 -2.1e-223)
               (* k (* y2 (* y0 (- y5))))
               (if (<= y4 2.9e-214)
                 (* a (* y (* y3 (- y5))))
                 (if (<= y4 32000000000.0)
                   (* (* y2 y5) (* y0 (- k)))
                   (if (<= y4 1.05e+250)
                     t_1
                     (* y2 (* t (* y4 (- c)))))))))))))))

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 * (k * (y * y4));
	double tmp;
	if (y4 <= -1.2e+219) {
		tmp = t_1;
	} else if (y4 <= -6.8e+161) {
		tmp = b * (j * (y0 * -x));
	} else if (y4 <= -9.5e-63) {
		tmp = j * (y0 * (y3 * y5));
	} else if (y4 <= -2.6e-82) {
		tmp = b * (k * (z * y0));
	} else if (y4 <= -8e-146) {
		tmp = (y2 * y5) * (t * a);
	} else if (y4 <= -2.1e-223) {
		tmp = k * (y2 * (y0 * -y5));
	} else if (y4 <= 2.9e-214) {
		tmp = a * (y * (y3 * -y5));
	} else if (y4 <= 32000000000.0) {
		tmp = (y2 * y5) * (y0 * -k);
	} else if (y4 <= 1.05e+250) {
		tmp = t_1;
	} else {
		tmp = y2 * (t * (y4 * -c));
	}
	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 * (k * (y * y4))
    if (y4 <= (-1.2d+219)) then
        tmp = t_1
    else if (y4 <= (-6.8d+161)) then
        tmp = b * (j * (y0 * -x))
    else if (y4 <= (-9.5d-63)) then
        tmp = j * (y0 * (y3 * y5))
    else if (y4 <= (-2.6d-82)) then
        tmp = b * (k * (z * y0))
    else if (y4 <= (-8d-146)) then
        tmp = (y2 * y5) * (t * a)
    else if (y4 <= (-2.1d-223)) then
        tmp = k * (y2 * (y0 * -y5))
    else if (y4 <= 2.9d-214) then
        tmp = a * (y * (y3 * -y5))
    else if (y4 <= 32000000000.0d0) then
        tmp = (y2 * y5) * (y0 * -k)
    else if (y4 <= 1.05d+250) then
        tmp = t_1
    else
        tmp = y2 * (t * (y4 * -c))
    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 * (k * (y * y4));
	double tmp;
	if (y4 <= -1.2e+219) {
		tmp = t_1;
	} else if (y4 <= -6.8e+161) {
		tmp = b * (j * (y0 * -x));
	} else if (y4 <= -9.5e-63) {
		tmp = j * (y0 * (y3 * y5));
	} else if (y4 <= -2.6e-82) {
		tmp = b * (k * (z * y0));
	} else if (y4 <= -8e-146) {
		tmp = (y2 * y5) * (t * a);
	} else if (y4 <= -2.1e-223) {
		tmp = k * (y2 * (y0 * -y5));
	} else if (y4 <= 2.9e-214) {
		tmp = a * (y * (y3 * -y5));
	} else if (y4 <= 32000000000.0) {
		tmp = (y2 * y5) * (y0 * -k);
	} else if (y4 <= 1.05e+250) {
		tmp = t_1;
	} else {
		tmp = y2 * (t * (y4 * -c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = -b * (k * (y * y4))
	tmp = 0
	if y4 <= -1.2e+219:
		tmp = t_1
	elif y4 <= -6.8e+161:
		tmp = b * (j * (y0 * -x))
	elif y4 <= -9.5e-63:
		tmp = j * (y0 * (y3 * y5))
	elif y4 <= -2.6e-82:
		tmp = b * (k * (z * y0))
	elif y4 <= -8e-146:
		tmp = (y2 * y5) * (t * a)
	elif y4 <= -2.1e-223:
		tmp = k * (y2 * (y0 * -y5))
	elif y4 <= 2.9e-214:
		tmp = a * (y * (y3 * -y5))
	elif y4 <= 32000000000.0:
		tmp = (y2 * y5) * (y0 * -k)
	elif y4 <= 1.05e+250:
		tmp = t_1
	else:
		tmp = y2 * (t * (y4 * -c))
	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) * Float64(k * Float64(y * y4)))
	tmp = 0.0
	if (y4 <= -1.2e+219)
		tmp = t_1;
	elseif (y4 <= -6.8e+161)
		tmp = Float64(b * Float64(j * Float64(y0 * Float64(-x))));
	elseif (y4 <= -9.5e-63)
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	elseif (y4 <= -2.6e-82)
		tmp = Float64(b * Float64(k * Float64(z * y0)));
	elseif (y4 <= -8e-146)
		tmp = Float64(Float64(y2 * y5) * Float64(t * a));
	elseif (y4 <= -2.1e-223)
		tmp = Float64(k * Float64(y2 * Float64(y0 * Float64(-y5))));
	elseif (y4 <= 2.9e-214)
		tmp = Float64(a * Float64(y * Float64(y3 * Float64(-y5))));
	elseif (y4 <= 32000000000.0)
		tmp = Float64(Float64(y2 * y5) * Float64(y0 * Float64(-k)));
	elseif (y4 <= 1.05e+250)
		tmp = t_1;
	else
		tmp = Float64(y2 * Float64(t * Float64(y4 * Float64(-c))));
	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 * (k * (y * y4));
	tmp = 0.0;
	if (y4 <= -1.2e+219)
		tmp = t_1;
	elseif (y4 <= -6.8e+161)
		tmp = b * (j * (y0 * -x));
	elseif (y4 <= -9.5e-63)
		tmp = j * (y0 * (y3 * y5));
	elseif (y4 <= -2.6e-82)
		tmp = b * (k * (z * y0));
	elseif (y4 <= -8e-146)
		tmp = (y2 * y5) * (t * a);
	elseif (y4 <= -2.1e-223)
		tmp = k * (y2 * (y0 * -y5));
	elseif (y4 <= 2.9e-214)
		tmp = a * (y * (y3 * -y5));
	elseif (y4 <= 32000000000.0)
		tmp = (y2 * y5) * (y0 * -k);
	elseif (y4 <= 1.05e+250)
		tmp = t_1;
	else
		tmp = y2 * (t * (y4 * -c));
	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[(k * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -1.2e+219], t$95$1, If[LessEqual[y4, -6.8e+161], N[(b * N[(j * N[(y0 * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -9.5e-63], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -2.6e-82], N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -8e-146], N[(N[(y2 * y5), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -2.1e-223], N[(k * N[(y2 * N[(y0 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2.9e-214], N[(a * N[(y * N[(y3 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 32000000000.0], N[(N[(y2 * y5), $MachinePrecision] * N[(y0 * (-k)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.05e+250], t$95$1, N[(y2 * N[(t * N[(y4 * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y4 < -1.2e219 or 3.2e10 < y4 < 1.0500000000000001e250

   1. Initial program 19.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 40.7%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in k around inf 44.2%

      \[\leadsto \color{blue}{k \cdot \left(-1 \cdot \left(b \cdot \left(y \cdot y4\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 44.2%

         \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(b \cdot \left(y \cdot y4\right)\right)\right)} \]

      2. mul-1-neg 44.2%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-b \cdot \left(y \cdot y4\right)\right)}\right) \]

      3. unsub-neg 44.2%

         \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \left(y \cdot y4\right)\right)} \]

      4. *-commutative 44.2%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \color{blue}{\left(y4 \cdot y\right)}\right) \]

   5. Simplified 44.2%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \left(y4 \cdot y\right)\right)} \]

   6. Taylor expanded in y2 around 0 46.4%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(k \cdot \left(y \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 46.4%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(k \cdot \left(y \cdot y4\right)\right)} \]

      2. neg-mul-1 46.4%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(k \cdot \left(y \cdot y4\right)\right) \]

      3. *-commutative 46.4%

         \[\leadsto \left(-b\right) \cdot \left(k \cdot \color{blue}{\left(y4 \cdot y\right)}\right) \]

   8. Simplified 46.4%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(k \cdot \left(y4 \cdot y\right)\right)} \]

   if -1.2e219 < y4 < -6.79999999999999986e161

   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 y0 around inf 31.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 31.7%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \color{blue}{\left(j \cdot x + \left(-k \cdot z\right)\right)}\right) \]

      2. +-commutative 31.7%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \color{blue}{\left(\left(-k \cdot z\right) + j \cdot x\right)}\right) \]

      3. mul-1-neg 31.7%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(\color{blue}{-1 \cdot \left(k \cdot z\right)} + j \cdot x\right)\right) \]

      4. +-commutative 31.7%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      5. mul-1-neg 31.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      6. unsub-neg 31.7%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      7. *-commutative 31.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      8. *-commutative 31.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

   4. Simplified 31.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   5. Taylor expanded in j around -inf 38.5%

      \[\leadsto y0 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 38.5%

         \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      2. mul-1-neg 38.5%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      3. unsub-neg 38.5%

         \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   7. Simplified 38.5%

      \[\leadsto y0 \cdot \color{blue}{\left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   8. Taylor expanded in y3 around 0 56.8%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot \left(x \cdot y0\right)\right)\right)} \]

   if -6.79999999999999986e161 < y4 < -9.50000000000000016e-63

   1. Initial program 23.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y0 around inf 36.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 36.1%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \color{blue}{\left(j \cdot x + \left(-k \cdot z\right)\right)}\right) \]

      2. +-commutative 36.1%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \color{blue}{\left(\left(-k \cdot z\right) + j \cdot x\right)}\right) \]

      3. mul-1-neg 36.1%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(\color{blue}{-1 \cdot \left(k \cdot z\right)} + j \cdot x\right)\right) \]

      4. +-commutative 36.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      5. mul-1-neg 36.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      6. unsub-neg 36.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      7. *-commutative 36.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      8. *-commutative 36.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

   4. Simplified 36.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   5. Taylor expanded in j around -inf 36.3%

      \[\leadsto y0 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 36.3%

         \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      2. mul-1-neg 36.3%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      3. unsub-neg 36.3%

         \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   7. Simplified 36.3%

      \[\leadsto y0 \cdot \color{blue}{\left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   8. Taylor expanded in y3 around inf 32.3%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]

   if -9.50000000000000016e-63 < y4 < -2.6e-82

   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 k around -inf 62.9%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 62.9%

         \[\leadsto \color{blue}{-k \cdot \left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. *-commutative 62.9%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot k} \]

      3. distribute-rgt-neg-in 62.9%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right)} \]

      4. +-commutative 62.9%

         \[\leadsto \left(\color{blue}{\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      5. mul-1-neg 62.9%

         \[\leadsto \left(\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      6. unsub-neg 62.9%

         \[\leadsto \left(\color{blue}{\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      7. *-commutative 62.9%

         \[\leadsto \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y} - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

   4. Simplified 62.9%

      \[\leadsto \color{blue}{\left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot y - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right)} \]

   5. Taylor expanded in y0 around -inf 75.6%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \cdot \left(-k\right) \]
   6. Step-by-step derivation

      1. +-commutative 75.6%

         \[\leadsto \left(y0 \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \cdot \left(-k\right) \]

      2. mul-1-neg 75.6%

         \[\leadsto \left(y0 \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \cdot \left(-k\right) \]

      3. unsub-neg 75.6%

         \[\leadsto \left(y0 \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \cdot \left(-k\right) \]

   7. Simplified 75.6%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \cdot \left(-k\right) \]

   8. Taylor expanded in y2 around 0 63.4%

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]

   if -2.6e-82 < y4 < -8.00000000000000021e-146

   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 j around inf 31.6%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 31.6%

         \[\leadsto \left(\left(\color{blue}{\left(-j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 31.6%

         \[\leadsto \left(\left(\left(-\color{blue}{\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 31.6%

      \[\leadsto \left(\left(\color{blue}{\left(-\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 57.2%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 57.2%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 57.2%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 57.2%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y2 around inf 44.5%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 44.5%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \left(y2 \cdot y5\right)} \]

   10. Simplified 44.5%

       \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \left(y2 \cdot y5\right)} \]

   if -8.00000000000000021e-146 < y4 < -2.09999999999999982e-223

   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 y4 around inf 23.6%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in k around inf 46.0%

      \[\leadsto \color{blue}{k \cdot \left(-1 \cdot \left(b \cdot \left(y \cdot y4\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 46.0%

         \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(b \cdot \left(y \cdot y4\right)\right)\right)} \]

      2. mul-1-neg 46.0%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-b \cdot \left(y \cdot y4\right)\right)}\right) \]

      3. unsub-neg 46.0%

         \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \left(y \cdot y4\right)\right)} \]

      4. *-commutative 46.0%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \color{blue}{\left(y4 \cdot y\right)}\right) \]

   5. Simplified 46.0%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \left(y4 \cdot y\right)\right)} \]

   6. Taylor expanded in y4 around 0 40.2%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 40.2%

         \[\leadsto \color{blue}{-k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)} \]

      2. *-commutative 40.2%

         \[\leadsto -\color{blue}{\left(y0 \cdot \left(y2 \cdot y5\right)\right) \cdot k} \]

      3. distribute-rgt-neg-in 40.2%

         \[\leadsto \color{blue}{\left(y0 \cdot \left(y2 \cdot y5\right)\right) \cdot \left(-k\right)} \]

      4. *-commutative 40.2%

         \[\leadsto \color{blue}{\left(\left(y2 \cdot y5\right) \cdot y0\right)} \cdot \left(-k\right) \]

      5. associate-*l* 45.6%

         \[\leadsto \color{blue}{\left(y2 \cdot \left(y5 \cdot y0\right)\right)} \cdot \left(-k\right) \]

      6. *-commutative 45.6%

         \[\leadsto \left(y2 \cdot \color{blue}{\left(y0 \cdot y5\right)}\right) \cdot \left(-k\right) \]

   8. Simplified 45.6%

      \[\leadsto \color{blue}{\left(y2 \cdot \left(y0 \cdot y5\right)\right) \cdot \left(-k\right)} \]

   if -2.09999999999999982e-223 < y4 < 2.89999999999999985e-214

   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 j around inf 32.6%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 32.6%

         \[\leadsto \left(\left(\color{blue}{\left(-j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 32.6%

         \[\leadsto \left(\left(\left(-\color{blue}{\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 32.6%

      \[\leadsto \left(\left(\color{blue}{\left(-\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 51.2%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 51.2%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 51.2%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 51.2%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y2 around 0 40.5%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 40.5%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot y\right) \cdot \left(y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 40.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y\right)} \cdot \left(y3 \cdot y5\right)\right) \]

   10. Simplified 40.5%

       \[\leadsto a \cdot \color{blue}{\left(\left(-y\right) \cdot \left(y3 \cdot y5\right)\right)} \]

   if 2.89999999999999985e-214 < y4 < 3.2e10

   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 y4 around inf 42.6%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in k around inf 33.8%

      \[\leadsto \color{blue}{k \cdot \left(-1 \cdot \left(b \cdot \left(y \cdot y4\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 33.8%

         \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(b \cdot \left(y \cdot y4\right)\right)\right)} \]

      2. mul-1-neg 33.8%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-b \cdot \left(y \cdot y4\right)\right)}\right) \]

      3. unsub-neg 33.8%

         \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \left(y \cdot y4\right)\right)} \]

      4. *-commutative 33.8%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \color{blue}{\left(y4 \cdot y\right)}\right) \]

   5. Simplified 33.8%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \left(y4 \cdot y\right)\right)} \]

   6. Taylor expanded in y4 around 0 29.2%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 29.2%

         \[\leadsto \color{blue}{-k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)} \]

      2. associate-*r* 31.4%

         \[\leadsto -\color{blue}{\left(k \cdot y0\right) \cdot \left(y2 \cdot y5\right)} \]

   8. Simplified 31.4%

      \[\leadsto \color{blue}{-\left(k \cdot y0\right) \cdot \left(y2 \cdot y5\right)} \]

   if 1.0500000000000001e250 < y4

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 33.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 33.8%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 33.8%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 33.8%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 33.8%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 33.8%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 33.8%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 33.8%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 33.8%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 33.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in t around inf 67.9%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   6. Taylor expanded in a around 0 47.0%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 47.0%

         \[\leadsto t \cdot \color{blue}{\left(-c \cdot \left(y2 \cdot y4\right)\right)} \]

      2. *-commutative 47.0%

         \[\leadsto t \cdot \left(-\color{blue}{\left(y2 \cdot y4\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in 47.0%

         \[\leadsto t \cdot \color{blue}{\left(\left(y2 \cdot y4\right) \cdot \left(-c\right)\right)} \]

   8. Simplified 47.0%

      \[\leadsto t \cdot \color{blue}{\left(\left(y2 \cdot y4\right) \cdot \left(-c\right)\right)} \]

   9. Taylor expanded in t around 0 46.8%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 46.8%

          \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

       2. distribute-lft-neg-in 46.8%

          \[\leadsto \color{blue}{\left(-c\right) \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

       3. *-commutative 46.8%

          \[\leadsto \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right) \cdot \left(-c\right)} \]

       4. associate-*r* 46.4%

          \[\leadsto \color{blue}{\left(\left(t \cdot y2\right) \cdot y4\right)} \cdot \left(-c\right) \]

       5. associate-*r* 56.8%

          \[\leadsto \color{blue}{\left(t \cdot y2\right) \cdot \left(y4 \cdot \left(-c\right)\right)} \]

       6. *-commutative 56.8%

          \[\leadsto \color{blue}{\left(y2 \cdot t\right)} \cdot \left(y4 \cdot \left(-c\right)\right) \]

       7. associate-*l* 78.2%

          \[\leadsto \color{blue}{y2 \cdot \left(t \cdot \left(y4 \cdot \left(-c\right)\right)\right)} \]

   11. Simplified 78.2%

       \[\leadsto \color{blue}{y2 \cdot \left(t \cdot \left(y4 \cdot \left(-c\right)\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.2 \cdot 10^{+219}:\\ \;\;\;\;\left(-b\right) \cdot \left(k \cdot \left(y \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -6.8 \cdot 10^{+161}:\\ \;\;\;\;b \cdot \left(j \cdot \left(y0 \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -9.5 \cdot 10^{-63}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq -2.6 \cdot 10^{-82}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -8 \cdot 10^{-146}:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;y4 \leq -2.1 \cdot 10^{-223}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y0 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 2.9 \cdot 10^{-214}:\\ \;\;\;\;a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 32000000000:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(y0 \cdot \left(-k\right)\right)\\ \mathbf{elif}\;y4 \leq 1.05 \cdot 10^{+250}:\\ \;\;\;\;\left(-b\right) \cdot \left(k \cdot \left(y \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(y4 \cdot \left(-c\right)\right)\right)\\ \end{array} \]

Alternative 18: 32.2% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+35}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-112}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-162}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{-249}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-284}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 9.7 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+88}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -2.8e+35)
   (* b (* j (- (* t y4) (* x y0))))
   (if (<= b -1.2e-112)
     (* t (* y2 (- (* a y5) (* c y4))))
     (if (<= b -1.1e-162)
       (* i (* k (- (* y y5) (* z y1))))
       (if (<= b -4.1e-249)
         (* j (* y1 (- (* x i) (* y3 y4))))
         (if (<= b 1.6e-284)
           (* j (* t (- (* b y4) (* i y5))))
           (if (<= b 9.7e-35)
             (* a (* y5 (- (* t y2) (* y y3))))
             (if (<= b 3.7e+88)
               (* j (* y0 (- (* y3 y5) (* x b))))
               (* a (* b (- (* x y) (* z t))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -2.8e+35) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -1.2e-112) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (b <= -1.1e-162) {
		tmp = i * (k * ((y * y5) - (z * y1)));
	} else if (b <= -4.1e-249) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (b <= 1.6e-284) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (b <= 9.7e-35) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (b <= 3.7e+88) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (b <= (-2.8d+35)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (b <= (-1.2d-112)) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (b <= (-1.1d-162)) then
        tmp = i * (k * ((y * y5) - (z * y1)))
    else if (b <= (-4.1d-249)) then
        tmp = j * (y1 * ((x * i) - (y3 * y4)))
    else if (b <= 1.6d-284) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (b <= 9.7d-35) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (b <= 3.7d+88) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else
        tmp = a * (b * ((x * y) - (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -2.8e+35) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -1.2e-112) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (b <= -1.1e-162) {
		tmp = i * (k * ((y * y5) - (z * y1)));
	} else if (b <= -4.1e-249) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (b <= 1.6e-284) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (b <= 9.7e-35) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (b <= 3.7e+88) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -2.8e+35:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif b <= -1.2e-112:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif b <= -1.1e-162:
		tmp = i * (k * ((y * y5) - (z * y1)))
	elif b <= -4.1e-249:
		tmp = j * (y1 * ((x * i) - (y3 * y4)))
	elif b <= 1.6e-284:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif b <= 9.7e-35:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif b <= 3.7e+88:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	else:
		tmp = a * (b * ((x * y) - (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (b <= -2.8e+35)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (b <= -1.2e-112)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (b <= -1.1e-162)
		tmp = Float64(i * Float64(k * Float64(Float64(y * y5) - Float64(z * y1))));
	elseif (b <= -4.1e-249)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (b <= 1.6e-284)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (b <= 9.7e-35)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (b <= 3.7e+88)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	else
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (b <= -2.8e+35)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (b <= -1.2e-112)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (b <= -1.1e-162)
		tmp = i * (k * ((y * y5) - (z * y1)));
	elseif (b <= -4.1e-249)
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	elseif (b <= 1.6e-284)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (b <= 9.7e-35)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (b <= 3.7e+88)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	else
		tmp = a * (b * ((x * y) - (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[b, -2.8e+35], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.2e-112], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.1e-162], N[(i * N[(k * N[(N[(y * y5), $MachinePrecision] - N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.1e-249], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6e-284], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.7e-35], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.7e+88], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if b < -2.79999999999999999e35

   1. Initial program 27.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 36.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 36.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 36.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 36.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 36.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 36.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in b around inf 55.7%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -2.79999999999999999e35 < b < -1.2e-112

   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 y2 around inf 48.7%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 48.7%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 48.7%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 48.7%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 52.4%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 52.4%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 52.4%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 52.4%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 52.4%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 52.4%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in t around inf 48.8%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   if -1.2e-112 < b < -1.1e-162

   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 k around -inf 23.9%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 23.9%

         \[\leadsto \color{blue}{-k \cdot \left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. *-commutative 23.9%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot k} \]

      3. distribute-rgt-neg-in 23.9%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right)} \]

      4. +-commutative 23.9%

         \[\leadsto \left(\color{blue}{\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      5. mul-1-neg 23.9%

         \[\leadsto \left(\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      6. unsub-neg 23.9%

         \[\leadsto \left(\color{blue}{\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      7. *-commutative 23.9%

         \[\leadsto \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y} - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

   4. Simplified 23.9%

      \[\leadsto \color{blue}{\left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot y - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right)} \]

   5. Taylor expanded in i around -inf 46.9%

      \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 46.9%

         \[\leadsto i \cdot \left(k \cdot \left(\color{blue}{y5 \cdot y} - y1 \cdot z\right)\right) \]

   7. Simplified 46.9%

      \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y5 \cdot y - y1 \cdot z\right)\right)} \]

   if -1.1e-162 < b < -4.10000000000000004e-249

   1. Initial program 52.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 47.4%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 47.4%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 47.4%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 47.4%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 47.4%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 47.4%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y1 around -inf 41.8%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 41.8%

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 41.8%

         \[\leadsto j \cdot \left(y1 \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 41.8%

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 41.8%

         \[\leadsto j \cdot \left(y1 \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 41.8%

         \[\leadsto j \cdot \left(y1 \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 41.8%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   if -4.10000000000000004e-249 < b < 1.60000000000000012e-284

   1. Initial program 49.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 47.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 47.0%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 47.0%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 47.0%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 47.0%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 47.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in t around inf 56.0%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 56.0%

         \[\leadsto j \cdot \left(t \cdot \left(\color{blue}{y4 \cdot b} - i \cdot y5\right)\right) \]

      2. *-commutative 56.0%

         \[\leadsto j \cdot \left(t \cdot \left(y4 \cdot b - \color{blue}{y5 \cdot i}\right)\right) \]

   7. Simplified 56.0%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(y4 \cdot b - y5 \cdot i\right)\right)} \]

   if 1.60000000000000012e-284 < b < 9.70000000000000073e-35

   1. Initial program 20.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 20.2%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 20.2%

         \[\leadsto \left(\left(\color{blue}{\left(-j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 21.7%

         \[\leadsto \left(\left(\left(-\color{blue}{\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 21.7%

      \[\leadsto \left(\left(\color{blue}{\left(-\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 37.6%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 37.6%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 37.6%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 37.6%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   if 9.70000000000000073e-35 < b < 3.69999999999999994e88

   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 j around inf 44.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 44.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 44.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 44.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 44.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 44.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y0 around -inf 47.9%

      \[\leadsto j \cdot \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 47.9%

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      2. mul-1-neg 47.9%

         \[\leadsto j \cdot \left(y0 \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      3. unsub-neg 47.9%

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

      4. *-commutative 47.9%

         \[\leadsto j \cdot \left(y0 \cdot \left(\color{blue}{y5 \cdot y3} - b \cdot x\right)\right) \]

      5. *-commutative 47.9%

         \[\leadsto j \cdot \left(y0 \cdot \left(y5 \cdot y3 - \color{blue}{x \cdot b}\right)\right) \]

   7. Simplified 47.9%

      \[\leadsto j \cdot \color{blue}{\left(y0 \cdot \left(y5 \cdot y3 - x \cdot b\right)\right)} \]

   if 3.69999999999999994e88 < b

   1. Initial program 20.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around inf 46.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. sub-neg 46.3%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. +-commutative 46.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. mul-1-neg 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. unsub-neg 46.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. mul-1-neg 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(-\color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. remove-double-neg 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \color{blue}{y5 \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. *-commutative 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 46.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in b around inf 63.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+35}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-112}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-162}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5 - z \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{-249}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-284}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 9.7 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+88}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]

Alternative 19: 31.8% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{if}\;b \leq -1.72 \cdot 10^{+37}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-227}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 6.7 \cdot 10^{-140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{-46}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 135000000:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{+95}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (* y2 (- (* a y5) (* c y4))))))
   (if (<= b -1.72e+37)
     (* b (* j (- (* t y4) (* x y0))))
     (if (<= b -2.8e-113)
       t_1
       (if (<= b 3.4e-227)
         (* x (* y2 (- (* c y0) (* a y1))))
         (if (<= b 6.7e-140)
           t_1
           (if (<= b 2.55e-46)
             (* j (* y1 (- (* x i) (* y3 y4))))
             (if (<= b 135000000.0)
               (* t (* y2 (* a y5)))
               (if (<= b 2.55e+95)
                 (* j (* y0 (- (* y3 y5) (* x b))))
                 (* a (* b (- (* x y) (* z t)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (y2 * ((a * y5) - (c * y4)));
	double tmp;
	if (b <= -1.72e+37) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -2.8e-113) {
		tmp = t_1;
	} else if (b <= 3.4e-227) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (b <= 6.7e-140) {
		tmp = t_1;
	} else if (b <= 2.55e-46) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (b <= 135000000.0) {
		tmp = t * (y2 * (a * y5));
	} else if (b <= 2.55e+95) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y2 * ((a * y5) - (c * y4)))
    if (b <= (-1.72d+37)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (b <= (-2.8d-113)) then
        tmp = t_1
    else if (b <= 3.4d-227) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (b <= 6.7d-140) then
        tmp = t_1
    else if (b <= 2.55d-46) then
        tmp = j * (y1 * ((x * i) - (y3 * y4)))
    else if (b <= 135000000.0d0) then
        tmp = t * (y2 * (a * y5))
    else if (b <= 2.55d+95) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else
        tmp = a * (b * ((x * y) - (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (y2 * ((a * y5) - (c * y4)));
	double tmp;
	if (b <= -1.72e+37) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -2.8e-113) {
		tmp = t_1;
	} else if (b <= 3.4e-227) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (b <= 6.7e-140) {
		tmp = t_1;
	} else if (b <= 2.55e-46) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (b <= 135000000.0) {
		tmp = t * (y2 * (a * y5));
	} else if (b <= 2.55e+95) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = t * (y2 * ((a * y5) - (c * y4)))
	tmp = 0
	if b <= -1.72e+37:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif b <= -2.8e-113:
		tmp = t_1
	elif b <= 3.4e-227:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif b <= 6.7e-140:
		tmp = t_1
	elif b <= 2.55e-46:
		tmp = j * (y1 * ((x * i) - (y3 * y4)))
	elif b <= 135000000.0:
		tmp = t * (y2 * (a * y5))
	elif b <= 2.55e+95:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	else:
		tmp = a * (b * ((x * y) - (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))))
	tmp = 0.0
	if (b <= -1.72e+37)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (b <= -2.8e-113)
		tmp = t_1;
	elseif (b <= 3.4e-227)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (b <= 6.7e-140)
		tmp = t_1;
	elseif (b <= 2.55e-46)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (b <= 135000000.0)
		tmp = Float64(t * Float64(y2 * Float64(a * y5)));
	elseif (b <= 2.55e+95)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	else
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = t * (y2 * ((a * y5) - (c * y4)));
	tmp = 0.0;
	if (b <= -1.72e+37)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (b <= -2.8e-113)
		tmp = t_1;
	elseif (b <= 3.4e-227)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (b <= 6.7e-140)
		tmp = t_1;
	elseif (b <= 2.55e-46)
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	elseif (b <= 135000000.0)
		tmp = t * (y2 * (a * y5));
	elseif (b <= 2.55e+95)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	else
		tmp = a * (b * ((x * y) - (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.72e+37], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.8e-113], t$95$1, If[LessEqual[b, 3.4e-227], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.7e-140], t$95$1, If[LessEqual[b, 2.55e-46], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 135000000.0], N[(t * N[(y2 * N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.55e+95], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -1.72000000000000002e37

   1. Initial program 27.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 36.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 36.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 36.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 36.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 36.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 36.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in b around inf 55.7%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -1.72000000000000002e37 < b < -2.8e-113 or 3.39999999999999979e-227 < b < 6.7e-140

   1. Initial program 34.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 39.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 39.0%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 39.0%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 39.0%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 42.9%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 42.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 42.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 42.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 42.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 42.9%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in t around inf 48.9%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   if -2.8e-113 < b < 3.39999999999999979e-227

   1. Initial program 40.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 44.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 44.0%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 44.0%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 44.0%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 45.9%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 45.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 45.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 45.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 45.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 45.9%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in x around inf 48.2%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 48.2%

         \[\leadsto x \cdot \left(y2 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right)\right) \]

      2. *-commutative 48.2%

         \[\leadsto x \cdot \left(y2 \cdot \left(y0 \cdot c - \color{blue}{y1 \cdot a}\right)\right) \]

   7. Simplified 48.2%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(y0 \cdot c - y1 \cdot a\right)\right)} \]

   if 6.7e-140 < b < 2.5499999999999999e-46

   1. Initial program 13.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 31.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 31.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 31.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 31.3%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 31.3%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 31.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y1 around -inf 45.0%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 45.0%

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 45.0%

         \[\leadsto j \cdot \left(y1 \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 45.0%

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 45.0%

         \[\leadsto j \cdot \left(y1 \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 45.0%

         \[\leadsto j \cdot \left(y1 \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 45.0%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   if 2.5499999999999999e-46 < b < 1.35e8

   1. Initial program 29.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 53.3%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 53.3%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 53.3%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 53.3%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 53.3%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 53.3%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 53.3%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 53.3%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 53.3%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 53.3%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in t around inf 53.9%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   6. Taylor expanded in a around inf 54.0%

      \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(a \cdot y5\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative 54.0%

         \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot a\right)}\right) \]

   8. Simplified 54.0%

      \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot a\right)}\right) \]

   if 1.35e8 < b < 2.55000000000000001e95

   1. Initial program 34.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 55.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 55.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 55.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 55.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 55.1%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 55.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y0 around -inf 51.1%

      \[\leadsto j \cdot \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 51.1%

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      2. mul-1-neg 51.1%

         \[\leadsto j \cdot \left(y0 \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      3. unsub-neg 51.1%

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

      4. *-commutative 51.1%

         \[\leadsto j \cdot \left(y0 \cdot \left(\color{blue}{y5 \cdot y3} - b \cdot x\right)\right) \]

      5. *-commutative 51.1%

         \[\leadsto j \cdot \left(y0 \cdot \left(y5 \cdot y3 - \color{blue}{x \cdot b}\right)\right) \]

   7. Simplified 51.1%

      \[\leadsto j \cdot \color{blue}{\left(y0 \cdot \left(y5 \cdot y3 - x \cdot b\right)\right)} \]

   if 2.55000000000000001e95 < b

   1. Initial program 20.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around inf 46.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. sub-neg 46.3%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. +-commutative 46.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. mul-1-neg 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. unsub-neg 46.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. mul-1-neg 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(-\color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. remove-double-neg 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \color{blue}{y5 \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. *-commutative 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 46.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in b around inf 63.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.72 \cdot 10^{+37}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-113}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-227}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 6.7 \cdot 10^{-140}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{-46}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 135000000:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{+95}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]

Alternative 20: 32.0% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{if}\;b \leq -5.5 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -6.3 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-228}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 1.92 \cdot 10^{-141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{-91}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 52:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c - k \cdot y5\right)\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{+92}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (* y2 (- (* a y5) (* c y4))))))
   (if (<= b -5.5e+36)
     (* b (* j (- (* t y4) (* x y0))))
     (if (<= b -6.3e-113)
       t_1
       (if (<= b 4.6e-228)
         (* x (* y2 (- (* c y0) (* a y1))))
         (if (<= b 1.92e-141)
           t_1
           (if (<= b 4.7e-91)
             (* j (* y1 (- (* x i) (* y3 y4))))
             (if (<= b 52.0)
               (* (* y0 y2) (- (* x c) (* k y5)))
               (if (<= b 8.6e+92)
                 (* j (* y0 (- (* y3 y5) (* x b))))
                 (* a (* b (- (* x y) (* z t)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (y2 * ((a * y5) - (c * y4)));
	double tmp;
	if (b <= -5.5e+36) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -6.3e-113) {
		tmp = t_1;
	} else if (b <= 4.6e-228) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (b <= 1.92e-141) {
		tmp = t_1;
	} else if (b <= 4.7e-91) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (b <= 52.0) {
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	} else if (b <= 8.6e+92) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y2 * ((a * y5) - (c * y4)))
    if (b <= (-5.5d+36)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (b <= (-6.3d-113)) then
        tmp = t_1
    else if (b <= 4.6d-228) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (b <= 1.92d-141) then
        tmp = t_1
    else if (b <= 4.7d-91) then
        tmp = j * (y1 * ((x * i) - (y3 * y4)))
    else if (b <= 52.0d0) then
        tmp = (y0 * y2) * ((x * c) - (k * y5))
    else if (b <= 8.6d+92) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else
        tmp = a * (b * ((x * y) - (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (y2 * ((a * y5) - (c * y4)));
	double tmp;
	if (b <= -5.5e+36) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -6.3e-113) {
		tmp = t_1;
	} else if (b <= 4.6e-228) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (b <= 1.92e-141) {
		tmp = t_1;
	} else if (b <= 4.7e-91) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (b <= 52.0) {
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	} else if (b <= 8.6e+92) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = t * (y2 * ((a * y5) - (c * y4)))
	tmp = 0
	if b <= -5.5e+36:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif b <= -6.3e-113:
		tmp = t_1
	elif b <= 4.6e-228:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif b <= 1.92e-141:
		tmp = t_1
	elif b <= 4.7e-91:
		tmp = j * (y1 * ((x * i) - (y3 * y4)))
	elif b <= 52.0:
		tmp = (y0 * y2) * ((x * c) - (k * y5))
	elif b <= 8.6e+92:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	else:
		tmp = a * (b * ((x * y) - (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))))
	tmp = 0.0
	if (b <= -5.5e+36)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (b <= -6.3e-113)
		tmp = t_1;
	elseif (b <= 4.6e-228)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (b <= 1.92e-141)
		tmp = t_1;
	elseif (b <= 4.7e-91)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (b <= 52.0)
		tmp = Float64(Float64(y0 * y2) * Float64(Float64(x * c) - Float64(k * y5)));
	elseif (b <= 8.6e+92)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	else
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = t * (y2 * ((a * y5) - (c * y4)));
	tmp = 0.0;
	if (b <= -5.5e+36)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (b <= -6.3e-113)
		tmp = t_1;
	elseif (b <= 4.6e-228)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (b <= 1.92e-141)
		tmp = t_1;
	elseif (b <= 4.7e-91)
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	elseif (b <= 52.0)
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	elseif (b <= 8.6e+92)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	else
		tmp = a * (b * ((x * y) - (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.5e+36], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.3e-113], t$95$1, If[LessEqual[b, 4.6e-228], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.92e-141], t$95$1, If[LessEqual[b, 4.7e-91], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 52.0], N[(N[(y0 * y2), $MachinePrecision] * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.6e+92], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -5.5000000000000002e36

   1. Initial program 27.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 36.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 36.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 36.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 36.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 36.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 36.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in b around inf 55.7%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -5.5000000000000002e36 < b < -6.2999999999999997e-113 or 4.5999999999999998e-228 < b < 1.9199999999999999e-141

   1. Initial program 34.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 39.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 39.0%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 39.0%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 39.0%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 42.9%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 42.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 42.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 42.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 42.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 42.9%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in t around inf 48.9%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   if -6.2999999999999997e-113 < b < 4.5999999999999998e-228

   1. Initial program 40.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 44.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 44.0%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 44.0%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 44.0%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 45.9%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 45.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 45.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 45.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 45.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 45.9%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in x around inf 48.2%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 48.2%

         \[\leadsto x \cdot \left(y2 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right)\right) \]

      2. *-commutative 48.2%

         \[\leadsto x \cdot \left(y2 \cdot \left(y0 \cdot c - \color{blue}{y1 \cdot a}\right)\right) \]

   7. Simplified 48.2%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(y0 \cdot c - y1 \cdot a\right)\right)} \]

   if 1.9199999999999999e-141 < b < 4.70000000000000006e-91

   1. Initial program 7.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 38.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 38.9%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 38.9%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 38.9%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 38.9%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 38.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y1 around -inf 54.8%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 54.8%

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 54.8%

         \[\leadsto j \cdot \left(y1 \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 54.8%

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 54.8%

         \[\leadsto j \cdot \left(y1 \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 54.8%

         \[\leadsto j \cdot \left(y1 \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 54.8%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   if 4.70000000000000006e-91 < b < 52

   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 y2 around inf 58.1%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 58.1%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 58.1%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 58.1%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 58.1%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 58.1%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 58.1%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 58.1%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 58.1%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 58.1%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in y0 around inf 47.1%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 50.7%

         \[\leadsto \color{blue}{\left(y0 \cdot y2\right) \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)} \]

      2. *-commutative 50.7%

         \[\leadsto \color{blue}{\left(y2 \cdot y0\right)} \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right) \]

      3. +-commutative 50.7%

         \[\leadsto \left(y2 \cdot y0\right) \cdot \color{blue}{\left(c \cdot x + -1 \cdot \left(k \cdot y5\right)\right)} \]

      4. mul-1-neg 50.7%

         \[\leadsto \left(y2 \cdot y0\right) \cdot \left(c \cdot x + \color{blue}{\left(-k \cdot y5\right)}\right) \]

      5. unsub-neg 50.7%

         \[\leadsto \left(y2 \cdot y0\right) \cdot \color{blue}{\left(c \cdot x - k \cdot y5\right)} \]

      6. *-commutative 50.7%

         \[\leadsto \left(y2 \cdot y0\right) \cdot \left(\color{blue}{x \cdot c} - k \cdot y5\right) \]

   7. Simplified 50.7%

      \[\leadsto \color{blue}{\left(y2 \cdot y0\right) \cdot \left(x \cdot c - k \cdot y5\right)} \]

   if 52 < b < 8.5999999999999996e92

   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 j around inf 52.5%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 52.5%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 52.5%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 52.5%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 52.5%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 52.5%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y0 around -inf 48.7%

      \[\leadsto j \cdot \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 48.7%

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      2. mul-1-neg 48.7%

         \[\leadsto j \cdot \left(y0 \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      3. unsub-neg 48.7%

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

      4. *-commutative 48.7%

         \[\leadsto j \cdot \left(y0 \cdot \left(\color{blue}{y5 \cdot y3} - b \cdot x\right)\right) \]

      5. *-commutative 48.7%

         \[\leadsto j \cdot \left(y0 \cdot \left(y5 \cdot y3 - \color{blue}{x \cdot b}\right)\right) \]

   7. Simplified 48.7%

      \[\leadsto j \cdot \color{blue}{\left(y0 \cdot \left(y5 \cdot y3 - x \cdot b\right)\right)} \]

   if 8.5999999999999996e92 < b

   1. Initial program 20.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around inf 46.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. sub-neg 46.3%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. +-commutative 46.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. mul-1-neg 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. unsub-neg 46.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. mul-1-neg 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(-\color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. remove-double-neg 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \color{blue}{y5 \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. *-commutative 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 46.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in b around inf 63.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -6.3 \cdot 10^{-113}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-228}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 1.92 \cdot 10^{-141}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{-91}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 52:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c - k \cdot y5\right)\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{+92}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]

Alternative 21: 31.8% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{if}\;b \leq -8 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -7.4 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-229}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.75 \cdot 10^{-90}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 9.7 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+90}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (* y2 (- (* a y5) (* c y4))))))
   (if (<= b -8e+36)
     (* b (* j (- (* t y4) (* x y0))))
     (if (<= b -7.4e-113)
       t_1
       (if (<= b 1.2e-229)
         (* x (* y2 (- (* c y0) (* a y1))))
         (if (<= b 4.7e-143)
           t_1
           (if (<= b 3.75e-90)
             (* j (* y1 (- (* x i) (* y3 y4))))
             (if (<= b 9.7e-35)
               (* a (* t (- (* y2 y5) (* z b))))
               (if (<= b 6e+90)
                 (* j (* y0 (- (* y3 y5) (* x b))))
                 (* a (* b (- (* x y) (* z t)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (y2 * ((a * y5) - (c * y4)));
	double tmp;
	if (b <= -8e+36) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -7.4e-113) {
		tmp = t_1;
	} else if (b <= 1.2e-229) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (b <= 4.7e-143) {
		tmp = t_1;
	} else if (b <= 3.75e-90) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (b <= 9.7e-35) {
		tmp = a * (t * ((y2 * y5) - (z * b)));
	} else if (b <= 6e+90) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y2 * ((a * y5) - (c * y4)))
    if (b <= (-8d+36)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (b <= (-7.4d-113)) then
        tmp = t_1
    else if (b <= 1.2d-229) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (b <= 4.7d-143) then
        tmp = t_1
    else if (b <= 3.75d-90) then
        tmp = j * (y1 * ((x * i) - (y3 * y4)))
    else if (b <= 9.7d-35) then
        tmp = a * (t * ((y2 * y5) - (z * b)))
    else if (b <= 6d+90) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else
        tmp = a * (b * ((x * y) - (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (y2 * ((a * y5) - (c * y4)));
	double tmp;
	if (b <= -8e+36) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -7.4e-113) {
		tmp = t_1;
	} else if (b <= 1.2e-229) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (b <= 4.7e-143) {
		tmp = t_1;
	} else if (b <= 3.75e-90) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (b <= 9.7e-35) {
		tmp = a * (t * ((y2 * y5) - (z * b)));
	} else if (b <= 6e+90) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = t * (y2 * ((a * y5) - (c * y4)))
	tmp = 0
	if b <= -8e+36:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif b <= -7.4e-113:
		tmp = t_1
	elif b <= 1.2e-229:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif b <= 4.7e-143:
		tmp = t_1
	elif b <= 3.75e-90:
		tmp = j * (y1 * ((x * i) - (y3 * y4)))
	elif b <= 9.7e-35:
		tmp = a * (t * ((y2 * y5) - (z * b)))
	elif b <= 6e+90:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	else:
		tmp = a * (b * ((x * y) - (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))))
	tmp = 0.0
	if (b <= -8e+36)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (b <= -7.4e-113)
		tmp = t_1;
	elseif (b <= 1.2e-229)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (b <= 4.7e-143)
		tmp = t_1;
	elseif (b <= 3.75e-90)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (b <= 9.7e-35)
		tmp = Float64(a * Float64(t * Float64(Float64(y2 * y5) - Float64(z * b))));
	elseif (b <= 6e+90)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	else
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = t * (y2 * ((a * y5) - (c * y4)));
	tmp = 0.0;
	if (b <= -8e+36)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (b <= -7.4e-113)
		tmp = t_1;
	elseif (b <= 1.2e-229)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (b <= 4.7e-143)
		tmp = t_1;
	elseif (b <= 3.75e-90)
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	elseif (b <= 9.7e-35)
		tmp = a * (t * ((y2 * y5) - (z * b)));
	elseif (b <= 6e+90)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	else
		tmp = a * (b * ((x * y) - (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8e+36], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7.4e-113], t$95$1, If[LessEqual[b, 1.2e-229], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.7e-143], t$95$1, If[LessEqual[b, 3.75e-90], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.7e-35], N[(a * N[(t * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e+90], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -8.00000000000000034e36

   1. Initial program 27.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 36.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 36.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 36.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 36.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 36.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 36.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in b around inf 55.7%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -8.00000000000000034e36 < b < -7.3999999999999996e-113 or 1.2e-229 < b < 4.70000000000000045e-143

   1. Initial program 34.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 39.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 39.0%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 39.0%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 39.0%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 42.9%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 42.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 42.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 42.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 42.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 42.9%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in t around inf 48.9%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   if -7.3999999999999996e-113 < b < 1.2e-229

   1. Initial program 40.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 44.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 44.0%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 44.0%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 44.0%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 45.9%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 45.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 45.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 45.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 45.9%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 45.9%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in x around inf 48.2%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 48.2%

         \[\leadsto x \cdot \left(y2 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right)\right) \]

      2. *-commutative 48.2%

         \[\leadsto x \cdot \left(y2 \cdot \left(y0 \cdot c - \color{blue}{y1 \cdot a}\right)\right) \]

   7. Simplified 48.2%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(y0 \cdot c - y1 \cdot a\right)\right)} \]

   if 4.70000000000000045e-143 < b < 3.7499999999999999e-90

   1. Initial program 7.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 38.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 38.9%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 38.9%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 38.9%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 38.9%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 38.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y1 around -inf 54.8%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 54.8%

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 54.8%

         \[\leadsto j \cdot \left(y1 \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 54.8%

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

      4. *-commutative 54.8%

         \[\leadsto j \cdot \left(y1 \cdot \left(\color{blue}{x \cdot i} - y3 \cdot y4\right)\right) \]

      5. *-commutative 54.8%

         \[\leadsto j \cdot \left(y1 \cdot \left(x \cdot i - \color{blue}{y4 \cdot y3}\right)\right) \]

   7. Simplified 54.8%

      \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(x \cdot i - y4 \cdot y3\right)\right)} \]

   if 3.7499999999999999e-90 < b < 9.70000000000000073e-35

   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 a around inf 67.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. sub-neg 67.3%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. +-commutative 67.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. mul-1-neg 67.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. unsub-neg 67.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 67.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 67.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. mul-1-neg 67.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(-\color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. remove-double-neg 67.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \color{blue}{y5 \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. *-commutative 67.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 67.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in t around -inf 55.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot \left(-1 \cdot \left(y2 \cdot y5\right) + b \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 55.3%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot \left(-1 \cdot \left(y2 \cdot y5\right) + b \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 55.3%

         \[\leadsto \color{blue}{a \cdot \left(-t \cdot \left(-1 \cdot \left(y2 \cdot y5\right) + b \cdot z\right)\right)} \]

      3. +-commutative 55.3%

         \[\leadsto a \cdot \left(-t \cdot \color{blue}{\left(b \cdot z + -1 \cdot \left(y2 \cdot y5\right)\right)}\right) \]

      4. mul-1-neg 55.3%

         \[\leadsto a \cdot \left(-t \cdot \left(b \cdot z + \color{blue}{\left(-y2 \cdot y5\right)}\right)\right) \]

      5. unsub-neg 55.3%

         \[\leadsto a \cdot \left(-t \cdot \color{blue}{\left(b \cdot z - y2 \cdot y5\right)}\right) \]

   7. Simplified 55.3%

      \[\leadsto \color{blue}{a \cdot \left(-t \cdot \left(b \cdot z - y2 \cdot y5\right)\right)} \]

   if 9.70000000000000073e-35 < b < 5.99999999999999957e90

   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 j around inf 44.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 44.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 44.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 44.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 44.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 44.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y0 around -inf 47.9%

      \[\leadsto j \cdot \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 47.9%

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      2. mul-1-neg 47.9%

         \[\leadsto j \cdot \left(y0 \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      3. unsub-neg 47.9%

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

      4. *-commutative 47.9%

         \[\leadsto j \cdot \left(y0 \cdot \left(\color{blue}{y5 \cdot y3} - b \cdot x\right)\right) \]

      5. *-commutative 47.9%

         \[\leadsto j \cdot \left(y0 \cdot \left(y5 \cdot y3 - \color{blue}{x \cdot b}\right)\right) \]

   7. Simplified 47.9%

      \[\leadsto j \cdot \color{blue}{\left(y0 \cdot \left(y5 \cdot y3 - x \cdot b\right)\right)} \]

   if 5.99999999999999957e90 < b

   1. Initial program 20.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around inf 46.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. sub-neg 46.3%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. +-commutative 46.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. mul-1-neg 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. unsub-neg 46.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. mul-1-neg 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(-\color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. remove-double-neg 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \color{blue}{y5 \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. *-commutative 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 46.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in b around inf 63.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -7.4 \cdot 10^{-113}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-229}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{-143}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 3.75 \cdot 10^{-90}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 9.7 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+90}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]

Alternative 22: 21.4% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ t_2 := t \cdot \left(y2 \cdot \left(a \cdot y5\right)\right)\\ \mathbf{if}\;y \leq -8 \cdot 10^{+226}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+123}:\\ \;\;\;\;\left(-b\right) \cdot \left(k \cdot \left(y \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{+98}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-289}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-218}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+113}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+270}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* k (* z y0)))) (t_2 (* t (* y2 (* a y5)))))
   (if (<= y -8e+226)
     (* a (* (* x y) b))
     (if (<= y -3.9e+123)
       (* (- b) (* k (* y y4)))
       (if (<= y -1.28e+98)
         (* j (* y0 (* y3 y5)))
         (if (<= y -4.8e-131)
           t_1
           (if (<= y 3.9e-289)
             t_2
             (if (<= y 4.8e-218)
               t_1
               (if (<= y 7.2e+113)
                 t_2
                 (if (<= y 3.4e+270)
                   (* a (* y (* x b)))
                   (* a (* y5 (* y (- y3))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (k * (z * y0));
	double t_2 = t * (y2 * (a * y5));
	double tmp;
	if (y <= -8e+226) {
		tmp = a * ((x * y) * b);
	} else if (y <= -3.9e+123) {
		tmp = -b * (k * (y * y4));
	} else if (y <= -1.28e+98) {
		tmp = j * (y0 * (y3 * y5));
	} else if (y <= -4.8e-131) {
		tmp = t_1;
	} else if (y <= 3.9e-289) {
		tmp = t_2;
	} else if (y <= 4.8e-218) {
		tmp = t_1;
	} else if (y <= 7.2e+113) {
		tmp = t_2;
	} else if (y <= 3.4e+270) {
		tmp = a * (y * (x * b));
	} else {
		tmp = a * (y5 * (y * -y3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (k * (z * y0))
    t_2 = t * (y2 * (a * y5))
    if (y <= (-8d+226)) then
        tmp = a * ((x * y) * b)
    else if (y <= (-3.9d+123)) then
        tmp = -b * (k * (y * y4))
    else if (y <= (-1.28d+98)) then
        tmp = j * (y0 * (y3 * y5))
    else if (y <= (-4.8d-131)) then
        tmp = t_1
    else if (y <= 3.9d-289) then
        tmp = t_2
    else if (y <= 4.8d-218) then
        tmp = t_1
    else if (y <= 7.2d+113) then
        tmp = t_2
    else if (y <= 3.4d+270) then
        tmp = a * (y * (x * b))
    else
        tmp = a * (y5 * (y * -y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (k * (z * y0));
	double t_2 = t * (y2 * (a * y5));
	double tmp;
	if (y <= -8e+226) {
		tmp = a * ((x * y) * b);
	} else if (y <= -3.9e+123) {
		tmp = -b * (k * (y * y4));
	} else if (y <= -1.28e+98) {
		tmp = j * (y0 * (y3 * y5));
	} else if (y <= -4.8e-131) {
		tmp = t_1;
	} else if (y <= 3.9e-289) {
		tmp = t_2;
	} else if (y <= 4.8e-218) {
		tmp = t_1;
	} else if (y <= 7.2e+113) {
		tmp = t_2;
	} else if (y <= 3.4e+270) {
		tmp = a * (y * (x * b));
	} else {
		tmp = a * (y5 * (y * -y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (k * (z * y0))
	t_2 = t * (y2 * (a * y5))
	tmp = 0
	if y <= -8e+226:
		tmp = a * ((x * y) * b)
	elif y <= -3.9e+123:
		tmp = -b * (k * (y * y4))
	elif y <= -1.28e+98:
		tmp = j * (y0 * (y3 * y5))
	elif y <= -4.8e-131:
		tmp = t_1
	elif y <= 3.9e-289:
		tmp = t_2
	elif y <= 4.8e-218:
		tmp = t_1
	elif y <= 7.2e+113:
		tmp = t_2
	elif y <= 3.4e+270:
		tmp = a * (y * (x * b))
	else:
		tmp = a * (y5 * (y * -y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(k * Float64(z * y0)))
	t_2 = Float64(t * Float64(y2 * Float64(a * y5)))
	tmp = 0.0
	if (y <= -8e+226)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (y <= -3.9e+123)
		tmp = Float64(Float64(-b) * Float64(k * Float64(y * y4)));
	elseif (y <= -1.28e+98)
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	elseif (y <= -4.8e-131)
		tmp = t_1;
	elseif (y <= 3.9e-289)
		tmp = t_2;
	elseif (y <= 4.8e-218)
		tmp = t_1;
	elseif (y <= 7.2e+113)
		tmp = t_2;
	elseif (y <= 3.4e+270)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	else
		tmp = Float64(a * Float64(y5 * Float64(y * 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 = b * (k * (z * y0));
	t_2 = t * (y2 * (a * y5));
	tmp = 0.0;
	if (y <= -8e+226)
		tmp = a * ((x * y) * b);
	elseif (y <= -3.9e+123)
		tmp = -b * (k * (y * y4));
	elseif (y <= -1.28e+98)
		tmp = j * (y0 * (y3 * y5));
	elseif (y <= -4.8e-131)
		tmp = t_1;
	elseif (y <= 3.9e-289)
		tmp = t_2;
	elseif (y <= 4.8e-218)
		tmp = t_1;
	elseif (y <= 7.2e+113)
		tmp = t_2;
	elseif (y <= 3.4e+270)
		tmp = a * (y * (x * b));
	else
		tmp = a * (y5 * (y * -y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(y2 * N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8e+226], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.9e+123], N[((-b) * N[(k * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.28e+98], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.8e-131], t$95$1, If[LessEqual[y, 3.9e-289], t$95$2, If[LessEqual[y, 4.8e-218], t$95$1, If[LessEqual[y, 7.2e+113], t$95$2, If[LessEqual[y, 3.4e+270], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(y * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -7.99999999999999969e226

   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 a around inf 59.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. sub-neg 59.1%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. +-commutative 59.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. mul-1-neg 59.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. unsub-neg 59.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 59.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 59.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. mul-1-neg 59.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(-\color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. remove-double-neg 59.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \color{blue}{y5 \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. *-commutative 59.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 59.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y1 around 0 59.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in x around inf 53.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

   if -7.99999999999999969e226 < y < -3.89999999999999993e123

   1. Initial program 32.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 25.8%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in k around inf 50.9%

      \[\leadsto \color{blue}{k \cdot \left(-1 \cdot \left(b \cdot \left(y \cdot y4\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.9%

         \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(b \cdot \left(y \cdot y4\right)\right)\right)} \]

      2. mul-1-neg 50.9%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-b \cdot \left(y \cdot y4\right)\right)}\right) \]

      3. unsub-neg 50.9%

         \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \left(y \cdot y4\right)\right)} \]

      4. *-commutative 50.9%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \color{blue}{\left(y4 \cdot y\right)}\right) \]

   5. Simplified 50.9%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \left(y4 \cdot y\right)\right)} \]

   6. Taylor expanded in y2 around 0 47.7%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(k \cdot \left(y \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 47.7%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(k \cdot \left(y \cdot y4\right)\right)} \]

      2. neg-mul-1 47.7%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(k \cdot \left(y \cdot y4\right)\right) \]

      3. *-commutative 47.7%

         \[\leadsto \left(-b\right) \cdot \left(k \cdot \color{blue}{\left(y4 \cdot y\right)}\right) \]

   8. Simplified 47.7%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(k \cdot \left(y4 \cdot y\right)\right)} \]

   if -3.89999999999999993e123 < y < -1.28000000000000006e98

   1. Initial program 20.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y0 around inf 61.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 61.3%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \color{blue}{\left(j \cdot x + \left(-k \cdot z\right)\right)}\right) \]

      2. +-commutative 61.3%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \color{blue}{\left(\left(-k \cdot z\right) + j \cdot x\right)}\right) \]

      3. mul-1-neg 61.3%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(\color{blue}{-1 \cdot \left(k \cdot z\right)} + j \cdot x\right)\right) \]

      4. +-commutative 61.3%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      5. mul-1-neg 61.3%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      6. unsub-neg 61.3%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      7. *-commutative 61.3%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      8. *-commutative 61.3%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

   4. Simplified 61.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   5. Taylor expanded in j around -inf 61.5%

      \[\leadsto y0 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 61.5%

         \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      2. mul-1-neg 61.5%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      3. unsub-neg 61.5%

         \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   7. Simplified 61.5%

      \[\leadsto y0 \cdot \color{blue}{\left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   8. Taylor expanded in y3 around inf 60.6%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]

   if -1.28000000000000006e98 < y < -4.7999999999999999e-131 or 3.8999999999999998e-289 < y < 4.8000000000000002e-218

   1. Initial program 32.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in k around -inf 43.6%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 43.6%

         \[\leadsto \color{blue}{-k \cdot \left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. *-commutative 43.6%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot k} \]

      3. distribute-rgt-neg-in 43.6%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right)} \]

      4. +-commutative 43.6%

         \[\leadsto \left(\color{blue}{\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      5. mul-1-neg 43.6%

         \[\leadsto \left(\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      6. unsub-neg 43.6%

         \[\leadsto \left(\color{blue}{\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      7. *-commutative 43.6%

         \[\leadsto \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y} - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

   4. Simplified 43.6%

      \[\leadsto \color{blue}{\left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot y - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right)} \]

   5. Taylor expanded in y0 around -inf 37.1%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \cdot \left(-k\right) \]
   6. Step-by-step derivation

      1. +-commutative 37.1%

         \[\leadsto \left(y0 \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \cdot \left(-k\right) \]

      2. mul-1-neg 37.1%

         \[\leadsto \left(y0 \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \cdot \left(-k\right) \]

      3. unsub-neg 37.1%

         \[\leadsto \left(y0 \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \cdot \left(-k\right) \]

   7. Simplified 37.1%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \cdot \left(-k\right) \]

   8. Taylor expanded in y2 around 0 32.8%

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]

   if -4.7999999999999999e-131 < y < 3.8999999999999998e-289 or 4.8000000000000002e-218 < y < 7.19999999999999984e113

   1. Initial program 33.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 47.1%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 47.1%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 47.1%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 47.1%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 48.1%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 48.1%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 48.1%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 48.1%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 48.1%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 48.1%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in t around inf 42.7%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   6. Taylor expanded in a around inf 31.8%

      \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(a \cdot y5\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative 31.8%

         \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot a\right)}\right) \]

   8. Simplified 31.8%

      \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot a\right)}\right) \]

   if 7.19999999999999984e113 < y < 3.40000000000000016e270

   1. Initial program 20.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around inf 31.4%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. sub-neg 31.4%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. +-commutative 31.4%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. mul-1-neg 31.4%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. unsub-neg 31.4%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 31.4%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 31.4%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. mul-1-neg 31.4%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(-\color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. remove-double-neg 31.4%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \color{blue}{y5 \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. *-commutative 31.4%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 31.4%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y1 around 0 41.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in x around inf 59.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 59.2%

         \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

   8. Simplified 59.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot x\right) \cdot y\right)} \]

   if 3.40000000000000016e270 < y

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 25.0%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 25.0%

         \[\leadsto \left(\left(\color{blue}{\left(-j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 25.0%

         \[\leadsto \left(\left(\left(-\color{blue}{\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 25.0%

      \[\leadsto \left(\left(\color{blue}{\left(-\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 75.3%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 75.3%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 75.3%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 75.3%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y2 around 0 75.3%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y3\right)\right)}\right) \]
   9. Step-by-step derivation

      1. neg-mul-1 75.3%

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(-y \cdot y3\right)}\right) \]

      2. distribute-lft-neg-in 75.3%

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(\left(-y\right) \cdot y3\right)}\right) \]

   10. Simplified 75.3%

       \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(\left(-y\right) \cdot y3\right)}\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+226}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+123}:\\ \;\;\;\;\left(-b\right) \cdot \left(k \cdot \left(y \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{+98}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-131}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-289}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-218}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+113}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+270}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \end{array} \]

Alternative 23: 22.2% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-b\right) \cdot \left(k \cdot \left(y \cdot y4\right)\right)\\ \mathbf{if}\;y4 \leq -3 \cdot 10^{+186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq -2.2 \cdot 10^{+158}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(x \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -9 \cdot 10^{-63}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq -4.6 \cdot 10^{-82}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -1.22 \cdot 10^{-185}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 2.9 \cdot 10^{-235}:\\ \;\;\;\;a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 2250000000000:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(y0 \cdot \left(-k\right)\right)\\ \mathbf{elif}\;y4 \leq 5.3 \cdot 10^{+248}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(y4 \cdot \left(-c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (- b) (* k (* y y4)))))
   (if (<= y4 -3e+186)
     t_1
     (if (<= y4 -2.2e+158)
       (* y0 (* b (* x (- j))))
       (if (<= y4 -9e-63)
         (* j (* y0 (* y3 y5)))
         (if (<= y4 -4.6e-82)
           (* b (* k (* z y0)))
           (if (<= y4 -1.22e-185)
             (* t (* a (* y2 y5)))
             (if (<= y4 2.9e-235)
               (* a (* y (* y3 (- y5))))
               (if (<= y4 2250000000000.0)
                 (* (* y2 y5) (* y0 (- k)))
                 (if (<= y4 5.3e+248) t_1 (* y2 (* t (* y4 (- c))))))))))))))

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 * (k * (y * y4));
	double tmp;
	if (y4 <= -3e+186) {
		tmp = t_1;
	} else if (y4 <= -2.2e+158) {
		tmp = y0 * (b * (x * -j));
	} else if (y4 <= -9e-63) {
		tmp = j * (y0 * (y3 * y5));
	} else if (y4 <= -4.6e-82) {
		tmp = b * (k * (z * y0));
	} else if (y4 <= -1.22e-185) {
		tmp = t * (a * (y2 * y5));
	} else if (y4 <= 2.9e-235) {
		tmp = a * (y * (y3 * -y5));
	} else if (y4 <= 2250000000000.0) {
		tmp = (y2 * y5) * (y0 * -k);
	} else if (y4 <= 5.3e+248) {
		tmp = t_1;
	} else {
		tmp = y2 * (t * (y4 * -c));
	}
	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 * (k * (y * y4))
    if (y4 <= (-3d+186)) then
        tmp = t_1
    else if (y4 <= (-2.2d+158)) then
        tmp = y0 * (b * (x * -j))
    else if (y4 <= (-9d-63)) then
        tmp = j * (y0 * (y3 * y5))
    else if (y4 <= (-4.6d-82)) then
        tmp = b * (k * (z * y0))
    else if (y4 <= (-1.22d-185)) then
        tmp = t * (a * (y2 * y5))
    else if (y4 <= 2.9d-235) then
        tmp = a * (y * (y3 * -y5))
    else if (y4 <= 2250000000000.0d0) then
        tmp = (y2 * y5) * (y0 * -k)
    else if (y4 <= 5.3d+248) then
        tmp = t_1
    else
        tmp = y2 * (t * (y4 * -c))
    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 * (k * (y * y4));
	double tmp;
	if (y4 <= -3e+186) {
		tmp = t_1;
	} else if (y4 <= -2.2e+158) {
		tmp = y0 * (b * (x * -j));
	} else if (y4 <= -9e-63) {
		tmp = j * (y0 * (y3 * y5));
	} else if (y4 <= -4.6e-82) {
		tmp = b * (k * (z * y0));
	} else if (y4 <= -1.22e-185) {
		tmp = t * (a * (y2 * y5));
	} else if (y4 <= 2.9e-235) {
		tmp = a * (y * (y3 * -y5));
	} else if (y4 <= 2250000000000.0) {
		tmp = (y2 * y5) * (y0 * -k);
	} else if (y4 <= 5.3e+248) {
		tmp = t_1;
	} else {
		tmp = y2 * (t * (y4 * -c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = -b * (k * (y * y4))
	tmp = 0
	if y4 <= -3e+186:
		tmp = t_1
	elif y4 <= -2.2e+158:
		tmp = y0 * (b * (x * -j))
	elif y4 <= -9e-63:
		tmp = j * (y0 * (y3 * y5))
	elif y4 <= -4.6e-82:
		tmp = b * (k * (z * y0))
	elif y4 <= -1.22e-185:
		tmp = t * (a * (y2 * y5))
	elif y4 <= 2.9e-235:
		tmp = a * (y * (y3 * -y5))
	elif y4 <= 2250000000000.0:
		tmp = (y2 * y5) * (y0 * -k)
	elif y4 <= 5.3e+248:
		tmp = t_1
	else:
		tmp = y2 * (t * (y4 * -c))
	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) * Float64(k * Float64(y * y4)))
	tmp = 0.0
	if (y4 <= -3e+186)
		tmp = t_1;
	elseif (y4 <= -2.2e+158)
		tmp = Float64(y0 * Float64(b * Float64(x * Float64(-j))));
	elseif (y4 <= -9e-63)
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	elseif (y4 <= -4.6e-82)
		tmp = Float64(b * Float64(k * Float64(z * y0)));
	elseif (y4 <= -1.22e-185)
		tmp = Float64(t * Float64(a * Float64(y2 * y5)));
	elseif (y4 <= 2.9e-235)
		tmp = Float64(a * Float64(y * Float64(y3 * Float64(-y5))));
	elseif (y4 <= 2250000000000.0)
		tmp = Float64(Float64(y2 * y5) * Float64(y0 * Float64(-k)));
	elseif (y4 <= 5.3e+248)
		tmp = t_1;
	else
		tmp = Float64(y2 * Float64(t * Float64(y4 * Float64(-c))));
	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 * (k * (y * y4));
	tmp = 0.0;
	if (y4 <= -3e+186)
		tmp = t_1;
	elseif (y4 <= -2.2e+158)
		tmp = y0 * (b * (x * -j));
	elseif (y4 <= -9e-63)
		tmp = j * (y0 * (y3 * y5));
	elseif (y4 <= -4.6e-82)
		tmp = b * (k * (z * y0));
	elseif (y4 <= -1.22e-185)
		tmp = t * (a * (y2 * y5));
	elseif (y4 <= 2.9e-235)
		tmp = a * (y * (y3 * -y5));
	elseif (y4 <= 2250000000000.0)
		tmp = (y2 * y5) * (y0 * -k);
	elseif (y4 <= 5.3e+248)
		tmp = t_1;
	else
		tmp = y2 * (t * (y4 * -c));
	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[(k * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -3e+186], t$95$1, If[LessEqual[y4, -2.2e+158], N[(y0 * N[(b * N[(x * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -9e-63], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -4.6e-82], N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.22e-185], N[(t * N[(a * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2.9e-235], N[(a * N[(y * N[(y3 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2250000000000.0], N[(N[(y2 * y5), $MachinePrecision] * N[(y0 * (-k)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 5.3e+248], t$95$1, N[(y2 * N[(t * N[(y4 * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y4 < -2.99999999999999982e186 or 2.25e12 < y4 < 5.3e248

   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 y4 around inf 39.4%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in k around inf 44.2%

      \[\leadsto \color{blue}{k \cdot \left(-1 \cdot \left(b \cdot \left(y \cdot y4\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 44.2%

         \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(b \cdot \left(y \cdot y4\right)\right)\right)} \]

      2. mul-1-neg 44.2%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-b \cdot \left(y \cdot y4\right)\right)}\right) \]

      3. unsub-neg 44.2%

         \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \left(y \cdot y4\right)\right)} \]

      4. *-commutative 44.2%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \color{blue}{\left(y4 \cdot y\right)}\right) \]

   5. Simplified 44.2%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \left(y4 \cdot y\right)\right)} \]

   6. Taylor expanded in y2 around 0 44.6%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(k \cdot \left(y \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 44.6%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(k \cdot \left(y \cdot y4\right)\right)} \]

      2. neg-mul-1 44.6%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(k \cdot \left(y \cdot y4\right)\right) \]

      3. *-commutative 44.6%

         \[\leadsto \left(-b\right) \cdot \left(k \cdot \color{blue}{\left(y4 \cdot y\right)}\right) \]

   8. Simplified 44.6%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(k \cdot \left(y4 \cdot y\right)\right)} \]

   if -2.99999999999999982e186 < y4 < -2.2000000000000001e158

   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 y0 around inf 33.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 33.5%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \color{blue}{\left(j \cdot x + \left(-k \cdot z\right)\right)}\right) \]

      2. +-commutative 33.5%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \color{blue}{\left(\left(-k \cdot z\right) + j \cdot x\right)}\right) \]

      3. mul-1-neg 33.5%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(\color{blue}{-1 \cdot \left(k \cdot z\right)} + j \cdot x\right)\right) \]

      4. +-commutative 33.5%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      5. mul-1-neg 33.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      6. unsub-neg 33.5%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      7. *-commutative 33.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      8. *-commutative 33.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

   4. Simplified 33.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   5. Taylor expanded in j around -inf 45.3%

      \[\leadsto y0 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 45.3%

         \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      2. mul-1-neg 45.3%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      3. unsub-neg 45.3%

         \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   7. Simplified 45.3%

      \[\leadsto y0 \cdot \color{blue}{\left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   8. Taylor expanded in y3 around 0 67.3%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot \left(x \cdot y0\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 67.3%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(j \cdot \left(x \cdot y0\right)\right)} \]

      2. neg-mul-1 67.3%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(j \cdot \left(x \cdot y0\right)\right) \]

      3. associate-*r* 78.1%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(\left(j \cdot x\right) \cdot y0\right)} \]

      4. associate-*r* 67.4%

         \[\leadsto \color{blue}{\left(\left(-b\right) \cdot \left(j \cdot x\right)\right) \cdot y0} \]

      5. distribute-lft-neg-in 67.4%

         \[\leadsto \color{blue}{\left(-b \cdot \left(j \cdot x\right)\right)} \cdot y0 \]

      6. distribute-rgt-neg-in 67.4%

         \[\leadsto \color{blue}{\left(b \cdot \left(-j \cdot x\right)\right)} \cdot y0 \]

   10. Simplified 67.4%

       \[\leadsto \color{blue}{\left(b \cdot \left(-j \cdot x\right)\right) \cdot y0} \]

   if -2.2000000000000001e158 < y4 < -8.9999999999999999e-63

   1. Initial program 23.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y0 around inf 36.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 36.1%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \color{blue}{\left(j \cdot x + \left(-k \cdot z\right)\right)}\right) \]

      2. +-commutative 36.1%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \color{blue}{\left(\left(-k \cdot z\right) + j \cdot x\right)}\right) \]

      3. mul-1-neg 36.1%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(\color{blue}{-1 \cdot \left(k \cdot z\right)} + j \cdot x\right)\right) \]

      4. +-commutative 36.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      5. mul-1-neg 36.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      6. unsub-neg 36.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      7. *-commutative 36.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      8. *-commutative 36.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

   4. Simplified 36.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   5. Taylor expanded in j around -inf 36.3%

      \[\leadsto y0 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 36.3%

         \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      2. mul-1-neg 36.3%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      3. unsub-neg 36.3%

         \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   7. Simplified 36.3%

      \[\leadsto y0 \cdot \color{blue}{\left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   8. Taylor expanded in y3 around inf 32.3%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]

   if -8.9999999999999999e-63 < y4 < -4.59999999999999994e-82

   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 k around -inf 62.9%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 62.9%

         \[\leadsto \color{blue}{-k \cdot \left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. *-commutative 62.9%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot k} \]

      3. distribute-rgt-neg-in 62.9%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right)} \]

      4. +-commutative 62.9%

         \[\leadsto \left(\color{blue}{\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      5. mul-1-neg 62.9%

         \[\leadsto \left(\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      6. unsub-neg 62.9%

         \[\leadsto \left(\color{blue}{\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      7. *-commutative 62.9%

         \[\leadsto \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y} - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

   4. Simplified 62.9%

      \[\leadsto \color{blue}{\left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot y - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right)} \]

   5. Taylor expanded in y0 around -inf 75.6%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \cdot \left(-k\right) \]
   6. Step-by-step derivation

      1. +-commutative 75.6%

         \[\leadsto \left(y0 \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \cdot \left(-k\right) \]

      2. mul-1-neg 75.6%

         \[\leadsto \left(y0 \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \cdot \left(-k\right) \]

      3. unsub-neg 75.6%

         \[\leadsto \left(y0 \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \cdot \left(-k\right) \]

   7. Simplified 75.6%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \cdot \left(-k\right) \]

   8. Taylor expanded in y2 around 0 63.4%

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]

   if -4.59999999999999994e-82 < y4 < -1.21999999999999996e-185

   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 y2 around inf 59.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 59.8%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 59.8%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 59.8%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 63.5%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 63.5%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 63.5%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 63.5%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 63.5%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 63.5%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in t around inf 42.1%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   6. Taylor expanded in a around inf 41.7%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(y2 \cdot y5\right)\right)} \]

   if -1.21999999999999996e-185 < y4 < 2.90000000000000009e-235

   1. Initial program 44.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 38.2%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 38.2%

         \[\leadsto \left(\left(\color{blue}{\left(-j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 40.5%

         \[\leadsto \left(\left(\left(-\color{blue}{\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 40.5%

      \[\leadsto \left(\left(\color{blue}{\left(-\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 54.7%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 54.7%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 54.7%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 54.7%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y2 around 0 40.6%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 40.6%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot y\right) \cdot \left(y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 40.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y\right)} \cdot \left(y3 \cdot y5\right)\right) \]

   10. Simplified 40.6%

       \[\leadsto a \cdot \color{blue}{\left(\left(-y\right) \cdot \left(y3 \cdot y5\right)\right)} \]

   if 2.90000000000000009e-235 < y4 < 2.25e12

   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 y4 around inf 43.0%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in k around inf 32.3%

      \[\leadsto \color{blue}{k \cdot \left(-1 \cdot \left(b \cdot \left(y \cdot y4\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 32.3%

         \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(b \cdot \left(y \cdot y4\right)\right)\right)} \]

      2. mul-1-neg 32.3%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-b \cdot \left(y \cdot y4\right)\right)}\right) \]

      3. unsub-neg 32.3%

         \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \left(y \cdot y4\right)\right)} \]

      4. *-commutative 32.3%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \color{blue}{\left(y4 \cdot y\right)}\right) \]

   5. Simplified 32.3%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \left(y4 \cdot y\right)\right)} \]

   6. Taylor expanded in y4 around 0 27.9%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 27.9%

         \[\leadsto \color{blue}{-k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)} \]

      2. associate-*r* 30.0%

         \[\leadsto -\color{blue}{\left(k \cdot y0\right) \cdot \left(y2 \cdot y5\right)} \]

   8. Simplified 30.0%

      \[\leadsto \color{blue}{-\left(k \cdot y0\right) \cdot \left(y2 \cdot y5\right)} \]

   if 5.3e248 < y4

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 33.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 33.8%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 33.8%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 33.8%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 33.8%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 33.8%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 33.8%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 33.8%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 33.8%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 33.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in t around inf 67.9%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   6. Taylor expanded in a around 0 47.0%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 47.0%

         \[\leadsto t \cdot \color{blue}{\left(-c \cdot \left(y2 \cdot y4\right)\right)} \]

      2. *-commutative 47.0%

         \[\leadsto t \cdot \left(-\color{blue}{\left(y2 \cdot y4\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in 47.0%

         \[\leadsto t \cdot \color{blue}{\left(\left(y2 \cdot y4\right) \cdot \left(-c\right)\right)} \]

   8. Simplified 47.0%

      \[\leadsto t \cdot \color{blue}{\left(\left(y2 \cdot y4\right) \cdot \left(-c\right)\right)} \]

   9. Taylor expanded in t around 0 46.8%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 46.8%

          \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

       2. distribute-lft-neg-in 46.8%

          \[\leadsto \color{blue}{\left(-c\right) \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

       3. *-commutative 46.8%

          \[\leadsto \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right) \cdot \left(-c\right)} \]

       4. associate-*r* 46.4%

          \[\leadsto \color{blue}{\left(\left(t \cdot y2\right) \cdot y4\right)} \cdot \left(-c\right) \]

       5. associate-*r* 56.8%

          \[\leadsto \color{blue}{\left(t \cdot y2\right) \cdot \left(y4 \cdot \left(-c\right)\right)} \]

       6. *-commutative 56.8%

          \[\leadsto \color{blue}{\left(y2 \cdot t\right)} \cdot \left(y4 \cdot \left(-c\right)\right) \]

       7. associate-*l* 78.2%

          \[\leadsto \color{blue}{y2 \cdot \left(t \cdot \left(y4 \cdot \left(-c\right)\right)\right)} \]

   11. Simplified 78.2%

       \[\leadsto \color{blue}{y2 \cdot \left(t \cdot \left(y4 \cdot \left(-c\right)\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -3 \cdot 10^{+186}:\\ \;\;\;\;\left(-b\right) \cdot \left(k \cdot \left(y \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -2.2 \cdot 10^{+158}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(x \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -9 \cdot 10^{-63}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq -4.6 \cdot 10^{-82}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -1.22 \cdot 10^{-185}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 2.9 \cdot 10^{-235}:\\ \;\;\;\;a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 2250000000000:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(y0 \cdot \left(-k\right)\right)\\ \mathbf{elif}\;y4 \leq 5.3 \cdot 10^{+248}:\\ \;\;\;\;\left(-b\right) \cdot \left(k \cdot \left(y \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(y4 \cdot \left(-c\right)\right)\right)\\ \end{array} \]

Alternative 24: 21.8% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-b\right) \cdot \left(k \cdot \left(y \cdot y4\right)\right)\\ \mathbf{if}\;y4 \leq -3.55 \cdot 10^{+221}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq -9 \cdot 10^{+160}:\\ \;\;\;\;b \cdot \left(j \cdot \left(y0 \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -4.2 \cdot 10^{-63}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq -6.2 \cdot 10^{-82}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq -5.6 \cdot 10^{-187}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 1.25 \cdot 10^{-234}:\\ \;\;\;\;a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 58000000000000:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(y0 \cdot \left(-k\right)\right)\\ \mathbf{elif}\;y4 \leq 4.5 \cdot 10^{+249}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(y4 \cdot \left(-c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (- b) (* k (* y y4)))))
   (if (<= y4 -3.55e+221)
     t_1
     (if (<= y4 -9e+160)
       (* b (* j (* y0 (- x))))
       (if (<= y4 -4.2e-63)
         (* j (* y0 (* y3 y5)))
         (if (<= y4 -6.2e-82)
           (* k (* y0 (* z b)))
           (if (<= y4 -5.6e-187)
             (* t (* a (* y2 y5)))
             (if (<= y4 1.25e-234)
               (* a (* y (* y3 (- y5))))
               (if (<= y4 58000000000000.0)
                 (* (* y2 y5) (* y0 (- k)))
                 (if (<= y4 4.5e+249) t_1 (* y2 (* t (* y4 (- c))))))))))))))

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 * (k * (y * y4));
	double tmp;
	if (y4 <= -3.55e+221) {
		tmp = t_1;
	} else if (y4 <= -9e+160) {
		tmp = b * (j * (y0 * -x));
	} else if (y4 <= -4.2e-63) {
		tmp = j * (y0 * (y3 * y5));
	} else if (y4 <= -6.2e-82) {
		tmp = k * (y0 * (z * b));
	} else if (y4 <= -5.6e-187) {
		tmp = t * (a * (y2 * y5));
	} else if (y4 <= 1.25e-234) {
		tmp = a * (y * (y3 * -y5));
	} else if (y4 <= 58000000000000.0) {
		tmp = (y2 * y5) * (y0 * -k);
	} else if (y4 <= 4.5e+249) {
		tmp = t_1;
	} else {
		tmp = y2 * (t * (y4 * -c));
	}
	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 * (k * (y * y4))
    if (y4 <= (-3.55d+221)) then
        tmp = t_1
    else if (y4 <= (-9d+160)) then
        tmp = b * (j * (y0 * -x))
    else if (y4 <= (-4.2d-63)) then
        tmp = j * (y0 * (y3 * y5))
    else if (y4 <= (-6.2d-82)) then
        tmp = k * (y0 * (z * b))
    else if (y4 <= (-5.6d-187)) then
        tmp = t * (a * (y2 * y5))
    else if (y4 <= 1.25d-234) then
        tmp = a * (y * (y3 * -y5))
    else if (y4 <= 58000000000000.0d0) then
        tmp = (y2 * y5) * (y0 * -k)
    else if (y4 <= 4.5d+249) then
        tmp = t_1
    else
        tmp = y2 * (t * (y4 * -c))
    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 * (k * (y * y4));
	double tmp;
	if (y4 <= -3.55e+221) {
		tmp = t_1;
	} else if (y4 <= -9e+160) {
		tmp = b * (j * (y0 * -x));
	} else if (y4 <= -4.2e-63) {
		tmp = j * (y0 * (y3 * y5));
	} else if (y4 <= -6.2e-82) {
		tmp = k * (y0 * (z * b));
	} else if (y4 <= -5.6e-187) {
		tmp = t * (a * (y2 * y5));
	} else if (y4 <= 1.25e-234) {
		tmp = a * (y * (y3 * -y5));
	} else if (y4 <= 58000000000000.0) {
		tmp = (y2 * y5) * (y0 * -k);
	} else if (y4 <= 4.5e+249) {
		tmp = t_1;
	} else {
		tmp = y2 * (t * (y4 * -c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = -b * (k * (y * y4))
	tmp = 0
	if y4 <= -3.55e+221:
		tmp = t_1
	elif y4 <= -9e+160:
		tmp = b * (j * (y0 * -x))
	elif y4 <= -4.2e-63:
		tmp = j * (y0 * (y3 * y5))
	elif y4 <= -6.2e-82:
		tmp = k * (y0 * (z * b))
	elif y4 <= -5.6e-187:
		tmp = t * (a * (y2 * y5))
	elif y4 <= 1.25e-234:
		tmp = a * (y * (y3 * -y5))
	elif y4 <= 58000000000000.0:
		tmp = (y2 * y5) * (y0 * -k)
	elif y4 <= 4.5e+249:
		tmp = t_1
	else:
		tmp = y2 * (t * (y4 * -c))
	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) * Float64(k * Float64(y * y4)))
	tmp = 0.0
	if (y4 <= -3.55e+221)
		tmp = t_1;
	elseif (y4 <= -9e+160)
		tmp = Float64(b * Float64(j * Float64(y0 * Float64(-x))));
	elseif (y4 <= -4.2e-63)
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	elseif (y4 <= -6.2e-82)
		tmp = Float64(k * Float64(y0 * Float64(z * b)));
	elseif (y4 <= -5.6e-187)
		tmp = Float64(t * Float64(a * Float64(y2 * y5)));
	elseif (y4 <= 1.25e-234)
		tmp = Float64(a * Float64(y * Float64(y3 * Float64(-y5))));
	elseif (y4 <= 58000000000000.0)
		tmp = Float64(Float64(y2 * y5) * Float64(y0 * Float64(-k)));
	elseif (y4 <= 4.5e+249)
		tmp = t_1;
	else
		tmp = Float64(y2 * Float64(t * Float64(y4 * Float64(-c))));
	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 * (k * (y * y4));
	tmp = 0.0;
	if (y4 <= -3.55e+221)
		tmp = t_1;
	elseif (y4 <= -9e+160)
		tmp = b * (j * (y0 * -x));
	elseif (y4 <= -4.2e-63)
		tmp = j * (y0 * (y3 * y5));
	elseif (y4 <= -6.2e-82)
		tmp = k * (y0 * (z * b));
	elseif (y4 <= -5.6e-187)
		tmp = t * (a * (y2 * y5));
	elseif (y4 <= 1.25e-234)
		tmp = a * (y * (y3 * -y5));
	elseif (y4 <= 58000000000000.0)
		tmp = (y2 * y5) * (y0 * -k);
	elseif (y4 <= 4.5e+249)
		tmp = t_1;
	else
		tmp = y2 * (t * (y4 * -c));
	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[(k * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -3.55e+221], t$95$1, If[LessEqual[y4, -9e+160], N[(b * N[(j * N[(y0 * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -4.2e-63], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -6.2e-82], N[(k * N[(y0 * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -5.6e-187], N[(t * N[(a * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.25e-234], N[(a * N[(y * N[(y3 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 58000000000000.0], N[(N[(y2 * y5), $MachinePrecision] * N[(y0 * (-k)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 4.5e+249], t$95$1, N[(y2 * N[(t * N[(y4 * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y4 < -3.54999999999999992e221 or 5.8e13 < y4 < 4.4999999999999996e249

   1. Initial program 19.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf 40.7%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in k around inf 44.2%

      \[\leadsto \color{blue}{k \cdot \left(-1 \cdot \left(b \cdot \left(y \cdot y4\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 44.2%

         \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(b \cdot \left(y \cdot y4\right)\right)\right)} \]

      2. mul-1-neg 44.2%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-b \cdot \left(y \cdot y4\right)\right)}\right) \]

      3. unsub-neg 44.2%

         \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \left(y \cdot y4\right)\right)} \]

      4. *-commutative 44.2%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \color{blue}{\left(y4 \cdot y\right)}\right) \]

   5. Simplified 44.2%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \left(y4 \cdot y\right)\right)} \]

   6. Taylor expanded in y2 around 0 46.4%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(k \cdot \left(y \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 46.4%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(k \cdot \left(y \cdot y4\right)\right)} \]

      2. neg-mul-1 46.4%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(k \cdot \left(y \cdot y4\right)\right) \]

      3. *-commutative 46.4%

         \[\leadsto \left(-b\right) \cdot \left(k \cdot \color{blue}{\left(y4 \cdot y\right)}\right) \]

   8. Simplified 46.4%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(k \cdot \left(y4 \cdot y\right)\right)} \]

   if -3.54999999999999992e221 < y4 < -8.99999999999999959e160

   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 y0 around inf 31.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 31.7%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \color{blue}{\left(j \cdot x + \left(-k \cdot z\right)\right)}\right) \]

      2. +-commutative 31.7%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \color{blue}{\left(\left(-k \cdot z\right) + j \cdot x\right)}\right) \]

      3. mul-1-neg 31.7%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(\color{blue}{-1 \cdot \left(k \cdot z\right)} + j \cdot x\right)\right) \]

      4. +-commutative 31.7%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      5. mul-1-neg 31.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      6. unsub-neg 31.7%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      7. *-commutative 31.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      8. *-commutative 31.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

   4. Simplified 31.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   5. Taylor expanded in j around -inf 38.5%

      \[\leadsto y0 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 38.5%

         \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      2. mul-1-neg 38.5%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      3. unsub-neg 38.5%

         \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   7. Simplified 38.5%

      \[\leadsto y0 \cdot \color{blue}{\left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   8. Taylor expanded in y3 around 0 56.8%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot \left(x \cdot y0\right)\right)\right)} \]

   if -8.99999999999999959e160 < y4 < -4.2e-63

   1. Initial program 23.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y0 around inf 36.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 36.1%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \color{blue}{\left(j \cdot x + \left(-k \cdot z\right)\right)}\right) \]

      2. +-commutative 36.1%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \color{blue}{\left(\left(-k \cdot z\right) + j \cdot x\right)}\right) \]

      3. mul-1-neg 36.1%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(\color{blue}{-1 \cdot \left(k \cdot z\right)} + j \cdot x\right)\right) \]

      4. +-commutative 36.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      5. mul-1-neg 36.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      6. unsub-neg 36.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      7. *-commutative 36.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      8. *-commutative 36.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

   4. Simplified 36.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   5. Taylor expanded in j around -inf 36.3%

      \[\leadsto y0 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 36.3%

         \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      2. mul-1-neg 36.3%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      3. unsub-neg 36.3%

         \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   7. Simplified 36.3%

      \[\leadsto y0 \cdot \color{blue}{\left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   8. Taylor expanded in y3 around inf 32.3%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]

   if -4.2e-63 < y4 < -6.19999999999999999e-82

   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 k around -inf 62.9%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 62.9%

         \[\leadsto \color{blue}{-k \cdot \left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. *-commutative 62.9%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot k} \]

      3. distribute-rgt-neg-in 62.9%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right)} \]

      4. +-commutative 62.9%

         \[\leadsto \left(\color{blue}{\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      5. mul-1-neg 62.9%

         \[\leadsto \left(\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      6. unsub-neg 62.9%

         \[\leadsto \left(\color{blue}{\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      7. *-commutative 62.9%

         \[\leadsto \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y} - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

   4. Simplified 62.9%

      \[\leadsto \color{blue}{\left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot y - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right)} \]

   5. Taylor expanded in y0 around -inf 75.6%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \cdot \left(-k\right) \]
   6. Step-by-step derivation

      1. +-commutative 75.6%

         \[\leadsto \left(y0 \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \cdot \left(-k\right) \]

      2. mul-1-neg 75.6%

         \[\leadsto \left(y0 \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \cdot \left(-k\right) \]

      3. unsub-neg 75.6%

         \[\leadsto \left(y0 \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \cdot \left(-k\right) \]

   7. Simplified 75.6%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \cdot \left(-k\right) \]

   8. Taylor expanded in y2 around 0 75.6%

      \[\leadsto \left(y0 \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right)}\right) \cdot \left(-k\right) \]
   9. Step-by-step derivation

      1. neg-mul-1 75.6%

         \[\leadsto \left(y0 \cdot \color{blue}{\left(-b \cdot z\right)}\right) \cdot \left(-k\right) \]

      2. distribute-rgt-neg-in 75.6%

         \[\leadsto \left(y0 \cdot \color{blue}{\left(b \cdot \left(-z\right)\right)}\right) \cdot \left(-k\right) \]

   10. Simplified 75.6%

       \[\leadsto \left(y0 \cdot \color{blue}{\left(b \cdot \left(-z\right)\right)}\right) \cdot \left(-k\right) \]

   if -6.19999999999999999e-82 < y4 < -5.6e-187

   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 y2 around inf 59.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 59.8%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 59.8%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 59.8%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 63.5%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 63.5%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 63.5%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 63.5%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 63.5%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 63.5%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in t around inf 42.1%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   6. Taylor expanded in a around inf 41.7%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(y2 \cdot y5\right)\right)} \]

   if -5.6e-187 < y4 < 1.24999999999999995e-234

   1. Initial program 44.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 38.2%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 38.2%

         \[\leadsto \left(\left(\color{blue}{\left(-j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 40.5%

         \[\leadsto \left(\left(\left(-\color{blue}{\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 40.5%

      \[\leadsto \left(\left(\color{blue}{\left(-\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 54.7%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 54.7%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 54.7%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 54.7%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y2 around 0 40.6%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 40.6%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot y\right) \cdot \left(y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 40.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y\right)} \cdot \left(y3 \cdot y5\right)\right) \]

   10. Simplified 40.6%

       \[\leadsto a \cdot \color{blue}{\left(\left(-y\right) \cdot \left(y3 \cdot y5\right)\right)} \]

   if 1.24999999999999995e-234 < y4 < 5.8e13

   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 y4 around inf 43.0%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Taylor expanded in k around inf 32.3%

      \[\leadsto \color{blue}{k \cdot \left(-1 \cdot \left(b \cdot \left(y \cdot y4\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 32.3%

         \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(b \cdot \left(y \cdot y4\right)\right)\right)} \]

      2. mul-1-neg 32.3%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-b \cdot \left(y \cdot y4\right)\right)}\right) \]

      3. unsub-neg 32.3%

         \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \left(y \cdot y4\right)\right)} \]

      4. *-commutative 32.3%

         \[\leadsto k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \color{blue}{\left(y4 \cdot y\right)}\right) \]

   5. Simplified 32.3%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - b \cdot \left(y4 \cdot y\right)\right)} \]

   6. Taylor expanded in y4 around 0 27.9%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 27.9%

         \[\leadsto \color{blue}{-k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)} \]

      2. associate-*r* 30.0%

         \[\leadsto -\color{blue}{\left(k \cdot y0\right) \cdot \left(y2 \cdot y5\right)} \]

   8. Simplified 30.0%

      \[\leadsto \color{blue}{-\left(k \cdot y0\right) \cdot \left(y2 \cdot y5\right)} \]

   if 4.4999999999999996e249 < y4

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 33.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 33.8%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 33.8%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 33.8%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 33.8%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 33.8%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 33.8%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 33.8%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 33.8%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 33.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in t around inf 67.9%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   6. Taylor expanded in a around 0 47.0%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 47.0%

         \[\leadsto t \cdot \color{blue}{\left(-c \cdot \left(y2 \cdot y4\right)\right)} \]

      2. *-commutative 47.0%

         \[\leadsto t \cdot \left(-\color{blue}{\left(y2 \cdot y4\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in 47.0%

         \[\leadsto t \cdot \color{blue}{\left(\left(y2 \cdot y4\right) \cdot \left(-c\right)\right)} \]

   8. Simplified 47.0%

      \[\leadsto t \cdot \color{blue}{\left(\left(y2 \cdot y4\right) \cdot \left(-c\right)\right)} \]

   9. Taylor expanded in t around 0 46.8%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 46.8%

          \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

       2. distribute-lft-neg-in 46.8%

          \[\leadsto \color{blue}{\left(-c\right) \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

       3. *-commutative 46.8%

          \[\leadsto \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right) \cdot \left(-c\right)} \]

       4. associate-*r* 46.4%

          \[\leadsto \color{blue}{\left(\left(t \cdot y2\right) \cdot y4\right)} \cdot \left(-c\right) \]

       5. associate-*r* 56.8%

          \[\leadsto \color{blue}{\left(t \cdot y2\right) \cdot \left(y4 \cdot \left(-c\right)\right)} \]

       6. *-commutative 56.8%

          \[\leadsto \color{blue}{\left(y2 \cdot t\right)} \cdot \left(y4 \cdot \left(-c\right)\right) \]

       7. associate-*l* 78.2%

          \[\leadsto \color{blue}{y2 \cdot \left(t \cdot \left(y4 \cdot \left(-c\right)\right)\right)} \]

   11. Simplified 78.2%

       \[\leadsto \color{blue}{y2 \cdot \left(t \cdot \left(y4 \cdot \left(-c\right)\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -3.55 \cdot 10^{+221}:\\ \;\;\;\;\left(-b\right) \cdot \left(k \cdot \left(y \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -9 \cdot 10^{+160}:\\ \;\;\;\;b \cdot \left(j \cdot \left(y0 \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -4.2 \cdot 10^{-63}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq -6.2 \cdot 10^{-82}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq -5.6 \cdot 10^{-187}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 1.25 \cdot 10^{-234}:\\ \;\;\;\;a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 58000000000000:\\ \;\;\;\;\left(y2 \cdot y5\right) \cdot \left(y0 \cdot \left(-k\right)\right)\\ \mathbf{elif}\;y4 \leq 4.5 \cdot 10^{+249}:\\ \;\;\;\;\left(-b\right) \cdot \left(k \cdot \left(y \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(y4 \cdot \left(-c\right)\right)\right)\\ \end{array} \]

Alternative 25: 31.8% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;b \leq -5.2 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-283}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-57} \lor \neg \left(b \leq 3.3 \cdot 10^{+16}\right) \land b \leq 4.8 \cdot 10^{+145}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y5 (- (* t y2) (* y y3))))))
   (if (<= b -5.2e+36)
     (* b (* j (- (* t y4) (* x y0))))
     (if (<= b -1.35e-279)
       t_1
       (if (<= b 1.25e-283)
         (* j (* t (- (* b y4) (* i y5))))
         (if (or (<= b 2.2e-57) (and (not (<= b 3.3e+16)) (<= b 4.8e+145)))
           t_1
           (* a (* b (- (* x y) (* z t))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (b <= -5.2e+36) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -1.35e-279) {
		tmp = t_1;
	} else if (b <= 1.25e-283) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if ((b <= 2.2e-57) || (!(b <= 3.3e+16) && (b <= 4.8e+145))) {
		tmp = t_1;
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y5 * ((t * y2) - (y * y3)))
    if (b <= (-5.2d+36)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (b <= (-1.35d-279)) then
        tmp = t_1
    else if (b <= 1.25d-283) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if ((b <= 2.2d-57) .or. (.not. (b <= 3.3d+16)) .and. (b <= 4.8d+145)) then
        tmp = t_1
    else
        tmp = a * (b * ((x * y) - (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (b <= -5.2e+36) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -1.35e-279) {
		tmp = t_1;
	} else if (b <= 1.25e-283) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if ((b <= 2.2e-57) || (!(b <= 3.3e+16) && (b <= 4.8e+145))) {
		tmp = t_1;
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y5 * ((t * y2) - (y * y3)))
	tmp = 0
	if b <= -5.2e+36:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif b <= -1.35e-279:
		tmp = t_1
	elif b <= 1.25e-283:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif (b <= 2.2e-57) or (not (b <= 3.3e+16) and (b <= 4.8e+145)):
		tmp = t_1
	else:
		tmp = a * (b * ((x * y) - (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	tmp = 0.0
	if (b <= -5.2e+36)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (b <= -1.35e-279)
		tmp = t_1;
	elseif (b <= 1.25e-283)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif ((b <= 2.2e-57) || (!(b <= 3.3e+16) && (b <= 4.8e+145)))
		tmp = t_1;
	else
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y5 * ((t * y2) - (y * y3)));
	tmp = 0.0;
	if (b <= -5.2e+36)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (b <= -1.35e-279)
		tmp = t_1;
	elseif (b <= 1.25e-283)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif ((b <= 2.2e-57) || (~((b <= 3.3e+16)) && (b <= 4.8e+145)))
		tmp = t_1;
	else
		tmp = a * (b * ((x * y) - (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.2e+36], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.35e-279], t$95$1, If[LessEqual[b, 1.25e-283], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 2.2e-57], And[N[Not[LessEqual[b, 3.3e+16]], $MachinePrecision], LessEqual[b, 4.8e+145]]], t$95$1, N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.2000000000000003e36

   1. Initial program 27.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 36.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 36.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 36.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 36.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 36.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 36.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in b around inf 55.7%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -5.2000000000000003e36 < b < -1.3500000000000001e-279 or 1.25e-283 < b < 2.19999999999999999e-57 or 3.3e16 < b < 4.79999999999999984e145

   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 j around inf 34.2%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 34.2%

         \[\leadsto \left(\left(\color{blue}{\left(-j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 34.9%

         \[\leadsto \left(\left(\left(-\color{blue}{\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 34.9%

      \[\leadsto \left(\left(\color{blue}{\left(-\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 35.4%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 35.4%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 35.4%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 35.4%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   if -1.3500000000000001e-279 < b < 1.25e-283

   1. Initial program 49.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 46.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 46.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 46.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 46.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 46.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 46.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in t around inf 57.2%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 57.2%

         \[\leadsto j \cdot \left(t \cdot \left(\color{blue}{y4 \cdot b} - i \cdot y5\right)\right) \]

      2. *-commutative 57.2%

         \[\leadsto j \cdot \left(t \cdot \left(y4 \cdot b - \color{blue}{y5 \cdot i}\right)\right) \]

   7. Simplified 57.2%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(y4 \cdot b - y5 \cdot i\right)\right)} \]

   if 2.19999999999999999e-57 < b < 3.3e16 or 4.79999999999999984e145 < b

   1. Initial program 17.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around inf 48.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. sub-neg 48.3%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. +-commutative 48.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. mul-1-neg 48.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. unsub-neg 48.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 48.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 48.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. mul-1-neg 48.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(-\color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. remove-double-neg 48.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \color{blue}{y5 \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. *-commutative 48.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 48.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in b around inf 64.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-279}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-283}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-57} \lor \neg \left(b \leq 3.3 \cdot 10^{+16}\right) \land b \leq 4.8 \cdot 10^{+145}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]

Alternative 26: 32.2% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;b \leq -2.45 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-280}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 9.7 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+88}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y5 (- (* t y2) (* y y3))))))
   (if (<= b -2.45e+36)
     (* b (* j (- (* t y4) (* x y0))))
     (if (<= b -2.8e-278)
       t_1
       (if (<= b 1.05e-280)
         (* j (* t (- (* b y4) (* i y5))))
         (if (<= b 9.7e-35)
           t_1
           (if (<= b 3.8e+88)
             (* j (* y0 (- (* y3 y5) (* x b))))
             (* a (* b (- (* x y) (* z t)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (b <= -2.45e+36) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -2.8e-278) {
		tmp = t_1;
	} else if (b <= 1.05e-280) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (b <= 9.7e-35) {
		tmp = t_1;
	} else if (b <= 3.8e+88) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y5 * ((t * y2) - (y * y3)))
    if (b <= (-2.45d+36)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (b <= (-2.8d-278)) then
        tmp = t_1
    else if (b <= 1.05d-280) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (b <= 9.7d-35) then
        tmp = t_1
    else if (b <= 3.8d+88) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else
        tmp = a * (b * ((x * y) - (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (b <= -2.45e+36) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (b <= -2.8e-278) {
		tmp = t_1;
	} else if (b <= 1.05e-280) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (b <= 9.7e-35) {
		tmp = t_1;
	} else if (b <= 3.8e+88) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y5 * ((t * y2) - (y * y3)))
	tmp = 0
	if b <= -2.45e+36:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif b <= -2.8e-278:
		tmp = t_1
	elif b <= 1.05e-280:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif b <= 9.7e-35:
		tmp = t_1
	elif b <= 3.8e+88:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	else:
		tmp = a * (b * ((x * y) - (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	tmp = 0.0
	if (b <= -2.45e+36)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (b <= -2.8e-278)
		tmp = t_1;
	elseif (b <= 1.05e-280)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (b <= 9.7e-35)
		tmp = t_1;
	elseif (b <= 3.8e+88)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	else
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y5 * ((t * y2) - (y * y3)));
	tmp = 0.0;
	if (b <= -2.45e+36)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (b <= -2.8e-278)
		tmp = t_1;
	elseif (b <= 1.05e-280)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (b <= 9.7e-35)
		tmp = t_1;
	elseif (b <= 3.8e+88)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	else
		tmp = a * (b * ((x * y) - (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.45e+36], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.8e-278], t$95$1, If[LessEqual[b, 1.05e-280], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.7e-35], t$95$1, If[LessEqual[b, 3.8e+88], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.4499999999999999e36

   1. Initial program 27.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 36.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 36.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 36.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 36.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 36.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 36.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in b around inf 55.7%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -2.4499999999999999e36 < b < -2.80000000000000008e-278 or 1.05e-280 < b < 9.70000000000000073e-35

   1. Initial program 30.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 30.2%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 30.2%

         \[\leadsto \left(\left(\color{blue}{\left(-j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 31.0%

         \[\leadsto \left(\left(\left(-\color{blue}{\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 31.0%

      \[\leadsto \left(\left(\color{blue}{\left(-\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   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%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 35.6%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 35.6%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   if -2.80000000000000008e-278 < b < 1.05e-280

   1. Initial program 49.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 46.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 46.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 46.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 46.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 46.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 46.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in t around inf 57.2%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 57.2%

         \[\leadsto j \cdot \left(t \cdot \left(\color{blue}{y4 \cdot b} - i \cdot y5\right)\right) \]

      2. *-commutative 57.2%

         \[\leadsto j \cdot \left(t \cdot \left(y4 \cdot b - \color{blue}{y5 \cdot i}\right)\right) \]

   7. Simplified 57.2%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(y4 \cdot b - y5 \cdot i\right)\right)} \]

   if 9.70000000000000073e-35 < b < 3.7999999999999997e88

   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 j around inf 44.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 44.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 44.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 44.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 44.2%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 44.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in y0 around -inf 47.9%

      \[\leadsto j \cdot \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 47.9%

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      2. mul-1-neg 47.9%

         \[\leadsto j \cdot \left(y0 \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      3. unsub-neg 47.9%

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

      4. *-commutative 47.9%

         \[\leadsto j \cdot \left(y0 \cdot \left(\color{blue}{y5 \cdot y3} - b \cdot x\right)\right) \]

      5. *-commutative 47.9%

         \[\leadsto j \cdot \left(y0 \cdot \left(y5 \cdot y3 - \color{blue}{x \cdot b}\right)\right) \]

   7. Simplified 47.9%

      \[\leadsto j \cdot \color{blue}{\left(y0 \cdot \left(y5 \cdot y3 - x \cdot b\right)\right)} \]

   if 3.7999999999999997e88 < b

   1. Initial program 20.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around inf 46.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. sub-neg 46.3%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. +-commutative 46.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. mul-1-neg 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. unsub-neg 46.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. mul-1-neg 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(-\color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. remove-double-neg 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \color{blue}{y5 \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. *-commutative 46.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 46.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in b around inf 63.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.45 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-278}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-280}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 9.7 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+88}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]

Alternative 27: 21.2% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(y2 \cdot \left(a \cdot y5\right)\right)\\ t_2 := b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+138}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-291}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-217}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+268}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (* y2 (* a y5)))) (t_2 (* b (* k (* z y0)))))
   (if (<= y -2e+138)
     (* a (* (* x y) b))
     (if (<= y -2e-126)
       t_2
       (if (<= y 7.5e-291)
         t_1
         (if (<= y 1.42e-217)
           t_2
           (if (<= y 6.4e+113)
             t_1
             (if (<= y 3.7e+268)
               (* a (* y (* x b)))
               (* a (* y5 (* y (- y3))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (y2 * (a * y5));
	double t_2 = b * (k * (z * y0));
	double tmp;
	if (y <= -2e+138) {
		tmp = a * ((x * y) * b);
	} else if (y <= -2e-126) {
		tmp = t_2;
	} else if (y <= 7.5e-291) {
		tmp = t_1;
	} else if (y <= 1.42e-217) {
		tmp = t_2;
	} else if (y <= 6.4e+113) {
		tmp = t_1;
	} else if (y <= 3.7e+268) {
		tmp = a * (y * (x * b));
	} else {
		tmp = a * (y5 * (y * -y3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (y2 * (a * y5))
    t_2 = b * (k * (z * y0))
    if (y <= (-2d+138)) then
        tmp = a * ((x * y) * b)
    else if (y <= (-2d-126)) then
        tmp = t_2
    else if (y <= 7.5d-291) then
        tmp = t_1
    else if (y <= 1.42d-217) then
        tmp = t_2
    else if (y <= 6.4d+113) then
        tmp = t_1
    else if (y <= 3.7d+268) then
        tmp = a * (y * (x * b))
    else
        tmp = a * (y5 * (y * -y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (y2 * (a * y5));
	double t_2 = b * (k * (z * y0));
	double tmp;
	if (y <= -2e+138) {
		tmp = a * ((x * y) * b);
	} else if (y <= -2e-126) {
		tmp = t_2;
	} else if (y <= 7.5e-291) {
		tmp = t_1;
	} else if (y <= 1.42e-217) {
		tmp = t_2;
	} else if (y <= 6.4e+113) {
		tmp = t_1;
	} else if (y <= 3.7e+268) {
		tmp = a * (y * (x * b));
	} else {
		tmp = a * (y5 * (y * -y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = t * (y2 * (a * y5))
	t_2 = b * (k * (z * y0))
	tmp = 0
	if y <= -2e+138:
		tmp = a * ((x * y) * b)
	elif y <= -2e-126:
		tmp = t_2
	elif y <= 7.5e-291:
		tmp = t_1
	elif y <= 1.42e-217:
		tmp = t_2
	elif y <= 6.4e+113:
		tmp = t_1
	elif y <= 3.7e+268:
		tmp = a * (y * (x * b))
	else:
		tmp = a * (y5 * (y * -y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(t * Float64(y2 * Float64(a * y5)))
	t_2 = Float64(b * Float64(k * Float64(z * y0)))
	tmp = 0.0
	if (y <= -2e+138)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (y <= -2e-126)
		tmp = t_2;
	elseif (y <= 7.5e-291)
		tmp = t_1;
	elseif (y <= 1.42e-217)
		tmp = t_2;
	elseif (y <= 6.4e+113)
		tmp = t_1;
	elseif (y <= 3.7e+268)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	else
		tmp = Float64(a * Float64(y5 * Float64(y * 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 = t * (y2 * (a * y5));
	t_2 = b * (k * (z * y0));
	tmp = 0.0;
	if (y <= -2e+138)
		tmp = a * ((x * y) * b);
	elseif (y <= -2e-126)
		tmp = t_2;
	elseif (y <= 7.5e-291)
		tmp = t_1;
	elseif (y <= 1.42e-217)
		tmp = t_2;
	elseif (y <= 6.4e+113)
		tmp = t_1;
	elseif (y <= 3.7e+268)
		tmp = a * (y * (x * b));
	else
		tmp = a * (y5 * (y * -y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(t * N[(y2 * N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+138], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2e-126], t$95$2, If[LessEqual[y, 7.5e-291], t$95$1, If[LessEqual[y, 1.42e-217], t$95$2, If[LessEqual[y, 6.4e+113], t$95$1, If[LessEqual[y, 3.7e+268], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(y * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.0000000000000001e138

   1. Initial program 27.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around inf 46.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. sub-neg 46.8%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. +-commutative 46.8%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. mul-1-neg 46.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. unsub-neg 46.8%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 46.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 46.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. mul-1-neg 46.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(-\color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. remove-double-neg 46.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \color{blue}{y5 \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. *-commutative 46.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 46.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y1 around 0 46.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in x around inf 42.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

   if -2.0000000000000001e138 < y < -1.9999999999999999e-126 or 7.49999999999999981e-291 < y < 1.41999999999999992e-217

   1. Initial program 30.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in k around -inf 40.0%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 40.0%

         \[\leadsto \color{blue}{-k \cdot \left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. *-commutative 40.0%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot k} \]

      3. distribute-rgt-neg-in 40.0%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right)} \]

      4. +-commutative 40.0%

         \[\leadsto \left(\color{blue}{\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      5. mul-1-neg 40.0%

         \[\leadsto \left(\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      6. unsub-neg 40.0%

         \[\leadsto \left(\color{blue}{\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      7. *-commutative 40.0%

         \[\leadsto \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y} - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

   4. Simplified 40.0%

      \[\leadsto \color{blue}{\left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot y - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right)} \]

   5. Taylor expanded in y0 around -inf 35.5%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \cdot \left(-k\right) \]
   6. Step-by-step derivation

      1. +-commutative 35.5%

         \[\leadsto \left(y0 \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \cdot \left(-k\right) \]

      2. mul-1-neg 35.5%

         \[\leadsto \left(y0 \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \cdot \left(-k\right) \]

      3. unsub-neg 35.5%

         \[\leadsto \left(y0 \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \cdot \left(-k\right) \]

   7. Simplified 35.5%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \cdot \left(-k\right) \]

   8. Taylor expanded in y2 around 0 31.7%

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]

   if -1.9999999999999999e-126 < y < 7.49999999999999981e-291 or 1.41999999999999992e-217 < y < 6.3999999999999996e113

   1. Initial program 33.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 47.1%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 47.1%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 47.1%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 47.1%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 48.1%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 48.1%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 48.1%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 48.1%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 48.1%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 48.1%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in t around inf 42.7%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   6. Taylor expanded in a around inf 31.8%

      \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(a \cdot y5\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative 31.8%

         \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot a\right)}\right) \]

   8. Simplified 31.8%

      \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot a\right)}\right) \]

   if 6.3999999999999996e113 < y < 3.70000000000000009e268

   1. Initial program 20.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around inf 31.4%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. sub-neg 31.4%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. +-commutative 31.4%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. mul-1-neg 31.4%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. unsub-neg 31.4%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 31.4%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 31.4%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. mul-1-neg 31.4%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(-\color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. remove-double-neg 31.4%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \color{blue}{y5 \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. *-commutative 31.4%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 31.4%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y1 around 0 41.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in x around inf 59.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 59.2%

         \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

   8. Simplified 59.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot x\right) \cdot y\right)} \]

   if 3.70000000000000009e268 < y

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 25.0%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 25.0%

         \[\leadsto \left(\left(\color{blue}{\left(-j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 25.0%

         \[\leadsto \left(\left(\left(-\color{blue}{\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 25.0%

      \[\leadsto \left(\left(\color{blue}{\left(-\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 75.3%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 75.3%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 75.3%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 75.3%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y2 around 0 75.3%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y3\right)\right)}\right) \]
   9. Step-by-step derivation

      1. neg-mul-1 75.3%

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(-y \cdot y3\right)}\right) \]

      2. distribute-lft-neg-in 75.3%

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(\left(-y\right) \cdot y3\right)}\right) \]

   10. Simplified 75.3%

       \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(\left(-y\right) \cdot y3\right)}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+138}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-126}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-291}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-217}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+113}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+268}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \end{array} \]

Alternative 28: 31.4% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+140}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(b \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-57} \lor \neg \left(b \leq 8.6 \cdot 10^{+15}\right) \land b \leq 8.5 \cdot 10^{+140}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -1.4e+140)
   (* y0 (* j (* b (- x))))
   (if (or (<= b 2.2e-57) (and (not (<= b 8.6e+15)) (<= b 8.5e+140)))
     (* a (* y5 (- (* t y2) (* y y3))))
     (* a (* b (- (* x y) (* z t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -1.4e+140) {
		tmp = y0 * (j * (b * -x));
	} else if ((b <= 2.2e-57) || (!(b <= 8.6e+15) && (b <= 8.5e+140))) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (b <= (-1.4d+140)) then
        tmp = y0 * (j * (b * -x))
    else if ((b <= 2.2d-57) .or. (.not. (b <= 8.6d+15)) .and. (b <= 8.5d+140)) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else
        tmp = a * (b * ((x * y) - (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -1.4e+140) {
		tmp = y0 * (j * (b * -x));
	} else if ((b <= 2.2e-57) || (!(b <= 8.6e+15) && (b <= 8.5e+140))) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -1.4e+140:
		tmp = y0 * (j * (b * -x))
	elif (b <= 2.2e-57) or (not (b <= 8.6e+15) and (b <= 8.5e+140)):
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	else:
		tmp = a * (b * ((x * y) - (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (b <= -1.4e+140)
		tmp = Float64(y0 * Float64(j * Float64(b * Float64(-x))));
	elseif ((b <= 2.2e-57) || (!(b <= 8.6e+15) && (b <= 8.5e+140)))
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	else
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (b <= -1.4e+140)
		tmp = y0 * (j * (b * -x));
	elseif ((b <= 2.2e-57) || (~((b <= 8.6e+15)) && (b <= 8.5e+140)))
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	else
		tmp = a * (b * ((x * y) - (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[b, -1.4e+140], N[(y0 * N[(j * N[(b * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 2.2e-57], And[N[Not[LessEqual[b, 8.6e+15]], $MachinePrecision], LessEqual[b, 8.5e+140]]], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.39999999999999991e140

   1. Initial program 23.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y0 around inf 29.6%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 29.6%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \color{blue}{\left(j \cdot x + \left(-k \cdot z\right)\right)}\right) \]

      2. +-commutative 29.6%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \color{blue}{\left(\left(-k \cdot z\right) + j \cdot x\right)}\right) \]

      3. mul-1-neg 29.6%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(\color{blue}{-1 \cdot \left(k \cdot z\right)} + j \cdot x\right)\right) \]

      4. +-commutative 29.6%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      5. mul-1-neg 29.6%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      6. unsub-neg 29.6%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      7. *-commutative 29.6%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      8. *-commutative 29.6%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

   4. Simplified 29.6%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   5. Taylor expanded in j around -inf 50.7%

      \[\leadsto y0 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 50.7%

         \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      2. mul-1-neg 50.7%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      3. unsub-neg 50.7%

         \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   7. Simplified 50.7%

      \[\leadsto y0 \cdot \color{blue}{\left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   8. Taylor expanded in y3 around 0 53.5%

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(-1 \cdot \left(b \cdot x\right)\right)}\right) \]
   9. Step-by-step derivation

      1. neg-mul-1 53.5%

         \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(-b \cdot x\right)}\right) \]

      2. distribute-rgt-neg-in 53.5%

         \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(b \cdot \left(-x\right)\right)}\right) \]

   10. Simplified 53.5%

       \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(b \cdot \left(-x\right)\right)}\right) \]

   if -1.39999999999999991e140 < b < 2.19999999999999999e-57 or 8.6e15 < b < 8.4999999999999996e140

   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 j around inf 34.7%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 34.7%

         \[\leadsto \left(\left(\color{blue}{\left(-j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 34.7%

         \[\leadsto \left(\left(\left(-\color{blue}{\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 34.7%

      \[\leadsto \left(\left(\color{blue}{\left(-\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 33.0%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 33.0%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 33.0%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 33.0%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   if 2.19999999999999999e-57 < b < 8.6e15 or 8.4999999999999996e140 < b

   1. Initial program 17.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around inf 48.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. sub-neg 48.3%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. +-commutative 48.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. mul-1-neg 48.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. unsub-neg 48.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 48.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 48.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. mul-1-neg 48.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(-\color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. remove-double-neg 48.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \color{blue}{y5 \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. *-commutative 48.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 48.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in b around inf 64.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+140}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(b \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-57} \lor \neg \left(b \leq 8.6 \cdot 10^{+15}\right) \land b \leq 8.5 \cdot 10^{+140}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]

Alternative 29: 32.4% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-56} \lor \neg \left(b \leq 2.8 \cdot 10^{+15}\right) \land b \leq 9 \cdot 10^{+143}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -1.65e+36)
   (* b (* j (- (* t y4) (* x y0))))
   (if (or (<= b 1.3e-56) (and (not (<= b 2.8e+15)) (<= b 9e+143)))
     (* a (* y5 (- (* t y2) (* y y3))))
     (* a (* b (- (* x y) (* z t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -1.65e+36) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if ((b <= 1.3e-56) || (!(b <= 2.8e+15) && (b <= 9e+143))) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (b <= (-1.65d+36)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if ((b <= 1.3d-56) .or. (.not. (b <= 2.8d+15)) .and. (b <= 9d+143)) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else
        tmp = a * (b * ((x * y) - (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -1.65e+36) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if ((b <= 1.3e-56) || (!(b <= 2.8e+15) && (b <= 9e+143))) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else {
		tmp = a * (b * ((x * y) - (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -1.65e+36:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif (b <= 1.3e-56) or (not (b <= 2.8e+15) and (b <= 9e+143)):
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	else:
		tmp = a * (b * ((x * y) - (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (b <= -1.65e+36)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif ((b <= 1.3e-56) || (!(b <= 2.8e+15) && (b <= 9e+143)))
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	else
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (b <= -1.65e+36)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif ((b <= 1.3e-56) || (~((b <= 2.8e+15)) && (b <= 9e+143)))
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	else
		tmp = a * (b * ((x * y) - (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[b, -1.65e+36], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 1.3e-56], And[N[Not[LessEqual[b, 2.8e+15]], $MachinePrecision], LessEqual[b, 9e+143]]], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.6499999999999999e36

   1. Initial program 27.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 36.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 36.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      2. mul-1-neg 36.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      3. unsub-neg 36.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

      4. *-commutative 36.6%

         \[\leadsto j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \color{blue}{\left(b \cdot y0 - i \cdot y1\right) \cdot x}\right) \]

   4. Simplified 36.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)} \]

   5. Taylor expanded in b around inf 55.7%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -1.6499999999999999e36 < b < 1.29999999999999998e-56 or 2.8e15 < b < 8.9999999999999993e143

   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 j around inf 34.8%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 34.8%

         \[\leadsto \left(\left(\color{blue}{\left(-j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 36.1%

         \[\leadsto \left(\left(\left(-\color{blue}{\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 36.1%

      \[\leadsto \left(\left(\color{blue}{\left(-\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 34.0%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 34.0%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 34.0%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 34.0%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   if 1.29999999999999998e-56 < b < 2.8e15 or 8.9999999999999993e143 < b

   1. Initial program 17.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around inf 48.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. sub-neg 48.3%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. +-commutative 48.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. mul-1-neg 48.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. unsub-neg 48.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 48.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 48.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. mul-1-neg 48.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(-\color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. remove-double-neg 48.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \color{blue}{y5 \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. *-commutative 48.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 48.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in b around inf 64.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-56} \lor \neg \left(b \leq 2.8 \cdot 10^{+15}\right) \land b \leq 9 \cdot 10^{+143}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]

Alternative 30: 21.8% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ t_2 := a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ t_3 := b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-123}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-290}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-215}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+113}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* (* x y) b)))
        (t_2 (* a (* t (* y2 y5))))
        (t_3 (* b (* k (* z y0)))))
   (if (<= y -3.3e+137)
     t_1
     (if (<= y -5e-123)
       t_3
       (if (<= y 1.55e-290)
         t_2
         (if (<= y 4.2e-215) t_3 (if (<= y 5.2e+113) 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 = a * ((x * y) * b);
	double t_2 = a * (t * (y2 * y5));
	double t_3 = b * (k * (z * y0));
	double tmp;
	if (y <= -3.3e+137) {
		tmp = t_1;
	} else if (y <= -5e-123) {
		tmp = t_3;
	} else if (y <= 1.55e-290) {
		tmp = t_2;
	} else if (y <= 4.2e-215) {
		tmp = t_3;
	} else if (y <= 5.2e+113) {
		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 = a * ((x * y) * b)
    t_2 = a * (t * (y2 * y5))
    t_3 = b * (k * (z * y0))
    if (y <= (-3.3d+137)) then
        tmp = t_1
    else if (y <= (-5d-123)) then
        tmp = t_3
    else if (y <= 1.55d-290) then
        tmp = t_2
    else if (y <= 4.2d-215) then
        tmp = t_3
    else if (y <= 5.2d+113) 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 = a * ((x * y) * b);
	double t_2 = a * (t * (y2 * y5));
	double t_3 = b * (k * (z * y0));
	double tmp;
	if (y <= -3.3e+137) {
		tmp = t_1;
	} else if (y <= -5e-123) {
		tmp = t_3;
	} else if (y <= 1.55e-290) {
		tmp = t_2;
	} else if (y <= 4.2e-215) {
		tmp = t_3;
	} else if (y <= 5.2e+113) {
		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 = a * ((x * y) * b)
	t_2 = a * (t * (y2 * y5))
	t_3 = b * (k * (z * y0))
	tmp = 0
	if y <= -3.3e+137:
		tmp = t_1
	elif y <= -5e-123:
		tmp = t_3
	elif y <= 1.55e-290:
		tmp = t_2
	elif y <= 4.2e-215:
		tmp = t_3
	elif y <= 5.2e+113:
		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(a * Float64(Float64(x * y) * b))
	t_2 = Float64(a * Float64(t * Float64(y2 * y5)))
	t_3 = Float64(b * Float64(k * Float64(z * y0)))
	tmp = 0.0
	if (y <= -3.3e+137)
		tmp = t_1;
	elseif (y <= -5e-123)
		tmp = t_3;
	elseif (y <= 1.55e-290)
		tmp = t_2;
	elseif (y <= 4.2e-215)
		tmp = t_3;
	elseif (y <= 5.2e+113)
		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 = a * ((x * y) * b);
	t_2 = a * (t * (y2 * y5));
	t_3 = b * (k * (z * y0));
	tmp = 0.0;
	if (y <= -3.3e+137)
		tmp = t_1;
	elseif (y <= -5e-123)
		tmp = t_3;
	elseif (y <= 1.55e-290)
		tmp = t_2;
	elseif (y <= 4.2e-215)
		tmp = t_3;
	elseif (y <= 5.2e+113)
		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[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.3e+137], t$95$1, If[LessEqual[y, -5e-123], t$95$3, If[LessEqual[y, 1.55e-290], t$95$2, If[LessEqual[y, 4.2e-215], t$95$3, If[LessEqual[y, 5.2e+113], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.30000000000000003e137 or 5.1999999999999998e113 < y

   1. Initial program 24.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around inf 40.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. sub-neg 40.1%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. +-commutative 40.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. mul-1-neg 40.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. unsub-neg 40.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 40.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 40.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. mul-1-neg 40.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(-\color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. remove-double-neg 40.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \color{blue}{y5 \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. *-commutative 40.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 40.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y1 around 0 45.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in x around inf 45.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

   if -3.30000000000000003e137 < y < -5.0000000000000003e-123 or 1.54999999999999995e-290 < y < 4.2e-215

   1. Initial program 30.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in k around -inf 40.0%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 40.0%

         \[\leadsto \color{blue}{-k \cdot \left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. *-commutative 40.0%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot k} \]

      3. distribute-rgt-neg-in 40.0%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right)} \]

      4. +-commutative 40.0%

         \[\leadsto \left(\color{blue}{\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      5. mul-1-neg 40.0%

         \[\leadsto \left(\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      6. unsub-neg 40.0%

         \[\leadsto \left(\color{blue}{\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      7. *-commutative 40.0%

         \[\leadsto \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y} - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

   4. Simplified 40.0%

      \[\leadsto \color{blue}{\left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot y - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right)} \]

   5. Taylor expanded in y0 around -inf 35.5%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \cdot \left(-k\right) \]
   6. Step-by-step derivation

      1. +-commutative 35.5%

         \[\leadsto \left(y0 \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \cdot \left(-k\right) \]

      2. mul-1-neg 35.5%

         \[\leadsto \left(y0 \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \cdot \left(-k\right) \]

      3. unsub-neg 35.5%

         \[\leadsto \left(y0 \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \cdot \left(-k\right) \]

   7. Simplified 35.5%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \cdot \left(-k\right) \]

   8. Taylor expanded in y2 around 0 31.7%

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]

   if -5.0000000000000003e-123 < y < 1.54999999999999995e-290 or 4.2e-215 < y < 5.1999999999999998e113

   1. Initial program 33.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 33.1%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 33.1%

         \[\leadsto \left(\left(\color{blue}{\left(-j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 34.0%

         \[\leadsto \left(\left(\left(-\color{blue}{\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 34.0%

      \[\leadsto \left(\left(\color{blue}{\left(-\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 33.8%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 33.8%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 33.8%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 33.8%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y2 around inf 29.0%

      \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(y2 \cdot y5\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+137}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-123}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-290}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-215}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \]

Alternative 31: 21.8% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ t_2 := t \cdot \left(a \cdot \left(y2 \cdot y5\right)\right)\\ t_3 := b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-129}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-288}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-214}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+113}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* (* x y) b)))
        (t_2 (* t (* a (* y2 y5))))
        (t_3 (* b (* k (* z y0)))))
   (if (<= y -3.3e+137)
     t_1
     (if (<= y -6.5e-129)
       t_3
       (if (<= y 1.25e-288)
         t_2
         (if (<= y 4.8e-214) t_3 (if (<= y 8.5e+113) 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 = a * ((x * y) * b);
	double t_2 = t * (a * (y2 * y5));
	double t_3 = b * (k * (z * y0));
	double tmp;
	if (y <= -3.3e+137) {
		tmp = t_1;
	} else if (y <= -6.5e-129) {
		tmp = t_3;
	} else if (y <= 1.25e-288) {
		tmp = t_2;
	} else if (y <= 4.8e-214) {
		tmp = t_3;
	} else if (y <= 8.5e+113) {
		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 = a * ((x * y) * b)
    t_2 = t * (a * (y2 * y5))
    t_3 = b * (k * (z * y0))
    if (y <= (-3.3d+137)) then
        tmp = t_1
    else if (y <= (-6.5d-129)) then
        tmp = t_3
    else if (y <= 1.25d-288) then
        tmp = t_2
    else if (y <= 4.8d-214) then
        tmp = t_3
    else if (y <= 8.5d+113) 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 = a * ((x * y) * b);
	double t_2 = t * (a * (y2 * y5));
	double t_3 = b * (k * (z * y0));
	double tmp;
	if (y <= -3.3e+137) {
		tmp = t_1;
	} else if (y <= -6.5e-129) {
		tmp = t_3;
	} else if (y <= 1.25e-288) {
		tmp = t_2;
	} else if (y <= 4.8e-214) {
		tmp = t_3;
	} else if (y <= 8.5e+113) {
		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 = a * ((x * y) * b)
	t_2 = t * (a * (y2 * y5))
	t_3 = b * (k * (z * y0))
	tmp = 0
	if y <= -3.3e+137:
		tmp = t_1
	elif y <= -6.5e-129:
		tmp = t_3
	elif y <= 1.25e-288:
		tmp = t_2
	elif y <= 4.8e-214:
		tmp = t_3
	elif y <= 8.5e+113:
		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(a * Float64(Float64(x * y) * b))
	t_2 = Float64(t * Float64(a * Float64(y2 * y5)))
	t_3 = Float64(b * Float64(k * Float64(z * y0)))
	tmp = 0.0
	if (y <= -3.3e+137)
		tmp = t_1;
	elseif (y <= -6.5e-129)
		tmp = t_3;
	elseif (y <= 1.25e-288)
		tmp = t_2;
	elseif (y <= 4.8e-214)
		tmp = t_3;
	elseif (y <= 8.5e+113)
		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 = a * ((x * y) * b);
	t_2 = t * (a * (y2 * y5));
	t_3 = b * (k * (z * y0));
	tmp = 0.0;
	if (y <= -3.3e+137)
		tmp = t_1;
	elseif (y <= -6.5e-129)
		tmp = t_3;
	elseif (y <= 1.25e-288)
		tmp = t_2;
	elseif (y <= 4.8e-214)
		tmp = t_3;
	elseif (y <= 8.5e+113)
		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[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(a * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.3e+137], t$95$1, If[LessEqual[y, -6.5e-129], t$95$3, If[LessEqual[y, 1.25e-288], t$95$2, If[LessEqual[y, 4.8e-214], t$95$3, If[LessEqual[y, 8.5e+113], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.30000000000000003e137 or 8.5000000000000001e113 < y

   1. Initial program 24.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around inf 40.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. sub-neg 40.1%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. +-commutative 40.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. mul-1-neg 40.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. unsub-neg 40.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 40.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 40.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. mul-1-neg 40.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(-\color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. remove-double-neg 40.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \color{blue}{y5 \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. *-commutative 40.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 40.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y1 around 0 45.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in x around inf 45.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

   if -3.30000000000000003e137 < y < -6.49999999999999952e-129 or 1.25000000000000003e-288 < y < 4.80000000000000041e-214

   1. Initial program 30.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in k around -inf 40.0%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 40.0%

         \[\leadsto \color{blue}{-k \cdot \left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. *-commutative 40.0%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot k} \]

      3. distribute-rgt-neg-in 40.0%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right)} \]

      4. +-commutative 40.0%

         \[\leadsto \left(\color{blue}{\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      5. mul-1-neg 40.0%

         \[\leadsto \left(\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      6. unsub-neg 40.0%

         \[\leadsto \left(\color{blue}{\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      7. *-commutative 40.0%

         \[\leadsto \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y} - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

   4. Simplified 40.0%

      \[\leadsto \color{blue}{\left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot y - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right)} \]

   5. Taylor expanded in y0 around -inf 35.5%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \cdot \left(-k\right) \]
   6. Step-by-step derivation

      1. +-commutative 35.5%

         \[\leadsto \left(y0 \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \cdot \left(-k\right) \]

      2. mul-1-neg 35.5%

         \[\leadsto \left(y0 \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \cdot \left(-k\right) \]

      3. unsub-neg 35.5%

         \[\leadsto \left(y0 \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \cdot \left(-k\right) \]

   7. Simplified 35.5%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \cdot \left(-k\right) \]

   8. Taylor expanded in y2 around 0 31.7%

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]

   if -6.49999999999999952e-129 < y < 1.25000000000000003e-288 or 4.80000000000000041e-214 < y < 8.5000000000000001e113

   1. Initial program 33.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 47.1%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 47.1%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 47.1%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 47.1%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 48.1%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 48.1%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 48.1%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 48.1%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 48.1%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 48.1%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in t around inf 42.7%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   6. Taylor expanded in a around inf 30.0%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(y2 \cdot y5\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+137}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-129}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-288}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-214}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+113}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \]

Alternative 32: 21.7% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ t_2 := t \cdot \left(y2 \cdot \left(a \cdot y5\right)\right)\\ t_3 := b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-124}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-285}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-212}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+113}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* (* x y) b)))
        (t_2 (* t (* y2 (* a y5))))
        (t_3 (* b (* k (* z y0)))))
   (if (<= y -1.5e+138)
     t_1
     (if (<= y -1e-124)
       t_3
       (if (<= y 2.7e-285)
         t_2
         (if (<= y 1.9e-212) t_3 (if (<= y 7.5e+113) 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 = a * ((x * y) * b);
	double t_2 = t * (y2 * (a * y5));
	double t_3 = b * (k * (z * y0));
	double tmp;
	if (y <= -1.5e+138) {
		tmp = t_1;
	} else if (y <= -1e-124) {
		tmp = t_3;
	} else if (y <= 2.7e-285) {
		tmp = t_2;
	} else if (y <= 1.9e-212) {
		tmp = t_3;
	} else if (y <= 7.5e+113) {
		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 = a * ((x * y) * b)
    t_2 = t * (y2 * (a * y5))
    t_3 = b * (k * (z * y0))
    if (y <= (-1.5d+138)) then
        tmp = t_1
    else if (y <= (-1d-124)) then
        tmp = t_3
    else if (y <= 2.7d-285) then
        tmp = t_2
    else if (y <= 1.9d-212) then
        tmp = t_3
    else if (y <= 7.5d+113) 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 = a * ((x * y) * b);
	double t_2 = t * (y2 * (a * y5));
	double t_3 = b * (k * (z * y0));
	double tmp;
	if (y <= -1.5e+138) {
		tmp = t_1;
	} else if (y <= -1e-124) {
		tmp = t_3;
	} else if (y <= 2.7e-285) {
		tmp = t_2;
	} else if (y <= 1.9e-212) {
		tmp = t_3;
	} else if (y <= 7.5e+113) {
		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 = a * ((x * y) * b)
	t_2 = t * (y2 * (a * y5))
	t_3 = b * (k * (z * y0))
	tmp = 0
	if y <= -1.5e+138:
		tmp = t_1
	elif y <= -1e-124:
		tmp = t_3
	elif y <= 2.7e-285:
		tmp = t_2
	elif y <= 1.9e-212:
		tmp = t_3
	elif y <= 7.5e+113:
		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(a * Float64(Float64(x * y) * b))
	t_2 = Float64(t * Float64(y2 * Float64(a * y5)))
	t_3 = Float64(b * Float64(k * Float64(z * y0)))
	tmp = 0.0
	if (y <= -1.5e+138)
		tmp = t_1;
	elseif (y <= -1e-124)
		tmp = t_3;
	elseif (y <= 2.7e-285)
		tmp = t_2;
	elseif (y <= 1.9e-212)
		tmp = t_3;
	elseif (y <= 7.5e+113)
		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 = a * ((x * y) * b);
	t_2 = t * (y2 * (a * y5));
	t_3 = b * (k * (z * y0));
	tmp = 0.0;
	if (y <= -1.5e+138)
		tmp = t_1;
	elseif (y <= -1e-124)
		tmp = t_3;
	elseif (y <= 2.7e-285)
		tmp = t_2;
	elseif (y <= 1.9e-212)
		tmp = t_3;
	elseif (y <= 7.5e+113)
		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[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(y2 * N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e+138], t$95$1, If[LessEqual[y, -1e-124], t$95$3, If[LessEqual[y, 2.7e-285], t$95$2, If[LessEqual[y, 1.9e-212], t$95$3, If[LessEqual[y, 7.5e+113], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.50000000000000005e138 or 7.5000000000000001e113 < y

   1. Initial program 24.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around inf 40.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. sub-neg 40.1%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. +-commutative 40.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. mul-1-neg 40.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. unsub-neg 40.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 40.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 40.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. mul-1-neg 40.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(-\color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. remove-double-neg 40.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \color{blue}{y5 \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. *-commutative 40.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 40.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y1 around 0 45.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in x around inf 45.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

   if -1.50000000000000005e138 < y < -9.99999999999999933e-125 or 2.6999999999999998e-285 < y < 1.90000000000000011e-212

   1. Initial program 30.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in k around -inf 40.0%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 40.0%

         \[\leadsto \color{blue}{-k \cdot \left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. *-commutative 40.0%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot k} \]

      3. distribute-rgt-neg-in 40.0%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right)} \]

      4. +-commutative 40.0%

         \[\leadsto \left(\color{blue}{\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) + -1 \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      5. mul-1-neg 40.0%

         \[\leadsto \left(\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) + \color{blue}{\left(-y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)}\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      6. unsub-neg 40.0%

         \[\leadsto \left(\color{blue}{\left(y \cdot \left(b \cdot y4 - i \cdot y5\right) - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

      7. *-commutative 40.0%

         \[\leadsto \left(\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y} - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right) \]

   4. Simplified 40.0%

      \[\leadsto \color{blue}{\left(\left(\left(b \cdot y4 - i \cdot y5\right) \cdot y - y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - z \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \cdot \left(-k\right)} \]

   5. Taylor expanded in y0 around -inf 35.5%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(-1 \cdot \left(b \cdot z\right) + y2 \cdot y5\right)\right)} \cdot \left(-k\right) \]
   6. Step-by-step derivation

      1. +-commutative 35.5%

         \[\leadsto \left(y0 \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \cdot \left(-k\right) \]

      2. mul-1-neg 35.5%

         \[\leadsto \left(y0 \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \cdot \left(-k\right) \]

      3. unsub-neg 35.5%

         \[\leadsto \left(y0 \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \cdot \left(-k\right) \]

   7. Simplified 35.5%

      \[\leadsto \color{blue}{\left(y0 \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \cdot \left(-k\right) \]

   8. Taylor expanded in y2 around 0 31.7%

      \[\leadsto \color{blue}{b \cdot \left(k \cdot \left(y0 \cdot z\right)\right)} \]

   if -9.99999999999999933e-125 < y < 2.6999999999999998e-285 or 1.90000000000000011e-212 < y < 7.5000000000000001e113

   1. Initial program 33.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 47.1%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 47.1%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 47.1%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 47.1%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 48.1%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 48.1%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 48.1%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 48.1%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 48.1%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 48.1%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in t around inf 42.7%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   6. Taylor expanded in a around inf 31.8%

      \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(a \cdot y5\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative 31.8%

         \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot a\right)}\right) \]

   8. Simplified 31.8%

      \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot a\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+138}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-124}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-285}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-212}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+113}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \]

Alternative 33: 28.3% accurate, 6.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -4.1 \cdot 10^{+76}:\\ \;\;\;\;a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 1.28 \cdot 10^{-11}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y3 \leq 3.55 \cdot 10^{+103}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 -4.1e+76)
   (* a (* y (* y3 (- y5))))
   (if (<= y3 1.28e-11)
     (* a (* b (- (* x y) (* z t))))
     (if (<= y3 3.55e+103) (* t (* y2 (* a y5))) (* 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 (y3 <= -4.1e+76) {
		tmp = a * (y * (y3 * -y5));
	} else if (y3 <= 1.28e-11) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y3 <= 3.55e+103) {
		tmp = t * (y2 * (a * y5));
	} 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 (y3 <= (-4.1d+76)) then
        tmp = a * (y * (y3 * -y5))
    else if (y3 <= 1.28d-11) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y3 <= 3.55d+103) then
        tmp = t * (y2 * (a * y5))
    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 (y3 <= -4.1e+76) {
		tmp = a * (y * (y3 * -y5));
	} else if (y3 <= 1.28e-11) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y3 <= 3.55e+103) {
		tmp = t * (y2 * (a * y5));
	} 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 y3 <= -4.1e+76:
		tmp = a * (y * (y3 * -y5))
	elif y3 <= 1.28e-11:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y3 <= 3.55e+103:
		tmp = t * (y2 * (a * y5))
	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 (y3 <= -4.1e+76)
		tmp = Float64(a * Float64(y * Float64(y3 * Float64(-y5))));
	elseif (y3 <= 1.28e-11)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y3 <= 3.55e+103)
		tmp = Float64(t * Float64(y2 * Float64(a * y5)));
	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 (y3 <= -4.1e+76)
		tmp = a * (y * (y3 * -y5));
	elseif (y3 <= 1.28e-11)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y3 <= 3.55e+103)
		tmp = t * (y2 * (a * y5));
	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[y3, -4.1e+76], N[(a * N[(y * N[(y3 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.28e-11], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 3.55e+103], N[(t * N[(y2 * N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y3 < -4.0999999999999998e76

   1. Initial program 19.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 19.9%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 19.9%

         \[\leadsto \left(\left(\color{blue}{\left(-j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 23.8%

         \[\leadsto \left(\left(\left(-\color{blue}{\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 23.8%

      \[\leadsto \left(\left(\color{blue}{\left(-\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 44.1%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 44.1%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 44.1%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 44.1%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y2 around 0 49.6%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 49.6%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot y\right) \cdot \left(y3 \cdot y5\right)\right)} \]

      2. neg-mul-1 49.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y\right)} \cdot \left(y3 \cdot y5\right)\right) \]

   10. Simplified 49.6%

       \[\leadsto a \cdot \color{blue}{\left(\left(-y\right) \cdot \left(y3 \cdot y5\right)\right)} \]

   if -4.0999999999999998e76 < y3 < 1.28e-11

   1. Initial program 35.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around inf 43.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. sub-neg 43.8%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. +-commutative 43.8%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. mul-1-neg 43.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. unsub-neg 43.8%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 43.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 43.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. mul-1-neg 43.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(-\color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. remove-double-neg 43.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \color{blue}{y5 \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. *-commutative 43.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 43.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in b around inf 31.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if 1.28e-11 < y3 < 3.5500000000000001e103

   1. Initial program 27.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y2 around inf 46.3%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 46.3%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(y1 \cdot y4 + \left(-y0 \cdot y5\right)\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. +-commutative 46.3%

         \[\leadsto y2 \cdot \left(\left(k \cdot \color{blue}{\left(\left(-y0 \cdot y5\right) + y1 \cdot y4\right)} + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. mul-1-neg 46.3%

         \[\leadsto y2 \cdot \left(\left(k \cdot \left(\color{blue}{-1 \cdot \left(y0 \cdot y5\right)} + y1 \cdot y4\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      4. fma-def 46.3%

         \[\leadsto y2 \cdot \left(\color{blue}{\mathsf{fma}\left(k, -1 \cdot \left(y0 \cdot y5\right) + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      5. mul-1-neg 46.3%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{\left(-y0 \cdot y5\right)} + y1 \cdot y4, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      6. +-commutative 46.3%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 + \left(-y0 \cdot y5\right)}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      7. sub-neg 46.3%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, \color{blue}{y1 \cdot y4 - y0 \cdot y5}, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      8. *-commutative 46.3%

         \[\leadsto y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot x}\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   4. Simplified 46.3%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, \left(c \cdot y0 - a \cdot y1\right) \cdot x\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in t around inf 47.4%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   6. Taylor expanded in a around inf 42.6%

      \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(a \cdot y5\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative 42.6%

         \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot a\right)}\right) \]

   8. Simplified 42.6%

      \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot a\right)}\right) \]

   if 3.5500000000000001e103 < y3

   1. Initial program 23.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y0 around inf 29.4%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. sub-neg 29.4%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \color{blue}{\left(j \cdot x + \left(-k \cdot z\right)\right)}\right) \]

      2. +-commutative 29.4%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \color{blue}{\left(\left(-k \cdot z\right) + j \cdot x\right)}\right) \]

      3. mul-1-neg 29.4%

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(\color{blue}{-1 \cdot \left(k \cdot z\right)} + j \cdot x\right)\right) \]

      4. +-commutative 29.4%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      5. mul-1-neg 29.4%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      6. unsub-neg 29.4%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      7. *-commutative 29.4%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

      8. *-commutative 29.4%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right) \]

   4. Simplified 29.4%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   5. Taylor expanded in j around -inf 37.9%

      \[\leadsto y0 \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 37.9%

         \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)}\right) \]

      2. mul-1-neg 37.9%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right)\right) \]

      3. unsub-neg 37.9%

         \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   7. Simplified 37.9%

      \[\leadsto y0 \cdot \color{blue}{\left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]

   8. Taylor expanded in y3 around inf 32.5%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 36.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -4.1 \cdot 10^{+76}:\\ \;\;\;\;a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 1.28 \cdot 10^{-11}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y3 \leq 3.55 \cdot 10^{+103}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \end{array} \]

Alternative 34: 22.6% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+45} \lor \neg \left(y \leq 5.5 \cdot 10^{+113}\right):\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y -5.4e+45) (not (<= y 5.5e+113)))
   (* a (* (* x y) b))
   (* a (* t (* y2 y5)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y <= -5.4e+45) || !(y <= 5.5e+113)) {
		tmp = a * ((x * y) * b);
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y <= (-5.4d+45)) .or. (.not. (y <= 5.5d+113))) then
        tmp = a * ((x * y) * b)
    else
        tmp = a * (t * (y2 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y <= -5.4e+45) || !(y <= 5.5e+113)) {
		tmp = a * ((x * y) * b);
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y <= -5.4e+45) or not (y <= 5.5e+113):
		tmp = a * ((x * y) * b)
	else:
		tmp = a * (t * (y2 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y <= -5.4e+45) || !(y <= 5.5e+113))
		tmp = Float64(a * Float64(Float64(x * y) * b));
	else
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y <= -5.4e+45) || ~((y <= 5.5e+113)))
		tmp = a * ((x * y) * b);
	else
		tmp = a * (t * (y2 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y, -5.4e+45], N[Not[LessEqual[y, 5.5e+113]], $MachinePrecision]], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.39999999999999968e45 or 5.5000000000000001e113 < y

   1. Initial program 24.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in a around inf 40.7%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. sub-neg 40.7%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. +-commutative 40.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. mul-1-neg 40.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. unsub-neg 40.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. *-commutative 40.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. *-commutative 40.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. mul-1-neg 40.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(-\color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. remove-double-neg 40.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \color{blue}{y5 \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. *-commutative 40.7%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 40.7%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y1 around 0 45.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in x around inf 39.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

   if -5.39999999999999968e45 < y < 5.5000000000000001e113

   1. Initial program 33.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in j around inf 31.6%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 31.6%

         \[\leadsto \left(\left(\color{blue}{\left(-j \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. associate-*r* 32.2%

         \[\leadsto \left(\left(\left(-\color{blue}{\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Simplified 32.2%

      \[\leadsto \left(\left(\color{blue}{\left(-\left(j \cdot x\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in a around inf 27.5%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 27.5%

         \[\leadsto a \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 27.5%

         \[\leadsto a \cdot \left(y5 \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 27.5%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y2 around inf 23.3%

      \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(y2 \cdot y5\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+45} \lor \neg \left(y \leq 5.5 \cdot 10^{+113}\right):\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]

Alternative 35: 17.3% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(\left(x \cdot y\right) \cdot b\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* (* x y) b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * ((x * y) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * ((x * y) * b)

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(Float64(x * y) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * ((x * y) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 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 a around inf 40.7%

   \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
3. Step-by-step derivation

   1. sub-neg 40.7%

      \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. +-commutative 40.7%

      \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. mul-1-neg 40.7%

      \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. unsub-neg 40.7%

      \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. *-commutative 40.7%

      \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. *-commutative 40.7%

      \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(--1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   7. mul-1-neg 40.7%

      \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \left(-\color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   8. remove-double-neg 40.7%

      \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + \color{blue}{y5 \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   9. *-commutative 40.7%

      \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

4. Simplified 40.7%

   \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

5. Taylor expanded in y1 around 0 42.0%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

6. Taylor expanded in x around inf 19.7%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

7. Final simplification 19.7%

   \[\leadsto a \cdot \left(\left(x \cdot y\right) \cdot b\right) \]

Developer target: 27.4% 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 2023271 
(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)))))