Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.1% → 41.5%

Time: 1.7min

Alternatives: 40

Speedup: 3.7×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 30.1% 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: 41.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot y4 - y0 \cdot y5\\ t_2 := y \cdot k - t \cdot j\\ t_3 := t \cdot y2 - y \cdot y3\\ t_4 := c \cdot y0 - a \cdot y1\\ t_5 := a \cdot y5 - c \cdot y4\\ t_6 := y2 \cdot \left(\left(x \cdot t_4 + k \cdot t_1\right) + t \cdot t_5\right)\\ t_7 := k \cdot y2 - j \cdot y3\\ t_8 := x \cdot j - z \cdot k\\ t_9 := y1 \cdot \left(y4 \cdot t_7 + \left(i \cdot t_8 + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ t_10 := z \cdot t - x \cdot y\\ \mathbf{if}\;y2 \leq -2.15 \cdot 10^{+14}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y2 \leq -2.22 \cdot 10^{-82}:\\ \;\;\;\;y5 \cdot \left(i \cdot t_2 + \left(a \cdot t_3 + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -2.9 \cdot 10^{-166}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot t_1 - z \cdot \left(i \cdot y1 - b \cdot y0\right)\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -2.35 \cdot 10^{-235}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;y2 \leq 1.4 \cdot 10^{-299}:\\ \;\;\;\;i \cdot \left(y1 \cdot t_8 + \left(y5 \cdot t_2 + c \cdot t_10\right)\right)\\ \mathbf{elif}\;y2 \leq 4.1 \cdot 10^{-212}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;y2 \leq 3.3 \cdot 10^{-117}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 8 \cdot 10^{-17}:\\ \;\;\;\;c \cdot \left(\left(i \cdot t_10 + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 1.12 \cdot 10^{+67}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot t_4 + \left(t_7 \cdot t_1 + t_3 \cdot t_5\right)\\ \mathbf{elif}\;y2 \leq 4.7 \cdot 10^{+111}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 1.4 \cdot 10^{+211}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y2 \cdot t_5\right)\\ \end{array} \end{array} \]

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 (- (* y k) (* t j)))
        (t_3 (- (* t y2) (* y y3)))
        (t_4 (- (* c y0) (* a y1)))
        (t_5 (- (* a y5) (* c y4)))
        (t_6 (* y2 (+ (+ (* x t_4) (* k t_1)) (* t t_5))))
        (t_7 (- (* k y2) (* j y3)))
        (t_8 (- (* x j) (* z k)))
        (t_9 (* y1 (+ (* y4 t_7) (+ (* i t_8) (* a (- (* z y3) (* x y2)))))))
        (t_10 (- (* z t) (* x y))))
   (if (<= y2 -2.15e+14)
     t_6
     (if (<= y2 -2.22e-82)
       (* y5 (+ (* i t_2) (+ (* a t_3) (* y0 (- (* j y3) (* k y2))))))
       (if (<= y2 -2.9e-166)
         (*
          k
          (-
           (- (* y2 t_1) (* z (- (* i y1) (* b y0))))
           (* y (- (* b y4) (* i y5)))))
         (if (<= y2 -2.35e-235)
           t_9
           (if (<= y2 1.4e-299)
             (* i (+ (* y1 t_8) (+ (* y5 t_2) (* c t_10))))
             (if (<= y2 4.1e-212)
               t_9
               (if (<= y2 3.3e-117)
                 (* y0 (* j (- (* y3 y5) (* x b))))
                 (if (<= y2 8e-17)
                   (*
                    c
                    (+
                     (+ (* i t_10) (* y0 (- (* x y2) (* z y3))))
                     (* y4 (- (* y y3) (* t y2)))))
                   (if (<= y2 1.12e+67)
                     (+ (* (* x y2) t_4) (+ (* t_7 t_1) (* t_3 t_5)))
                     (if (<= y2 4.7e+111)
                       (* y4 (* t (- (* b j) (* c y2))))
                       (if (<= y2 1.4e+211) t_6 (* t (* y2 t_5)))))))))))))))

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 = (y * k) - (t * j);
	double t_3 = (t * y2) - (y * y3);
	double t_4 = (c * y0) - (a * y1);
	double t_5 = (a * y5) - (c * y4);
	double t_6 = y2 * (((x * t_4) + (k * t_1)) + (t * t_5));
	double t_7 = (k * y2) - (j * y3);
	double t_8 = (x * j) - (z * k);
	double t_9 = y1 * ((y4 * t_7) + ((i * t_8) + (a * ((z * y3) - (x * y2)))));
	double t_10 = (z * t) - (x * y);
	double tmp;
	if (y2 <= -2.15e+14) {
		tmp = t_6;
	} else if (y2 <= -2.22e-82) {
		tmp = y5 * ((i * t_2) + ((a * t_3) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y2 <= -2.9e-166) {
		tmp = k * (((y2 * t_1) - (z * ((i * y1) - (b * y0)))) - (y * ((b * y4) - (i * y5))));
	} else if (y2 <= -2.35e-235) {
		tmp = t_9;
	} else if (y2 <= 1.4e-299) {
		tmp = i * ((y1 * t_8) + ((y5 * t_2) + (c * t_10)));
	} else if (y2 <= 4.1e-212) {
		tmp = t_9;
	} else if (y2 <= 3.3e-117) {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	} else if (y2 <= 8e-17) {
		tmp = c * (((i * t_10) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y2 <= 1.12e+67) {
		tmp = ((x * y2) * t_4) + ((t_7 * t_1) + (t_3 * t_5));
	} else if (y2 <= 4.7e+111) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (y2 <= 1.4e+211) {
		tmp = t_6;
	} else {
		tmp = t * (y2 * t_5);
	}
	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_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 = (y1 * y4) - (y0 * y5)
    t_2 = (y * k) - (t * j)
    t_3 = (t * y2) - (y * y3)
    t_4 = (c * y0) - (a * y1)
    t_5 = (a * y5) - (c * y4)
    t_6 = y2 * (((x * t_4) + (k * t_1)) + (t * t_5))
    t_7 = (k * y2) - (j * y3)
    t_8 = (x * j) - (z * k)
    t_9 = y1 * ((y4 * t_7) + ((i * t_8) + (a * ((z * y3) - (x * y2)))))
    t_10 = (z * t) - (x * y)
    if (y2 <= (-2.15d+14)) then
        tmp = t_6
    else if (y2 <= (-2.22d-82)) then
        tmp = y5 * ((i * t_2) + ((a * t_3) + (y0 * ((j * y3) - (k * y2)))))
    else if (y2 <= (-2.9d-166)) then
        tmp = k * (((y2 * t_1) - (z * ((i * y1) - (b * y0)))) - (y * ((b * y4) - (i * y5))))
    else if (y2 <= (-2.35d-235)) then
        tmp = t_9
    else if (y2 <= 1.4d-299) then
        tmp = i * ((y1 * t_8) + ((y5 * t_2) + (c * t_10)))
    else if (y2 <= 4.1d-212) then
        tmp = t_9
    else if (y2 <= 3.3d-117) then
        tmp = y0 * (j * ((y3 * y5) - (x * b)))
    else if (y2 <= 8d-17) then
        tmp = c * (((i * t_10) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
    else if (y2 <= 1.12d+67) then
        tmp = ((x * y2) * t_4) + ((t_7 * t_1) + (t_3 * t_5))
    else if (y2 <= 4.7d+111) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    else if (y2 <= 1.4d+211) then
        tmp = t_6
    else
        tmp = t * (y2 * t_5)
    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 = (y * k) - (t * j);
	double t_3 = (t * y2) - (y * y3);
	double t_4 = (c * y0) - (a * y1);
	double t_5 = (a * y5) - (c * y4);
	double t_6 = y2 * (((x * t_4) + (k * t_1)) + (t * t_5));
	double t_7 = (k * y2) - (j * y3);
	double t_8 = (x * j) - (z * k);
	double t_9 = y1 * ((y4 * t_7) + ((i * t_8) + (a * ((z * y3) - (x * y2)))));
	double t_10 = (z * t) - (x * y);
	double tmp;
	if (y2 <= -2.15e+14) {
		tmp = t_6;
	} else if (y2 <= -2.22e-82) {
		tmp = y5 * ((i * t_2) + ((a * t_3) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y2 <= -2.9e-166) {
		tmp = k * (((y2 * t_1) - (z * ((i * y1) - (b * y0)))) - (y * ((b * y4) - (i * y5))));
	} else if (y2 <= -2.35e-235) {
		tmp = t_9;
	} else if (y2 <= 1.4e-299) {
		tmp = i * ((y1 * t_8) + ((y5 * t_2) + (c * t_10)));
	} else if (y2 <= 4.1e-212) {
		tmp = t_9;
	} else if (y2 <= 3.3e-117) {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	} else if (y2 <= 8e-17) {
		tmp = c * (((i * t_10) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y2 <= 1.12e+67) {
		tmp = ((x * y2) * t_4) + ((t_7 * t_1) + (t_3 * t_5));
	} else if (y2 <= 4.7e+111) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (y2 <= 1.4e+211) {
		tmp = t_6;
	} else {
		tmp = t * (y2 * t_5);
	}
	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 = (y * k) - (t * j)
	t_3 = (t * y2) - (y * y3)
	t_4 = (c * y0) - (a * y1)
	t_5 = (a * y5) - (c * y4)
	t_6 = y2 * (((x * t_4) + (k * t_1)) + (t * t_5))
	t_7 = (k * y2) - (j * y3)
	t_8 = (x * j) - (z * k)
	t_9 = y1 * ((y4 * t_7) + ((i * t_8) + (a * ((z * y3) - (x * y2)))))
	t_10 = (z * t) - (x * y)
	tmp = 0
	if y2 <= -2.15e+14:
		tmp = t_6
	elif y2 <= -2.22e-82:
		tmp = y5 * ((i * t_2) + ((a * t_3) + (y0 * ((j * y3) - (k * y2)))))
	elif y2 <= -2.9e-166:
		tmp = k * (((y2 * t_1) - (z * ((i * y1) - (b * y0)))) - (y * ((b * y4) - (i * y5))))
	elif y2 <= -2.35e-235:
		tmp = t_9
	elif y2 <= 1.4e-299:
		tmp = i * ((y1 * t_8) + ((y5 * t_2) + (c * t_10)))
	elif y2 <= 4.1e-212:
		tmp = t_9
	elif y2 <= 3.3e-117:
		tmp = y0 * (j * ((y3 * y5) - (x * b)))
	elif y2 <= 8e-17:
		tmp = c * (((i * t_10) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
	elif y2 <= 1.12e+67:
		tmp = ((x * y2) * t_4) + ((t_7 * t_1) + (t_3 * t_5))
	elif y2 <= 4.7e+111:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	elif y2 <= 1.4e+211:
		tmp = t_6
	else:
		tmp = t * (y2 * t_5)
	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(y * k) - Float64(t * j))
	t_3 = Float64(Float64(t * y2) - Float64(y * y3))
	t_4 = Float64(Float64(c * y0) - Float64(a * y1))
	t_5 = Float64(Float64(a * y5) - Float64(c * y4))
	t_6 = Float64(y2 * Float64(Float64(Float64(x * t_4) + Float64(k * t_1)) + Float64(t * t_5)))
	t_7 = Float64(Float64(k * y2) - Float64(j * y3))
	t_8 = Float64(Float64(x * j) - Float64(z * k))
	t_9 = Float64(y1 * Float64(Float64(y4 * t_7) + Float64(Float64(i * t_8) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2))))))
	t_10 = Float64(Float64(z * t) - Float64(x * y))
	tmp = 0.0
	if (y2 <= -2.15e+14)
		tmp = t_6;
	elseif (y2 <= -2.22e-82)
		tmp = Float64(y5 * Float64(Float64(i * t_2) + Float64(Float64(a * t_3) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))));
	elseif (y2 <= -2.9e-166)
		tmp = Float64(k * Float64(Float64(Float64(y2 * t_1) - Float64(z * Float64(Float64(i * y1) - Float64(b * y0)))) - Float64(y * Float64(Float64(b * y4) - Float64(i * y5)))));
	elseif (y2 <= -2.35e-235)
		tmp = t_9;
	elseif (y2 <= 1.4e-299)
		tmp = Float64(i * Float64(Float64(y1 * t_8) + Float64(Float64(y5 * t_2) + Float64(c * t_10))));
	elseif (y2 <= 4.1e-212)
		tmp = t_9;
	elseif (y2 <= 3.3e-117)
		tmp = Float64(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (y2 <= 8e-17)
		tmp = Float64(c * Float64(Float64(Float64(i * t_10) + Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y2 <= 1.12e+67)
		tmp = Float64(Float64(Float64(x * y2) * t_4) + Float64(Float64(t_7 * t_1) + Float64(t_3 * t_5)));
	elseif (y2 <= 4.7e+111)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (y2 <= 1.4e+211)
		tmp = t_6;
	else
		tmp = Float64(t * Float64(y2 * t_5));
	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 = (y * k) - (t * j);
	t_3 = (t * y2) - (y * y3);
	t_4 = (c * y0) - (a * y1);
	t_5 = (a * y5) - (c * y4);
	t_6 = y2 * (((x * t_4) + (k * t_1)) + (t * t_5));
	t_7 = (k * y2) - (j * y3);
	t_8 = (x * j) - (z * k);
	t_9 = y1 * ((y4 * t_7) + ((i * t_8) + (a * ((z * y3) - (x * y2)))));
	t_10 = (z * t) - (x * y);
	tmp = 0.0;
	if (y2 <= -2.15e+14)
		tmp = t_6;
	elseif (y2 <= -2.22e-82)
		tmp = y5 * ((i * t_2) + ((a * t_3) + (y0 * ((j * y3) - (k * y2)))));
	elseif (y2 <= -2.9e-166)
		tmp = k * (((y2 * t_1) - (z * ((i * y1) - (b * y0)))) - (y * ((b * y4) - (i * y5))));
	elseif (y2 <= -2.35e-235)
		tmp = t_9;
	elseif (y2 <= 1.4e-299)
		tmp = i * ((y1 * t_8) + ((y5 * t_2) + (c * t_10)));
	elseif (y2 <= 4.1e-212)
		tmp = t_9;
	elseif (y2 <= 3.3e-117)
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	elseif (y2 <= 8e-17)
		tmp = c * (((i * t_10) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (y2 <= 1.12e+67)
		tmp = ((x * y2) * t_4) + ((t_7 * t_1) + (t_3 * t_5));
	elseif (y2 <= 4.7e+111)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	elseif (y2 <= 1.4e+211)
		tmp = t_6;
	else
		tmp = t * (y2 * t_5);
	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[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(y2 * N[(N[(N[(x * t$95$4), $MachinePrecision] + N[(k * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(y1 * N[(N[(y4 * t$95$7), $MachinePrecision] + N[(N[(i * t$95$8), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -2.15e+14], t$95$6, If[LessEqual[y2, -2.22e-82], N[(y5 * N[(N[(i * t$95$2), $MachinePrecision] + N[(N[(a * t$95$3), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.9e-166], N[(k * N[(N[(N[(y2 * t$95$1), $MachinePrecision] - N[(z * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.35e-235], t$95$9, If[LessEqual[y2, 1.4e-299], N[(i * N[(N[(y1 * t$95$8), $MachinePrecision] + N[(N[(y5 * t$95$2), $MachinePrecision] + N[(c * t$95$10), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.1e-212], t$95$9, If[LessEqual[y2, 3.3e-117], N[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 8e-17], N[(c * N[(N[(N[(i * t$95$10), $MachinePrecision] + N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.12e+67], N[(N[(N[(x * y2), $MachinePrecision] * t$95$4), $MachinePrecision] + N[(N[(t$95$7 * t$95$1), $MachinePrecision] + N[(t$95$3 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.7e+111], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.4e+211], t$95$6, N[(t * N[(y2 * t$95$5), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y2 < -2.15e14 or 4.70000000000000008e111 < y2 < 1.4e211

   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. Step-by-step derivation

      1. associate-+l- 25.0%

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

   3. Simplified 25.0%

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

   4. Taylor expanded in y2 around inf 66.9%

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

   if -2.15e14 < y2 < -2.22000000000000011e-82

   1. Initial program 14.3%

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

      1. associate-+l- 14.3%

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

   3. Simplified 14.3%

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

   4. Taylor expanded in y5 around -inf 60.6%

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

      1. mul-1-neg 60.6%

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

      2. associate--l+ 60.6%

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

      3. *-commutative 60.6%

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

   6. Simplified 60.6%

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

   if -2.22000000000000011e-82 < y2 < -2.9e-166

   1. Initial program 18.4%

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

      1. +-commutative 18.4%

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

      2. fma-def 18.4%

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

      3. *-commutative 18.4%

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

      4. *-commutative 18.4%

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

   3. Simplified 24.3%

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

   4. Taylor expanded in k around inf 65.2%

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

   if -2.9e-166 < y2 < -2.35e-235 or 1.4000000000000001e-299 < y2 < 4.10000000000000014e-212

   1. Initial program 44.6%

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

      1. associate-+l- 44.6%

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

   3. Simplified 44.6%

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

   4. Taylor expanded in y1 around inf 60.9%

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

      1. associate--l+ 60.9%

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

      2. *-commutative 60.9%

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

      3. *-commutative 60.9%

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

      4. distribute-lft-out-- 60.9%

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

      5. *-commutative 60.9%

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

   6. Simplified 60.9%

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

   if -2.35e-235 < y2 < 1.4000000000000001e-299

   1. Initial program 26.6%

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

      1. associate-+l- 26.6%

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

   3. Simplified 26.6%

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

   4. Taylor expanded in i around -inf 58.5%

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

   if 4.10000000000000014e-212 < y2 < 3.30000000000000015e-117

   1. Initial program 47.3%

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

      1. +-commutative 47.3%

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

      2. fma-def 47.3%

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

      3. *-commutative 47.3%

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

      4. *-commutative 47.3%

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

   3. Simplified 47.3%

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

   4. Taylor expanded in j around inf 48.2%

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

   5. Taylor expanded in y0 around inf 63.1%

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

   if 3.30000000000000015e-117 < y2 < 8.00000000000000057e-17

   1. Initial program 13.6%

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

      1. associate-+l- 13.6%

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

   3. Simplified 13.6%

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

   4. Taylor expanded in c around inf 69.1%

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

   if 8.00000000000000057e-17 < y2 < 1.12e67

   1. Initial program 30.8%

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

      1. associate-+l- 30.8%

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

   3. Simplified 30.8%

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

   4. Taylor expanded in y2 around inf 61.6%

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

      1. *-commutative 61.6%

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

      2. *-commutative 61.6%

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

      3. *-commutative 61.6%

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

   6. Simplified 61.6%

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

   if 1.12e67 < y2 < 4.70000000000000008e111

   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. Step-by-step derivation

      1. associate-+l- 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in y4 around inf 33.8%

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

   5. Taylor expanded in t around inf 83.8%

      \[\leadsto y4 \cdot \color{blue}{\left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 83.8%

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

      2. *-commutative 83.8%

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

   7. Simplified 83.8%

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

   if 1.4e211 < y2

   1. Initial program 9.5%

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

      1. associate-+l- 9.5%

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

   3. Simplified 9.5%

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

   4. Taylor expanded in y2 around inf 52.7%

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

   5. Taylor expanded in t around -inf 71.8%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 71.8%

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

      2. neg-mul-1 71.8%

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

      3. *-commutative 71.8%

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

   7. Simplified 71.8%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(y2 \cdot \left(y4 \cdot c - a \cdot y5\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2.15 \cdot 10^{+14}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -2.22 \cdot 10^{-82}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -2.9 \cdot 10^{-166}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - z \cdot \left(i \cdot y1 - b \cdot y0\right)\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -2.35 \cdot 10^{-235}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.4 \cdot 10^{-299}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 4.1 \cdot 10^{-212}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 3.3 \cdot 10^{-117}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 8 \cdot 10^{-17}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 1.12 \cdot 10^{+67}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 4.7 \cdot 10^{+111}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 1.4 \cdot 10^{+211}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \]

Alternative 2: 53.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 86.1%

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

   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. Step-by-step derivation

      1. +-commutative 0.0%

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

      2. fma-def 3.3%

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

      3. *-commutative 3.3%

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

      4. *-commutative 3.3%

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

   3. Simplified 9.4%

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

   4. Taylor expanded in y0 around inf 39.1%

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

      1. *-commutative 39.1%

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

      2. mul-1-neg 39.1%

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

      3. *-commutative 39.1%

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

      4. *-commutative 39.1%

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

   6. Simplified 39.1%

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

4. Final simplification 53.1%

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

Alternative 3: 40.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot y4 - y0 \cdot y5\\ t_2 := y \cdot k - t \cdot j\\ t_3 := a \cdot y5 - c \cdot y4\\ t_4 := y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot t_1\right) + t \cdot t_3\right)\\ t_5 := i \cdot y1 - b \cdot y0\\ t_6 := x \cdot j - z \cdot k\\ t_7 := y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(i \cdot t_6 + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ t_8 := z \cdot t - x \cdot y\\ \mathbf{if}\;y2 \leq -2.4 \cdot 10^{+19}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y2 \leq -3.3 \cdot 10^{-83}:\\ \;\;\;\;y5 \cdot \left(i \cdot t_2 + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -4.2 \cdot 10^{-166}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot t_1 - z \cdot t_5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -1.75 \cdot 10^{-238}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;y2 \leq 8 \cdot 10^{-300}:\\ \;\;\;\;i \cdot \left(y1 \cdot t_6 + \left(y5 \cdot t_2 + c \cdot t_8\right)\right)\\ \mathbf{elif}\;y2 \leq 7.5 \cdot 10^{-212}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;y2 \leq 5.5 \cdot 10^{-117}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 5.5 \cdot 10^{-6}:\\ \;\;\;\;c \cdot \left(\left(i \cdot t_8 + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 9 \cdot 10^{+51}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y2 \leq 4.7 \cdot 10^{+111}:\\ \;\;\;\;j \cdot \left(x \cdot t_5\right)\\ \mathbf{elif}\;y2 \leq 1.9 \cdot 10^{+211}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y2 \cdot t_3\right)\\ \end{array} \end{array} \]

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 (- (* y k) (* t j)))
        (t_3 (- (* a y5) (* c y4)))
        (t_4 (* y2 (+ (+ (* x (- (* c y0) (* a y1))) (* k t_1)) (* t t_3))))
        (t_5 (- (* i y1) (* b y0)))
        (t_6 (- (* x j) (* z k)))
        (t_7
         (*
          y1
          (+
           (* y4 (- (* k y2) (* j y3)))
           (+ (* i t_6) (* a (- (* z y3) (* x y2)))))))
        (t_8 (- (* z t) (* x y))))
   (if (<= y2 -2.4e+19)
     t_4
     (if (<= y2 -3.3e-83)
       (*
        y5
        (+
         (* i t_2)
         (+ (* a (- (* t y2) (* y y3))) (* y0 (- (* j y3) (* k y2))))))
       (if (<= y2 -4.2e-166)
         (* k (- (- (* y2 t_1) (* z t_5)) (* y (- (* b y4) (* i y5)))))
         (if (<= y2 -1.75e-238)
           t_7
           (if (<= y2 8e-300)
             (* i (+ (* y1 t_6) (+ (* y5 t_2) (* c t_8))))
             (if (<= y2 7.5e-212)
               t_7
               (if (<= y2 5.5e-117)
                 (* y0 (* j (- (* y3 y5) (* x b))))
                 (if (<= y2 5.5e-6)
                   (*
                    c
                    (+
                     (+ (* i t_8) (* y0 (- (* x y2) (* z y3))))
                     (* y4 (- (* y y3) (* t y2)))))
                   (if (<= y2 9e+51)
                     t_4
                     (if (<= y2 4.7e+111)
                       (* j (* x t_5))
                       (if (<= y2 1.9e+211) t_4 (* t (* y2 t_3)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double t_2 = (y * k) - (t * j);
	double t_3 = (a * y5) - (c * y4);
	double t_4 = y2 * (((x * ((c * y0) - (a * y1))) + (k * t_1)) + (t * t_3));
	double t_5 = (i * y1) - (b * y0);
	double t_6 = (x * j) - (z * k);
	double t_7 = y1 * ((y4 * ((k * y2) - (j * y3))) + ((i * t_6) + (a * ((z * y3) - (x * y2)))));
	double t_8 = (z * t) - (x * y);
	double tmp;
	if (y2 <= -2.4e+19) {
		tmp = t_4;
	} else if (y2 <= -3.3e-83) {
		tmp = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y2 <= -4.2e-166) {
		tmp = k * (((y2 * t_1) - (z * t_5)) - (y * ((b * y4) - (i * y5))));
	} else if (y2 <= -1.75e-238) {
		tmp = t_7;
	} else if (y2 <= 8e-300) {
		tmp = i * ((y1 * t_6) + ((y5 * t_2) + (c * t_8)));
	} else if (y2 <= 7.5e-212) {
		tmp = t_7;
	} else if (y2 <= 5.5e-117) {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	} else if (y2 <= 5.5e-6) {
		tmp = c * (((i * t_8) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y2 <= 9e+51) {
		tmp = t_4;
	} else if (y2 <= 4.7e+111) {
		tmp = j * (x * t_5);
	} else if (y2 <= 1.9e+211) {
		tmp = t_4;
	} else {
		tmp = t * (y2 * t_3);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_1 = (y1 * y4) - (y0 * y5)
    t_2 = (y * k) - (t * j)
    t_3 = (a * y5) - (c * y4)
    t_4 = y2 * (((x * ((c * y0) - (a * y1))) + (k * t_1)) + (t * t_3))
    t_5 = (i * y1) - (b * y0)
    t_6 = (x * j) - (z * k)
    t_7 = y1 * ((y4 * ((k * y2) - (j * y3))) + ((i * t_6) + (a * ((z * y3) - (x * y2)))))
    t_8 = (z * t) - (x * y)
    if (y2 <= (-2.4d+19)) then
        tmp = t_4
    else if (y2 <= (-3.3d-83)) then
        tmp = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))))
    else if (y2 <= (-4.2d-166)) then
        tmp = k * (((y2 * t_1) - (z * t_5)) - (y * ((b * y4) - (i * y5))))
    else if (y2 <= (-1.75d-238)) then
        tmp = t_7
    else if (y2 <= 8d-300) then
        tmp = i * ((y1 * t_6) + ((y5 * t_2) + (c * t_8)))
    else if (y2 <= 7.5d-212) then
        tmp = t_7
    else if (y2 <= 5.5d-117) then
        tmp = y0 * (j * ((y3 * y5) - (x * b)))
    else if (y2 <= 5.5d-6) then
        tmp = c * (((i * t_8) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
    else if (y2 <= 9d+51) then
        tmp = t_4
    else if (y2 <= 4.7d+111) then
        tmp = j * (x * t_5)
    else if (y2 <= 1.9d+211) then
        tmp = t_4
    else
        tmp = t * (y2 * t_3)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double t_2 = (y * k) - (t * j);
	double t_3 = (a * y5) - (c * y4);
	double t_4 = y2 * (((x * ((c * y0) - (a * y1))) + (k * t_1)) + (t * t_3));
	double t_5 = (i * y1) - (b * y0);
	double t_6 = (x * j) - (z * k);
	double t_7 = y1 * ((y4 * ((k * y2) - (j * y3))) + ((i * t_6) + (a * ((z * y3) - (x * y2)))));
	double t_8 = (z * t) - (x * y);
	double tmp;
	if (y2 <= -2.4e+19) {
		tmp = t_4;
	} else if (y2 <= -3.3e-83) {
		tmp = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y2 <= -4.2e-166) {
		tmp = k * (((y2 * t_1) - (z * t_5)) - (y * ((b * y4) - (i * y5))));
	} else if (y2 <= -1.75e-238) {
		tmp = t_7;
	} else if (y2 <= 8e-300) {
		tmp = i * ((y1 * t_6) + ((y5 * t_2) + (c * t_8)));
	} else if (y2 <= 7.5e-212) {
		tmp = t_7;
	} else if (y2 <= 5.5e-117) {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	} else if (y2 <= 5.5e-6) {
		tmp = c * (((i * t_8) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y2 <= 9e+51) {
		tmp = t_4;
	} else if (y2 <= 4.7e+111) {
		tmp = j * (x * t_5);
	} else if (y2 <= 1.9e+211) {
		tmp = t_4;
	} else {
		tmp = t * (y2 * t_3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y1 * y4) - (y0 * y5)
	t_2 = (y * k) - (t * j)
	t_3 = (a * y5) - (c * y4)
	t_4 = y2 * (((x * ((c * y0) - (a * y1))) + (k * t_1)) + (t * t_3))
	t_5 = (i * y1) - (b * y0)
	t_6 = (x * j) - (z * k)
	t_7 = y1 * ((y4 * ((k * y2) - (j * y3))) + ((i * t_6) + (a * ((z * y3) - (x * y2)))))
	t_8 = (z * t) - (x * y)
	tmp = 0
	if y2 <= -2.4e+19:
		tmp = t_4
	elif y2 <= -3.3e-83:
		tmp = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))))
	elif y2 <= -4.2e-166:
		tmp = k * (((y2 * t_1) - (z * t_5)) - (y * ((b * y4) - (i * y5))))
	elif y2 <= -1.75e-238:
		tmp = t_7
	elif y2 <= 8e-300:
		tmp = i * ((y1 * t_6) + ((y5 * t_2) + (c * t_8)))
	elif y2 <= 7.5e-212:
		tmp = t_7
	elif y2 <= 5.5e-117:
		tmp = y0 * (j * ((y3 * y5) - (x * b)))
	elif y2 <= 5.5e-6:
		tmp = c * (((i * t_8) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
	elif y2 <= 9e+51:
		tmp = t_4
	elif y2 <= 4.7e+111:
		tmp = j * (x * t_5)
	elif y2 <= 1.9e+211:
		tmp = t_4
	else:
		tmp = t * (y2 * t_3)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_2 = Float64(Float64(y * k) - Float64(t * j))
	t_3 = Float64(Float64(a * y5) - Float64(c * y4))
	t_4 = Float64(y2 * Float64(Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(k * t_1)) + Float64(t * t_3)))
	t_5 = Float64(Float64(i * y1) - Float64(b * y0))
	t_6 = Float64(Float64(x * j) - Float64(z * k))
	t_7 = Float64(y1 * Float64(Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))) + Float64(Float64(i * t_6) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2))))))
	t_8 = Float64(Float64(z * t) - Float64(x * y))
	tmp = 0.0
	if (y2 <= -2.4e+19)
		tmp = t_4;
	elseif (y2 <= -3.3e-83)
		tmp = Float64(y5 * Float64(Float64(i * t_2) + Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))));
	elseif (y2 <= -4.2e-166)
		tmp = Float64(k * Float64(Float64(Float64(y2 * t_1) - Float64(z * t_5)) - Float64(y * Float64(Float64(b * y4) - Float64(i * y5)))));
	elseif (y2 <= -1.75e-238)
		tmp = t_7;
	elseif (y2 <= 8e-300)
		tmp = Float64(i * Float64(Float64(y1 * t_6) + Float64(Float64(y5 * t_2) + Float64(c * t_8))));
	elseif (y2 <= 7.5e-212)
		tmp = t_7;
	elseif (y2 <= 5.5e-117)
		tmp = Float64(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (y2 <= 5.5e-6)
		tmp = Float64(c * Float64(Float64(Float64(i * t_8) + Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y2 <= 9e+51)
		tmp = t_4;
	elseif (y2 <= 4.7e+111)
		tmp = Float64(j * Float64(x * t_5));
	elseif (y2 <= 1.9e+211)
		tmp = t_4;
	else
		tmp = Float64(t * Float64(y2 * t_3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y1 * y4) - (y0 * y5);
	t_2 = (y * k) - (t * j);
	t_3 = (a * y5) - (c * y4);
	t_4 = y2 * (((x * ((c * y0) - (a * y1))) + (k * t_1)) + (t * t_3));
	t_5 = (i * y1) - (b * y0);
	t_6 = (x * j) - (z * k);
	t_7 = y1 * ((y4 * ((k * y2) - (j * y3))) + ((i * t_6) + (a * ((z * y3) - (x * y2)))));
	t_8 = (z * t) - (x * y);
	tmp = 0.0;
	if (y2 <= -2.4e+19)
		tmp = t_4;
	elseif (y2 <= -3.3e-83)
		tmp = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	elseif (y2 <= -4.2e-166)
		tmp = k * (((y2 * t_1) - (z * t_5)) - (y * ((b * y4) - (i * y5))));
	elseif (y2 <= -1.75e-238)
		tmp = t_7;
	elseif (y2 <= 8e-300)
		tmp = i * ((y1 * t_6) + ((y5 * t_2) + (c * t_8)));
	elseif (y2 <= 7.5e-212)
		tmp = t_7;
	elseif (y2 <= 5.5e-117)
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	elseif (y2 <= 5.5e-6)
		tmp = c * (((i * t_8) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (y2 <= 9e+51)
		tmp = t_4;
	elseif (y2 <= 4.7e+111)
		tmp = j * (x * t_5);
	elseif (y2 <= 1.9e+211)
		tmp = t_4;
	else
		tmp = t * (y2 * t_3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y2 * N[(N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(y1 * N[(N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * t$95$6), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -2.4e+19], t$95$4, If[LessEqual[y2, -3.3e-83], N[(y5 * N[(N[(i * t$95$2), $MachinePrecision] + N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -4.2e-166], N[(k * N[(N[(N[(y2 * t$95$1), $MachinePrecision] - N[(z * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.75e-238], t$95$7, If[LessEqual[y2, 8e-300], N[(i * N[(N[(y1 * t$95$6), $MachinePrecision] + N[(N[(y5 * t$95$2), $MachinePrecision] + N[(c * t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 7.5e-212], t$95$7, If[LessEqual[y2, 5.5e-117], N[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5.5e-6], N[(c * N[(N[(N[(i * t$95$8), $MachinePrecision] + N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 9e+51], t$95$4, If[LessEqual[y2, 4.7e+111], N[(j * N[(x * t$95$5), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.9e+211], t$95$4, N[(t * N[(y2 * t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y2 < -2.4e19 or 5.4999999999999999e-6 < y2 < 8.9999999999999999e51 or 4.70000000000000008e111 < y2 < 1.90000000000000008e211

   1. Initial program 24.0%

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

      1. associate-+l- 24.0%

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

   3. Simplified 24.0%

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

   4. Taylor expanded in y2 around inf 68.2%

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

   if -2.4e19 < y2 < -3.2999999999999999e-83

   1. Initial program 14.3%

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

      1. associate-+l- 14.3%

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

   3. Simplified 14.3%

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

   4. Taylor expanded in y5 around -inf 60.6%

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

      1. mul-1-neg 60.6%

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

      2. associate--l+ 60.6%

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

      3. *-commutative 60.6%

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

   6. Simplified 60.6%

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

   if -3.2999999999999999e-83 < y2 < -4.1999999999999999e-166

   1. Initial program 18.4%

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

      1. +-commutative 18.4%

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

      2. fma-def 18.4%

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

      3. *-commutative 18.4%

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

      4. *-commutative 18.4%

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

   3. Simplified 24.3%

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

   4. Taylor expanded in k around inf 65.2%

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

   if -4.1999999999999999e-166 < y2 < -1.74999999999999998e-238 or 8.0000000000000002e-300 < y2 < 7.50000000000000012e-212

   1. Initial program 44.6%

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

      1. associate-+l- 44.6%

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

   3. Simplified 44.6%

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

   4. Taylor expanded in y1 around inf 60.9%

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

      1. associate--l+ 60.9%

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

      2. *-commutative 60.9%

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

      3. *-commutative 60.9%

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

      4. distribute-lft-out-- 60.9%

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

      5. *-commutative 60.9%

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

   6. Simplified 60.9%

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

   if -1.74999999999999998e-238 < y2 < 8.0000000000000002e-300

   1. Initial program 26.6%

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

      1. associate-+l- 26.6%

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

   3. Simplified 26.6%

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

   4. Taylor expanded in i around -inf 58.5%

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

   if 7.50000000000000012e-212 < y2 < 5.50000000000000025e-117

   1. Initial program 47.3%

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

      1. +-commutative 47.3%

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

      2. fma-def 47.3%

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

      3. *-commutative 47.3%

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

      4. *-commutative 47.3%

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

   3. Simplified 47.3%

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

   4. Taylor expanded in j around inf 48.2%

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

   5. Taylor expanded in y0 around inf 63.1%

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

   if 5.50000000000000025e-117 < y2 < 5.4999999999999999e-6

   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. Step-by-step derivation

      1. associate-+l- 23.1%

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

   3. Simplified 23.1%

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

   4. Taylor expanded in c around inf 66.4%

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

   if 8.9999999999999999e51 < y2 < 4.70000000000000008e111

   1. Initial program 16.7%

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

      1. +-commutative 16.7%

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

      2. fma-def 25.0%

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

      3. *-commutative 25.0%

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

      4. *-commutative 25.0%

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

   3. Simplified 25.0%

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

   4. Taylor expanded in j around inf 42.0%

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

   5. Taylor expanded in x around inf 50.9%

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

   if 1.90000000000000008e211 < y2

   1. Initial program 9.5%

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

      1. associate-+l- 9.5%

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

   3. Simplified 9.5%

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

   4. Taylor expanded in y2 around inf 52.7%

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

   5. Taylor expanded in t around -inf 71.8%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 71.8%

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

      2. neg-mul-1 71.8%

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

      3. *-commutative 71.8%

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

   7. Simplified 71.8%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(y2 \cdot \left(y4 \cdot c - a \cdot y5\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2.4 \cdot 10^{+19}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -3.3 \cdot 10^{-83}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -4.2 \cdot 10^{-166}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - z \cdot \left(i \cdot y1 - b \cdot y0\right)\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -1.75 \cdot 10^{-238}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 8 \cdot 10^{-300}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 7.5 \cdot 10^{-212}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(i \cdot \left(x \cdot j - z \cdot k\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 5.5 \cdot 10^{-117}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 5.5 \cdot 10^{-6}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 9 \cdot 10^{+51}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 4.7 \cdot 10^{+111}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 1.9 \cdot 10^{+211}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \]

Alternative 4: 40.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_2 := c \cdot y0 - a \cdot y1\\ t_3 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_2\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;y4 \leq -1.85 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq -6.2 \cdot 10^{+108}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y4 \leq -5 \cdot 10^{+86}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq -9.8 \cdot 10^{-231}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_2 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 7.4 \cdot 10^{-260}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y4 \leq 5.2 \cdot 10^{-234}:\\ \;\;\;\;z \cdot \left(c \cdot \left(y0 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 2.2 \cdot 10^{-164}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq 1.46 \cdot 10^{-114}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y4 \leq 1.35 \cdot 10^{-59}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y4 \leq 2.4 \cdot 10^{-31}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2))))))
        (t_2 (- (* c y0) (* a y1)))
        (t_3
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 t_2))
           (* j (- (* i y1) (* b y0)))))))
   (if (<= y4 -1.85e+158)
     t_1
     (if (<= y4 -6.2e+108)
       t_3
       (if (<= y4 -5e+86)
         (* y0 (* j (- (* y3 y5) (* x b))))
         (if (<= y4 -9.8e-231)
           (*
            y2
            (+
             (+ (* x t_2) (* k (- (* y1 y4) (* y0 y5))))
             (* t (- (* a y5) (* c y4)))))
           (if (<= y4 7.4e-260)
             t_3
             (if (<= y4 5.2e-234)
               (* z (* c (* y0 (- y3))))
               (if (<= y4 2.2e-164)
                 (* i (* y (- (* k y5) (* x c))))
                 (if (<= y4 1.46e-114)
                   t_3
                   (if (<= y4 1.35e-59)
                     (* y5 (* i (- (* y k) (* t j))))
                     (if (<= y4 2.4e-31)
                       (* z (* y3 (- (* a y1) (* c y0))))
                       t_1))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_2 = (c * y0) - (a * y1);
	double t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y4 <= -1.85e+158) {
		tmp = t_1;
	} else if (y4 <= -6.2e+108) {
		tmp = t_3;
	} else if (y4 <= -5e+86) {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	} else if (y4 <= -9.8e-231) {
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y4 <= 7.4e-260) {
		tmp = t_3;
	} else if (y4 <= 5.2e-234) {
		tmp = z * (c * (y0 * -y3));
	} else if (y4 <= 2.2e-164) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (y4 <= 1.46e-114) {
		tmp = t_3;
	} else if (y4 <= 1.35e-59) {
		tmp = y5 * (i * ((y * k) - (t * j)));
	} else if (y4 <= 2.4e-31) {
		tmp = z * (y3 * ((a * y1) - (c * y0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    t_2 = (c * y0) - (a * y1)
    t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))))
    if (y4 <= (-1.85d+158)) then
        tmp = t_1
    else if (y4 <= (-6.2d+108)) then
        tmp = t_3
    else if (y4 <= (-5d+86)) then
        tmp = y0 * (j * ((y3 * y5) - (x * b)))
    else if (y4 <= (-9.8d-231)) then
        tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if (y4 <= 7.4d-260) then
        tmp = t_3
    else if (y4 <= 5.2d-234) then
        tmp = z * (c * (y0 * -y3))
    else if (y4 <= 2.2d-164) then
        tmp = i * (y * ((k * y5) - (x * c)))
    else if (y4 <= 1.46d-114) then
        tmp = t_3
    else if (y4 <= 1.35d-59) then
        tmp = y5 * (i * ((y * k) - (t * j)))
    else if (y4 <= 2.4d-31) then
        tmp = z * (y3 * ((a * y1) - (c * y0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_2 = (c * y0) - (a * y1);
	double t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y4 <= -1.85e+158) {
		tmp = t_1;
	} else if (y4 <= -6.2e+108) {
		tmp = t_3;
	} else if (y4 <= -5e+86) {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	} else if (y4 <= -9.8e-231) {
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y4 <= 7.4e-260) {
		tmp = t_3;
	} else if (y4 <= 5.2e-234) {
		tmp = z * (c * (y0 * -y3));
	} else if (y4 <= 2.2e-164) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (y4 <= 1.46e-114) {
		tmp = t_3;
	} else if (y4 <= 1.35e-59) {
		tmp = y5 * (i * ((y * k) - (t * j)));
	} else if (y4 <= 2.4e-31) {
		tmp = z * (y3 * ((a * y1) - (c * y0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	t_2 = (c * y0) - (a * y1)
	t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))))
	tmp = 0
	if y4 <= -1.85e+158:
		tmp = t_1
	elif y4 <= -6.2e+108:
		tmp = t_3
	elif y4 <= -5e+86:
		tmp = y0 * (j * ((y3 * y5) - (x * b)))
	elif y4 <= -9.8e-231:
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif y4 <= 7.4e-260:
		tmp = t_3
	elif y4 <= 5.2e-234:
		tmp = z * (c * (y0 * -y3))
	elif y4 <= 2.2e-164:
		tmp = i * (y * ((k * y5) - (x * c)))
	elif y4 <= 1.46e-114:
		tmp = t_3
	elif y4 <= 1.35e-59:
		tmp = y5 * (i * ((y * k) - (t * j)))
	elif y4 <= 2.4e-31:
		tmp = z * (y3 * ((a * y1) - (c * y0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	t_3 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_2)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (y4 <= -1.85e+158)
		tmp = t_1;
	elseif (y4 <= -6.2e+108)
		tmp = t_3;
	elseif (y4 <= -5e+86)
		tmp = Float64(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (y4 <= -9.8e-231)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_2) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y4 <= 7.4e-260)
		tmp = t_3;
	elseif (y4 <= 5.2e-234)
		tmp = Float64(z * Float64(c * Float64(y0 * Float64(-y3))));
	elseif (y4 <= 2.2e-164)
		tmp = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))));
	elseif (y4 <= 1.46e-114)
		tmp = t_3;
	elseif (y4 <= 1.35e-59)
		tmp = Float64(y5 * Float64(i * Float64(Float64(y * k) - Float64(t * j))));
	elseif (y4 <= 2.4e-31)
		tmp = Float64(z * Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	t_2 = (c * y0) - (a * y1);
	t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (y4 <= -1.85e+158)
		tmp = t_1;
	elseif (y4 <= -6.2e+108)
		tmp = t_3;
	elseif (y4 <= -5e+86)
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	elseif (y4 <= -9.8e-231)
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif (y4 <= 7.4e-260)
		tmp = t_3;
	elseif (y4 <= 5.2e-234)
		tmp = z * (c * (y0 * -y3));
	elseif (y4 <= 2.2e-164)
		tmp = i * (y * ((k * y5) - (x * c)));
	elseif (y4 <= 1.46e-114)
		tmp = t_3;
	elseif (y4 <= 1.35e-59)
		tmp = y5 * (i * ((y * k) - (t * j)));
	elseif (y4 <= 2.4e-31)
		tmp = z * (y3 * ((a * y1) - (c * y0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -1.85e+158], t$95$1, If[LessEqual[y4, -6.2e+108], t$95$3, If[LessEqual[y4, -5e+86], N[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -9.8e-231], N[(y2 * N[(N[(N[(x * t$95$2), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 7.4e-260], t$95$3, If[LessEqual[y4, 5.2e-234], N[(z * N[(c * N[(y0 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2.2e-164], N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.46e-114], t$95$3, If[LessEqual[y4, 1.35e-59], N[(y5 * N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2.4e-31], N[(z * N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y4 < -1.85000000000000005e158 or 2.4e-31 < y4

   1. Initial program 29.2%

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

      1. associate-+l- 29.2%

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

   3. Simplified 29.2%

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

   4. Taylor expanded in y4 around inf 63.7%

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

   if -1.85000000000000005e158 < y4 < -6.2000000000000003e108 or -9.80000000000000007e-231 < y4 < 7.4000000000000004e-260 or 2.19999999999999988e-164 < y4 < 1.45999999999999993e-114

   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. Step-by-step derivation

      1. associate-+l- 17.6%

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

   3. Simplified 17.6%

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

   4. Taylor expanded in x around inf 61.0%

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

   if -6.2000000000000003e108 < y4 < -4.9999999999999998e86

   1. Initial program 33.1%

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

      1. +-commutative 33.1%

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

      2. fma-def 33.1%

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

      3. *-commutative 33.1%

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

      4. *-commutative 33.1%

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

   3. Simplified 33.1%

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

   4. Taylor expanded in j around inf 18.1%

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

   5. Taylor expanded in y0 around inf 83.6%

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

   if -4.9999999999999998e86 < y4 < -9.80000000000000007e-231

   1. Initial program 26.7%

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

      1. associate-+l- 26.7%

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

   3. Simplified 26.7%

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

   4. Taylor expanded in y2 around inf 48.5%

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

   if 7.4000000000000004e-260 < y4 < 5.19999999999999978e-234

   1. Initial program 33.1%

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

      1. associate-+l- 33.1%

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

   3. Simplified 33.1%

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

   4. Taylor expanded in z around -inf 34.5%

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

      1. mul-1-neg 34.5%

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

      2. *-commutative 34.5%

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

      3. associate--l+ 34.5%

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

      4. *-commutative 34.5%

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

      5. *-commutative 34.5%

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

      6. *-commutative 34.5%

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

      7. *-commutative 34.5%

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

      8. *-commutative 34.5%

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

      9. *-commutative 34.5%

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

      10. *-commutative 34.5%

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

      11. *-commutative 34.5%

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

   6. Simplified 34.5%

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

   7. Taylor expanded in y3 around inf 51.8%

      \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3\right)} \]
   8. Step-by-step derivation

      1. *-commutative 51.8%

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

   9. Simplified 51.8%

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

   10. Taylor expanded in y0 around inf 67.6%

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

       1. *-commutative 67.6%

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

       2. *-commutative 67.6%

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

   12. Simplified 67.6%

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

   if 5.19999999999999978e-234 < y4 < 2.19999999999999988e-164

   1. Initial program 15.4%

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

      1. associate-+l- 15.4%

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

   3. Simplified 15.4%

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

   4. Taylor expanded in i around -inf 38.5%

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

   5. Taylor expanded in y around inf 69.7%

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

      1. +-commutative 69.7%

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

      2. mul-1-neg 69.7%

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

      3. unsub-neg 69.7%

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

      4. *-commutative 69.7%

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

   7. Simplified 69.7%

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

   if 1.45999999999999993e-114 < y4 < 1.3499999999999999e-59

   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. Step-by-step derivation

      1. associate-+l- 46.2%

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

   3. Simplified 46.2%

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

   4. Taylor expanded in y5 around -inf 61.6%

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

      1. mul-1-neg 61.6%

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

      2. associate--l+ 61.6%

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

      3. *-commutative 61.6%

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

   6. Simplified 61.6%

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

   7. Taylor expanded in i around inf 47.2%

      \[\leadsto -\color{blue}{\left(t \cdot j - k \cdot y\right) \cdot \left(i \cdot y5\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 54.4%

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

      2. *-commutative 54.4%

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

      3. *-commutative 54.4%

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

      4. *-commutative 54.4%

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

   9. Simplified 54.4%

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

   if 1.3499999999999999e-59 < y4 < 2.4e-31

   1. Initial program 1.2%

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

      1. associate-+l- 1.2%

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

   3. Simplified 1.2%

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

   4. Taylor expanded in z around -inf 35.1%

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

      1. mul-1-neg 35.1%

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

      2. *-commutative 35.1%

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

      3. associate--l+ 35.1%

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

      4. *-commutative 35.1%

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

      5. *-commutative 35.1%

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

      6. *-commutative 35.1%

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

      7. *-commutative 35.1%

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

      8. *-commutative 35.1%

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

      9. *-commutative 35.1%

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

      10. *-commutative 35.1%

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

      11. *-commutative 35.1%

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

   6. Simplified 35.1%

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

   7. Taylor expanded in y3 around inf 68.1%

      \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3\right)} \]
   8. Step-by-step derivation

      1. *-commutative 68.1%

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

   9. Simplified 68.1%

      \[\leadsto -z \cdot \color{blue}{\left(\left(y0 \cdot c - a \cdot y1\right) \cdot y3\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.85 \cdot 10^{+158}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -6.2 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -5 \cdot 10^{+86}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq -9.8 \cdot 10^{-231}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 7.4 \cdot 10^{-260}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 5.2 \cdot 10^{-234}:\\ \;\;\;\;z \cdot \left(c \cdot \left(y0 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 2.2 \cdot 10^{-164}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq 1.46 \cdot 10^{-114}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 1.35 \cdot 10^{-59}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y4 \leq 2.4 \cdot 10^{-31}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]

Alternative 5: 40.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ t_2 := a \cdot y5 - c \cdot y4\\ t_3 := y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot t_2\right)\\ \mathbf{if}\;y2 \leq -4.7 \cdot 10^{+15}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y2 \leq -2.2 \cdot 10^{-145}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.25 \cdot 10^{-220}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 6 \cdot 10^{-124}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 1.4 \cdot 10^{-80}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;y2 \leq 5.9 \cdot 10^{-36}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 8200:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 8.6 \cdot 10^{+51}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y2 \leq 4.5 \cdot 10^{+112}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 6.6 \cdot 10^{+210}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y2 \cdot t_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y
          (+
           (* k (- (* i y5) (* b y4)))
           (+ (* x (- (* a b) (* c i))) (* y3 (- (* c y4) (* a y5)))))))
        (t_2 (- (* a y5) (* c y4)))
        (t_3
         (*
          y2
          (+
           (+ (* x (- (* c y0) (* a y1))) (* k (- (* y1 y4) (* y0 y5))))
           (* t t_2)))))
   (if (<= y2 -4.7e+15)
     t_3
     (if (<= y2 -2.2e-145)
       (*
        y5
        (+
         (* i (- (* y k) (* t j)))
         (+ (* a (- (* t y2) (* y y3))) (* y0 (- (* j y3) (* k y2))))))
       (if (<= y2 1.25e-220)
         t_1
         (if (<= y2 6e-124)
           (* y0 (* j (- (* y3 y5) (* x b))))
           (if (<= y2 1.4e-80)
             (* i (* y (- (* k y5) (* x c))))
             (if (<= y2 5.9e-36)
               (* y0 (* y3 (* j y5)))
               (if (<= y2 8200.0)
                 t_1
                 (if (<= y2 8.6e+51)
                   t_3
                   (if (<= y2 4.5e+112)
                     (* j (* x (- (* i y1) (* b y0))))
                     (if (<= y2 6.6e+210) t_3 (* t (* y2 t_2))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * ((k * ((i * y5) - (b * y4))) + ((x * ((a * b) - (c * i))) + (y3 * ((c * y4) - (a * y5)))));
	double t_2 = (a * y5) - (c * y4);
	double t_3 = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_2));
	double tmp;
	if (y2 <= -4.7e+15) {
		tmp = t_3;
	} else if (y2 <= -2.2e-145) {
		tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y2 <= 1.25e-220) {
		tmp = t_1;
	} else if (y2 <= 6e-124) {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	} else if (y2 <= 1.4e-80) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (y2 <= 5.9e-36) {
		tmp = y0 * (y3 * (j * y5));
	} else if (y2 <= 8200.0) {
		tmp = t_1;
	} else if (y2 <= 8.6e+51) {
		tmp = t_3;
	} else if (y2 <= 4.5e+112) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y2 <= 6.6e+210) {
		tmp = t_3;
	} else {
		tmp = t * (y2 * t_2);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * ((k * ((i * y5) - (b * y4))) + ((x * ((a * b) - (c * i))) + (y3 * ((c * y4) - (a * y5)))))
    t_2 = (a * y5) - (c * y4)
    t_3 = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_2))
    if (y2 <= (-4.7d+15)) then
        tmp = t_3
    else if (y2 <= (-2.2d-145)) then
        tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))))
    else if (y2 <= 1.25d-220) then
        tmp = t_1
    else if (y2 <= 6d-124) then
        tmp = y0 * (j * ((y3 * y5) - (x * b)))
    else if (y2 <= 1.4d-80) then
        tmp = i * (y * ((k * y5) - (x * c)))
    else if (y2 <= 5.9d-36) then
        tmp = y0 * (y3 * (j * y5))
    else if (y2 <= 8200.0d0) then
        tmp = t_1
    else if (y2 <= 8.6d+51) then
        tmp = t_3
    else if (y2 <= 4.5d+112) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (y2 <= 6.6d+210) then
        tmp = t_3
    else
        tmp = t * (y2 * t_2)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * ((k * ((i * y5) - (b * y4))) + ((x * ((a * b) - (c * i))) + (y3 * ((c * y4) - (a * y5)))));
	double t_2 = (a * y5) - (c * y4);
	double t_3 = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_2));
	double tmp;
	if (y2 <= -4.7e+15) {
		tmp = t_3;
	} else if (y2 <= -2.2e-145) {
		tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y2 <= 1.25e-220) {
		tmp = t_1;
	} else if (y2 <= 6e-124) {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	} else if (y2 <= 1.4e-80) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (y2 <= 5.9e-36) {
		tmp = y0 * (y3 * (j * y5));
	} else if (y2 <= 8200.0) {
		tmp = t_1;
	} else if (y2 <= 8.6e+51) {
		tmp = t_3;
	} else if (y2 <= 4.5e+112) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y2 <= 6.6e+210) {
		tmp = t_3;
	} else {
		tmp = t * (y2 * t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y * ((k * ((i * y5) - (b * y4))) + ((x * ((a * b) - (c * i))) + (y3 * ((c * y4) - (a * y5)))))
	t_2 = (a * y5) - (c * y4)
	t_3 = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_2))
	tmp = 0
	if y2 <= -4.7e+15:
		tmp = t_3
	elif y2 <= -2.2e-145:
		tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))))
	elif y2 <= 1.25e-220:
		tmp = t_1
	elif y2 <= 6e-124:
		tmp = y0 * (j * ((y3 * y5) - (x * b)))
	elif y2 <= 1.4e-80:
		tmp = i * (y * ((k * y5) - (x * c)))
	elif y2 <= 5.9e-36:
		tmp = y0 * (y3 * (j * y5))
	elif y2 <= 8200.0:
		tmp = t_1
	elif y2 <= 8.6e+51:
		tmp = t_3
	elif y2 <= 4.5e+112:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif y2 <= 6.6e+210:
		tmp = t_3
	else:
		tmp = t * (y2 * 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(y * Float64(Float64(k * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(Float64(x * Float64(Float64(a * b) - Float64(c * i))) + Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))))
	t_2 = Float64(Float64(a * y5) - Float64(c * y4))
	t_3 = Float64(y2 * Float64(Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * t_2)))
	tmp = 0.0
	if (y2 <= -4.7e+15)
		tmp = t_3;
	elseif (y2 <= -2.2e-145)
		tmp = Float64(y5 * Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))));
	elseif (y2 <= 1.25e-220)
		tmp = t_1;
	elseif (y2 <= 6e-124)
		tmp = Float64(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (y2 <= 1.4e-80)
		tmp = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))));
	elseif (y2 <= 5.9e-36)
		tmp = Float64(y0 * Float64(y3 * Float64(j * y5)));
	elseif (y2 <= 8200.0)
		tmp = t_1;
	elseif (y2 <= 8.6e+51)
		tmp = t_3;
	elseif (y2 <= 4.5e+112)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (y2 <= 6.6e+210)
		tmp = t_3;
	else
		tmp = Float64(t * Float64(y2 * t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y * ((k * ((i * y5) - (b * y4))) + ((x * ((a * b) - (c * i))) + (y3 * ((c * y4) - (a * y5)))));
	t_2 = (a * y5) - (c * y4);
	t_3 = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_2));
	tmp = 0.0;
	if (y2 <= -4.7e+15)
		tmp = t_3;
	elseif (y2 <= -2.2e-145)
		tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	elseif (y2 <= 1.25e-220)
		tmp = t_1;
	elseif (y2 <= 6e-124)
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	elseif (y2 <= 1.4e-80)
		tmp = i * (y * ((k * y5) - (x * c)));
	elseif (y2 <= 5.9e-36)
		tmp = y0 * (y3 * (j * y5));
	elseif (y2 <= 8200.0)
		tmp = t_1;
	elseif (y2 <= 8.6e+51)
		tmp = t_3;
	elseif (y2 <= 4.5e+112)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (y2 <= 6.6e+210)
		tmp = t_3;
	else
		tmp = t * (y2 * 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[(y * N[(N[(k * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y2 * N[(N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -4.7e+15], t$95$3, If[LessEqual[y2, -2.2e-145], N[(y5 * N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.25e-220], t$95$1, If[LessEqual[y2, 6e-124], N[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.4e-80], N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5.9e-36], N[(y0 * N[(y3 * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 8200.0], t$95$1, If[LessEqual[y2, 8.6e+51], t$95$3, If[LessEqual[y2, 4.5e+112], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 6.6e+210], t$95$3, N[(t * N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y2 < -4.7e15 or 8200 < y2 < 8.5999999999999994e51 or 4.4999999999999999e112 < y2 < 6.5999999999999999e210

   1. Initial program 24.7%

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

      1. associate-+l- 24.7%

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

   3. Simplified 24.7%

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

   4. Taylor expanded in y2 around inf 69.2%

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

   if -4.7e15 < y2 < -2.19999999999999999e-145

   1. Initial program 11.2%

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

      1. associate-+l- 11.2%

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

   3. Simplified 11.2%

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

   4. Taylor expanded in y5 around -inf 48.9%

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

      1. mul-1-neg 48.9%

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

      2. associate--l+ 48.9%

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

      3. *-commutative 48.9%

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

   6. Simplified 48.9%

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

   if -2.19999999999999999e-145 < y2 < 1.25e-220 or 5.89999999999999995e-36 < y2 < 8200

   1. Initial program 38.3%

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

      1. +-commutative 38.3%

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

      2. fma-def 43.8%

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

      3. *-commutative 43.8%

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

      4. *-commutative 43.8%

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

   3. Simplified 43.8%

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

   4. Taylor expanded in y around inf 51.7%

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

      1. mul-1-neg 51.7%

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

      2. *-commutative 51.7%

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

      3. *-commutative 51.7%

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

      4. *-commutative 51.7%

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

      5. *-commutative 51.7%

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

   6. Simplified 51.7%

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

   if 1.25e-220 < y2 < 6e-124

   1. Initial program 38.8%

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

      1. +-commutative 38.8%

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

      2. fma-def 38.8%

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

      3. *-commutative 38.8%

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

      4. *-commutative 38.8%

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

   3. Simplified 38.8%

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

   4. Taylor expanded in j around inf 34.3%

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

   5. Taylor expanded in y0 around inf 61.1%

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

   if 6e-124 < y2 < 1.39999999999999995e-80

   1. Initial program 41.7%

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

      1. associate-+l- 41.7%

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

   3. Simplified 41.7%

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

   4. Taylor expanded in i around -inf 66.7%

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

   5. Taylor expanded in y around inf 75.6%

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

      1. +-commutative 75.6%

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

      2. mul-1-neg 75.6%

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

      3. unsub-neg 75.6%

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

      4. *-commutative 75.6%

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

   7. Simplified 75.6%

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

   if 1.39999999999999995e-80 < y2 < 5.89999999999999995e-36

   1. Initial program 8.3%

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

      1. +-commutative 8.3%

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

      2. fma-def 8.3%

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

      3. *-commutative 8.3%

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

      4. *-commutative 8.3%

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

   3. Simplified 8.3%

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

   4. Taylor expanded in j around inf 51.5%

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

   5. Taylor expanded in y5 around inf 52.2%

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

      1. *-commutative 52.2%

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

      2. mul-1-neg 52.2%

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

      3. unsub-neg 52.2%

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

      4. *-commutative 52.2%

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

   7. Simplified 52.2%

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

   8. Taylor expanded in y0 around inf 67.1%

      \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 67.1%

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

   10. Simplified 67.1%

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

   if 8.5999999999999994e51 < y2 < 4.4999999999999999e112

   1. Initial program 16.7%

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

      1. +-commutative 16.7%

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

      2. fma-def 25.0%

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

      3. *-commutative 25.0%

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

      4. *-commutative 25.0%

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

   3. Simplified 25.0%

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

   4. Taylor expanded in j around inf 42.0%

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

   5. Taylor expanded in x around inf 50.9%

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

   if 6.5999999999999999e210 < y2

   1. Initial program 9.5%

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

      1. associate-+l- 9.5%

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

   3. Simplified 9.5%

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

   4. Taylor expanded in y2 around inf 52.7%

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

   5. Taylor expanded in t around -inf 71.8%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 71.8%

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

      2. neg-mul-1 71.8%

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

      3. *-commutative 71.8%

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

   7. Simplified 71.8%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(y2 \cdot \left(y4 \cdot c - a \cdot y5\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -4.7 \cdot 10^{+15}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -2.2 \cdot 10^{-145}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.25 \cdot 10^{-220}:\\ \;\;\;\;y \cdot \left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 6 \cdot 10^{-124}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 1.4 \cdot 10^{-80}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;y2 \leq 5.9 \cdot 10^{-36}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 8200:\\ \;\;\;\;y \cdot \left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 8.6 \cdot 10^{+51}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 4.5 \cdot 10^{+112}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 6.6 \cdot 10^{+210}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \]

Alternative 6: 40.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot k - t \cdot j\\ t_2 := a \cdot y5 - c \cdot y4\\ t_3 := y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot t_2\right)\\ \mathbf{if}\;y2 \leq -1.15 \cdot 10^{+23}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y2 \leq -9.5 \cdot 10^{-241}:\\ \;\;\;\;y5 \cdot \left(i \cdot t_1 + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 6.2 \cdot 10^{-220}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot t_1 + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 4 \cdot 10^{-126}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 4.7 \cdot 10^{-80}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;y2 \leq 7.2 \cdot 10^{-36}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 43000:\\ \;\;\;\;y \cdot \left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 7.5 \cdot 10^{+50}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y2 \leq 3.4 \cdot 10^{+118}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 5 \cdot 10^{+211}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y2 \cdot t_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y k) (* t j)))
        (t_2 (- (* a y5) (* c y4)))
        (t_3
         (*
          y2
          (+
           (+ (* x (- (* c y0) (* a y1))) (* k (- (* y1 y4) (* y0 y5))))
           (* t t_2)))))
   (if (<= y2 -1.15e+23)
     t_3
     (if (<= y2 -9.5e-241)
       (*
        y5
        (+
         (* i t_1)
         (+ (* a (- (* t y2) (* y y3))) (* y0 (- (* j y3) (* k y2))))))
       (if (<= y2 6.2e-220)
         (*
          i
          (+
           (* y1 (- (* x j) (* z k)))
           (+ (* y5 t_1) (* c (- (* z t) (* x y))))))
         (if (<= y2 4e-126)
           (* y0 (* j (- (* y3 y5) (* x b))))
           (if (<= y2 4.7e-80)
             (* i (* y (- (* k y5) (* x c))))
             (if (<= y2 7.2e-36)
               (* y0 (* y3 (* j y5)))
               (if (<= y2 43000.0)
                 (*
                  y
                  (+
                   (* k (- (* i y5) (* b y4)))
                   (+ (* x (- (* a b) (* c i))) (* y3 (- (* c y4) (* a y5))))))
                 (if (<= y2 7.5e+50)
                   t_3
                   (if (<= y2 3.4e+118)
                     (* j (* x (- (* i y1) (* b y0))))
                     (if (<= y2 5e+211) t_3 (* t (* y2 t_2))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * k) - (t * j);
	double t_2 = (a * y5) - (c * y4);
	double t_3 = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_2));
	double tmp;
	if (y2 <= -1.15e+23) {
		tmp = t_3;
	} else if (y2 <= -9.5e-241) {
		tmp = y5 * ((i * t_1) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y2 <= 6.2e-220) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * t_1) + (c * ((z * t) - (x * y)))));
	} else if (y2 <= 4e-126) {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	} else if (y2 <= 4.7e-80) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (y2 <= 7.2e-36) {
		tmp = y0 * (y3 * (j * y5));
	} else if (y2 <= 43000.0) {
		tmp = y * ((k * ((i * y5) - (b * y4))) + ((x * ((a * b) - (c * i))) + (y3 * ((c * y4) - (a * y5)))));
	} else if (y2 <= 7.5e+50) {
		tmp = t_3;
	} else if (y2 <= 3.4e+118) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y2 <= 5e+211) {
		tmp = t_3;
	} else {
		tmp = t * (y2 * t_2);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y * k) - (t * j)
    t_2 = (a * y5) - (c * y4)
    t_3 = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_2))
    if (y2 <= (-1.15d+23)) then
        tmp = t_3
    else if (y2 <= (-9.5d-241)) then
        tmp = y5 * ((i * t_1) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))))
    else if (y2 <= 6.2d-220) then
        tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * t_1) + (c * ((z * t) - (x * y)))))
    else if (y2 <= 4d-126) then
        tmp = y0 * (j * ((y3 * y5) - (x * b)))
    else if (y2 <= 4.7d-80) then
        tmp = i * (y * ((k * y5) - (x * c)))
    else if (y2 <= 7.2d-36) then
        tmp = y0 * (y3 * (j * y5))
    else if (y2 <= 43000.0d0) then
        tmp = y * ((k * ((i * y5) - (b * y4))) + ((x * ((a * b) - (c * i))) + (y3 * ((c * y4) - (a * y5)))))
    else if (y2 <= 7.5d+50) then
        tmp = t_3
    else if (y2 <= 3.4d+118) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (y2 <= 5d+211) then
        tmp = t_3
    else
        tmp = t * (y2 * t_2)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * k) - (t * j);
	double t_2 = (a * y5) - (c * y4);
	double t_3 = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_2));
	double tmp;
	if (y2 <= -1.15e+23) {
		tmp = t_3;
	} else if (y2 <= -9.5e-241) {
		tmp = y5 * ((i * t_1) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y2 <= 6.2e-220) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * t_1) + (c * ((z * t) - (x * y)))));
	} else if (y2 <= 4e-126) {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	} else if (y2 <= 4.7e-80) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (y2 <= 7.2e-36) {
		tmp = y0 * (y3 * (j * y5));
	} else if (y2 <= 43000.0) {
		tmp = y * ((k * ((i * y5) - (b * y4))) + ((x * ((a * b) - (c * i))) + (y3 * ((c * y4) - (a * y5)))));
	} else if (y2 <= 7.5e+50) {
		tmp = t_3;
	} else if (y2 <= 3.4e+118) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y2 <= 5e+211) {
		tmp = t_3;
	} else {
		tmp = t * (y2 * t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y * k) - (t * j)
	t_2 = (a * y5) - (c * y4)
	t_3 = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_2))
	tmp = 0
	if y2 <= -1.15e+23:
		tmp = t_3
	elif y2 <= -9.5e-241:
		tmp = y5 * ((i * t_1) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))))
	elif y2 <= 6.2e-220:
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * t_1) + (c * ((z * t) - (x * y)))))
	elif y2 <= 4e-126:
		tmp = y0 * (j * ((y3 * y5) - (x * b)))
	elif y2 <= 4.7e-80:
		tmp = i * (y * ((k * y5) - (x * c)))
	elif y2 <= 7.2e-36:
		tmp = y0 * (y3 * (j * y5))
	elif y2 <= 43000.0:
		tmp = y * ((k * ((i * y5) - (b * y4))) + ((x * ((a * b) - (c * i))) + (y3 * ((c * y4) - (a * y5)))))
	elif y2 <= 7.5e+50:
		tmp = t_3
	elif y2 <= 3.4e+118:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif y2 <= 5e+211:
		tmp = t_3
	else:
		tmp = t * (y2 * t_2)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * k) - Float64(t * j))
	t_2 = Float64(Float64(a * y5) - Float64(c * y4))
	t_3 = Float64(y2 * Float64(Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * t_2)))
	tmp = 0.0
	if (y2 <= -1.15e+23)
		tmp = t_3;
	elseif (y2 <= -9.5e-241)
		tmp = Float64(y5 * Float64(Float64(i * t_1) + Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))));
	elseif (y2 <= 6.2e-220)
		tmp = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(y5 * t_1) + Float64(c * Float64(Float64(z * t) - Float64(x * y))))));
	elseif (y2 <= 4e-126)
		tmp = Float64(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (y2 <= 4.7e-80)
		tmp = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))));
	elseif (y2 <= 7.2e-36)
		tmp = Float64(y0 * Float64(y3 * Float64(j * y5)));
	elseif (y2 <= 43000.0)
		tmp = Float64(y * Float64(Float64(k * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(Float64(x * Float64(Float64(a * b) - Float64(c * i))) + Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))));
	elseif (y2 <= 7.5e+50)
		tmp = t_3;
	elseif (y2 <= 3.4e+118)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (y2 <= 5e+211)
		tmp = t_3;
	else
		tmp = Float64(t * Float64(y2 * t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y * k) - (t * j);
	t_2 = (a * y5) - (c * y4);
	t_3 = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_2));
	tmp = 0.0;
	if (y2 <= -1.15e+23)
		tmp = t_3;
	elseif (y2 <= -9.5e-241)
		tmp = y5 * ((i * t_1) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	elseif (y2 <= 6.2e-220)
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * t_1) + (c * ((z * t) - (x * y)))));
	elseif (y2 <= 4e-126)
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	elseif (y2 <= 4.7e-80)
		tmp = i * (y * ((k * y5) - (x * c)));
	elseif (y2 <= 7.2e-36)
		tmp = y0 * (y3 * (j * y5));
	elseif (y2 <= 43000.0)
		tmp = y * ((k * ((i * y5) - (b * y4))) + ((x * ((a * b) - (c * i))) + (y3 * ((c * y4) - (a * y5)))));
	elseif (y2 <= 7.5e+50)
		tmp = t_3;
	elseif (y2 <= 3.4e+118)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (y2 <= 5e+211)
		tmp = t_3;
	else
		tmp = t * (y2 * t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y2 * N[(N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.15e+23], t$95$3, If[LessEqual[y2, -9.5e-241], N[(y5 * N[(N[(i * t$95$1), $MachinePrecision] + N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 6.2e-220], N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y5 * t$95$1), $MachinePrecision] + N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4e-126], N[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.7e-80], N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 7.2e-36], N[(y0 * N[(y3 * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 43000.0], N[(y * N[(N[(k * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 7.5e+50], t$95$3, If[LessEqual[y2, 3.4e+118], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5e+211], t$95$3, N[(t * N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y2 < -1.15e23 or 43000 < y2 < 7.4999999999999999e50 or 3.39999999999999986e118 < y2 < 4.9999999999999995e211

   1. Initial program 24.7%

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

      1. associate-+l- 24.7%

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

   3. Simplified 24.7%

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

   4. Taylor expanded in y2 around inf 69.2%

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

   if -1.15e23 < y2 < -9.49999999999999971e-241

   1. Initial program 26.2%

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

      1. associate-+l- 26.2%

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

   3. Simplified 26.2%

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

   4. Taylor expanded in y5 around -inf 45.6%

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

      1. mul-1-neg 45.6%

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

      2. associate--l+ 45.6%

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

      3. *-commutative 45.6%

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

   6. Simplified 45.6%

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

   if -9.49999999999999971e-241 < y2 < 6.20000000000000023e-220

   1. Initial program 32.5%

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

      1. associate-+l- 32.5%

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

   3. Simplified 32.5%

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

   4. Taylor expanded in i around -inf 56.7%

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

   if 6.20000000000000023e-220 < y2 < 3.9999999999999998e-126

   1. Initial program 38.8%

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

      1. +-commutative 38.8%

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

      2. fma-def 38.8%

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

      3. *-commutative 38.8%

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

      4. *-commutative 38.8%

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

   3. Simplified 38.8%

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

   4. Taylor expanded in j around inf 34.3%

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

   5. Taylor expanded in y0 around inf 61.1%

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

   if 3.9999999999999998e-126 < y2 < 4.69999999999999973e-80

   1. Initial program 41.7%

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

      1. associate-+l- 41.7%

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

   3. Simplified 41.7%

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

   4. Taylor expanded in i around -inf 66.7%

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

   5. Taylor expanded in y around inf 75.6%

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

      1. +-commutative 75.6%

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

      2. mul-1-neg 75.6%

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

      3. unsub-neg 75.6%

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

      4. *-commutative 75.6%

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

   7. Simplified 75.6%

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

   if 4.69999999999999973e-80 < y2 < 7.20000000000000064e-36

   1. Initial program 8.3%

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

      1. +-commutative 8.3%

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

      2. fma-def 8.3%

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

      3. *-commutative 8.3%

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

      4. *-commutative 8.3%

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

   3. Simplified 8.3%

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

   4. Taylor expanded in j around inf 51.5%

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

   5. Taylor expanded in y5 around inf 52.2%

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

      1. *-commutative 52.2%

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

      2. mul-1-neg 52.2%

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

      3. unsub-neg 52.2%

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

      4. *-commutative 52.2%

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

   7. Simplified 52.2%

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

   8. Taylor expanded in y0 around inf 67.1%

      \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 67.1%

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

   10. Simplified 67.1%

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

   if 7.20000000000000064e-36 < y2 < 43000

   1. Initial program 37.5%

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

      1. +-commutative 37.5%

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

      2. fma-def 50.0%

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

      3. *-commutative 50.0%

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

      4. *-commutative 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in y around inf 75.4%

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

      1. mul-1-neg 75.4%

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

      2. *-commutative 75.4%

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

      3. *-commutative 75.4%

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

      4. *-commutative 75.4%

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

      5. *-commutative 75.4%

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

   6. Simplified 75.4%

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

   if 7.4999999999999999e50 < y2 < 3.39999999999999986e118

   1. Initial program 16.7%

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

      1. +-commutative 16.7%

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

      2. fma-def 25.0%

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

      3. *-commutative 25.0%

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

      4. *-commutative 25.0%

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

   3. Simplified 25.0%

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

   4. Taylor expanded in j around inf 42.0%

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

   5. Taylor expanded in x around inf 50.9%

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

   if 4.9999999999999995e211 < y2

   1. Initial program 9.5%

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

      1. associate-+l- 9.5%

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

   3. Simplified 9.5%

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

   4. Taylor expanded in y2 around inf 52.7%

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

   5. Taylor expanded in t around -inf 71.8%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 71.8%

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

      2. neg-mul-1 71.8%

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

      3. *-commutative 71.8%

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

   7. Simplified 71.8%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(y2 \cdot \left(y4 \cdot c - a \cdot y5\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.15 \cdot 10^{+23}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -9.5 \cdot 10^{-241}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 6.2 \cdot 10^{-220}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 4 \cdot 10^{-126}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 4.7 \cdot 10^{-80}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;y2 \leq 7.2 \cdot 10^{-36}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 43000:\\ \;\;\;\;y \cdot \left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 7.5 \cdot 10^{+50}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 3.4 \cdot 10^{+118}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 5 \cdot 10^{+211}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \]

Alternative 7: 41.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot y4 - y0 \cdot y5\\ t_2 := y \cdot k - t \cdot j\\ t_3 := a \cdot y5 - c \cdot y4\\ t_4 := y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot t_1\right) + t \cdot t_3\right)\\ t_5 := z \cdot t - x \cdot y\\ t_6 := c \cdot \left(\left(i \cdot t_5 + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_7 := i \cdot y1 - b \cdot y0\\ \mathbf{if}\;y2 \leq -90000000:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y2 \leq -1.26 \cdot 10^{-85}:\\ \;\;\;\;y5 \cdot \left(i \cdot t_2 + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -3 \cdot 10^{-166}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot t_1 - z \cdot t_7\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -8.5 \cdot 10^{-254}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y2 \leq 2 \cdot 10^{-219}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot t_2 + c \cdot t_5\right)\right)\\ \mathbf{elif}\;y2 \leq 1.35 \cdot 10^{-117}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 5.6 \cdot 10^{-6}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y2 \leq 4.8 \cdot 10^{+50}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y2 \leq 9.2 \cdot 10^{+117}:\\ \;\;\;\;j \cdot \left(x \cdot t_7\right)\\ \mathbf{elif}\;y2 \leq 5.8 \cdot 10^{+211}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y2 \cdot t_3\right)\\ \end{array} \end{array} \]

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 (- (* y k) (* t j)))
        (t_3 (- (* a y5) (* c y4)))
        (t_4 (* y2 (+ (+ (* x (- (* c y0) (* a y1))) (* k t_1)) (* t t_3))))
        (t_5 (- (* z t) (* x y)))
        (t_6
         (*
          c
          (+
           (+ (* i t_5) (* y0 (- (* x y2) (* z y3))))
           (* y4 (- (* y y3) (* t y2))))))
        (t_7 (- (* i y1) (* b y0))))
   (if (<= y2 -90000000.0)
     t_4
     (if (<= y2 -1.26e-85)
       (*
        y5
        (+
         (* i t_2)
         (+ (* a (- (* t y2) (* y y3))) (* y0 (- (* j y3) (* k y2))))))
       (if (<= y2 -3e-166)
         (* k (- (- (* y2 t_1) (* z t_7)) (* y (- (* b y4) (* i y5)))))
         (if (<= y2 -8.5e-254)
           t_6
           (if (<= y2 2e-219)
             (* i (+ (* y1 (- (* x j) (* z k))) (+ (* y5 t_2) (* c t_5))))
             (if (<= y2 1.35e-117)
               (* y0 (* j (- (* y3 y5) (* x b))))
               (if (<= y2 5.6e-6)
                 t_6
                 (if (<= y2 4.8e+50)
                   t_4
                   (if (<= y2 9.2e+117)
                     (* j (* x t_7))
                     (if (<= y2 5.8e+211) t_4 (* t (* y2 t_3))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double t_2 = (y * k) - (t * j);
	double t_3 = (a * y5) - (c * y4);
	double t_4 = y2 * (((x * ((c * y0) - (a * y1))) + (k * t_1)) + (t * t_3));
	double t_5 = (z * t) - (x * y);
	double t_6 = c * (((i * t_5) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	double t_7 = (i * y1) - (b * y0);
	double tmp;
	if (y2 <= -90000000.0) {
		tmp = t_4;
	} else if (y2 <= -1.26e-85) {
		tmp = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y2 <= -3e-166) {
		tmp = k * (((y2 * t_1) - (z * t_7)) - (y * ((b * y4) - (i * y5))));
	} else if (y2 <= -8.5e-254) {
		tmp = t_6;
	} else if (y2 <= 2e-219) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * t_2) + (c * t_5)));
	} else if (y2 <= 1.35e-117) {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	} else if (y2 <= 5.6e-6) {
		tmp = t_6;
	} else if (y2 <= 4.8e+50) {
		tmp = t_4;
	} else if (y2 <= 9.2e+117) {
		tmp = j * (x * t_7);
	} else if (y2 <= 5.8e+211) {
		tmp = t_4;
	} else {
		tmp = t * (y2 * t_3);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_1 = (y1 * y4) - (y0 * y5)
    t_2 = (y * k) - (t * j)
    t_3 = (a * y5) - (c * y4)
    t_4 = y2 * (((x * ((c * y0) - (a * y1))) + (k * t_1)) + (t * t_3))
    t_5 = (z * t) - (x * y)
    t_6 = c * (((i * t_5) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
    t_7 = (i * y1) - (b * y0)
    if (y2 <= (-90000000.0d0)) then
        tmp = t_4
    else if (y2 <= (-1.26d-85)) then
        tmp = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))))
    else if (y2 <= (-3d-166)) then
        tmp = k * (((y2 * t_1) - (z * t_7)) - (y * ((b * y4) - (i * y5))))
    else if (y2 <= (-8.5d-254)) then
        tmp = t_6
    else if (y2 <= 2d-219) then
        tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * t_2) + (c * t_5)))
    else if (y2 <= 1.35d-117) then
        tmp = y0 * (j * ((y3 * y5) - (x * b)))
    else if (y2 <= 5.6d-6) then
        tmp = t_6
    else if (y2 <= 4.8d+50) then
        tmp = t_4
    else if (y2 <= 9.2d+117) then
        tmp = j * (x * t_7)
    else if (y2 <= 5.8d+211) then
        tmp = t_4
    else
        tmp = t * (y2 * t_3)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double t_2 = (y * k) - (t * j);
	double t_3 = (a * y5) - (c * y4);
	double t_4 = y2 * (((x * ((c * y0) - (a * y1))) + (k * t_1)) + (t * t_3));
	double t_5 = (z * t) - (x * y);
	double t_6 = c * (((i * t_5) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	double t_7 = (i * y1) - (b * y0);
	double tmp;
	if (y2 <= -90000000.0) {
		tmp = t_4;
	} else if (y2 <= -1.26e-85) {
		tmp = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y2 <= -3e-166) {
		tmp = k * (((y2 * t_1) - (z * t_7)) - (y * ((b * y4) - (i * y5))));
	} else if (y2 <= -8.5e-254) {
		tmp = t_6;
	} else if (y2 <= 2e-219) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * t_2) + (c * t_5)));
	} else if (y2 <= 1.35e-117) {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	} else if (y2 <= 5.6e-6) {
		tmp = t_6;
	} else if (y2 <= 4.8e+50) {
		tmp = t_4;
	} else if (y2 <= 9.2e+117) {
		tmp = j * (x * t_7);
	} else if (y2 <= 5.8e+211) {
		tmp = t_4;
	} else {
		tmp = t * (y2 * t_3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y1 * y4) - (y0 * y5)
	t_2 = (y * k) - (t * j)
	t_3 = (a * y5) - (c * y4)
	t_4 = y2 * (((x * ((c * y0) - (a * y1))) + (k * t_1)) + (t * t_3))
	t_5 = (z * t) - (x * y)
	t_6 = c * (((i * t_5) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
	t_7 = (i * y1) - (b * y0)
	tmp = 0
	if y2 <= -90000000.0:
		tmp = t_4
	elif y2 <= -1.26e-85:
		tmp = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))))
	elif y2 <= -3e-166:
		tmp = k * (((y2 * t_1) - (z * t_7)) - (y * ((b * y4) - (i * y5))))
	elif y2 <= -8.5e-254:
		tmp = t_6
	elif y2 <= 2e-219:
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * t_2) + (c * t_5)))
	elif y2 <= 1.35e-117:
		tmp = y0 * (j * ((y3 * y5) - (x * b)))
	elif y2 <= 5.6e-6:
		tmp = t_6
	elif y2 <= 4.8e+50:
		tmp = t_4
	elif y2 <= 9.2e+117:
		tmp = j * (x * t_7)
	elif y2 <= 5.8e+211:
		tmp = t_4
	else:
		tmp = t * (y2 * t_3)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_2 = Float64(Float64(y * k) - Float64(t * j))
	t_3 = Float64(Float64(a * y5) - Float64(c * y4))
	t_4 = Float64(y2 * Float64(Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(k * t_1)) + Float64(t * t_3)))
	t_5 = Float64(Float64(z * t) - Float64(x * y))
	t_6 = Float64(c * Float64(Float64(Float64(i * t_5) + Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_7 = Float64(Float64(i * y1) - Float64(b * y0))
	tmp = 0.0
	if (y2 <= -90000000.0)
		tmp = t_4;
	elseif (y2 <= -1.26e-85)
		tmp = Float64(y5 * Float64(Float64(i * t_2) + Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))));
	elseif (y2 <= -3e-166)
		tmp = Float64(k * Float64(Float64(Float64(y2 * t_1) - Float64(z * t_7)) - Float64(y * Float64(Float64(b * y4) - Float64(i * y5)))));
	elseif (y2 <= -8.5e-254)
		tmp = t_6;
	elseif (y2 <= 2e-219)
		tmp = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(y5 * t_2) + Float64(c * t_5))));
	elseif (y2 <= 1.35e-117)
		tmp = Float64(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (y2 <= 5.6e-6)
		tmp = t_6;
	elseif (y2 <= 4.8e+50)
		tmp = t_4;
	elseif (y2 <= 9.2e+117)
		tmp = Float64(j * Float64(x * t_7));
	elseif (y2 <= 5.8e+211)
		tmp = t_4;
	else
		tmp = Float64(t * Float64(y2 * t_3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y1 * y4) - (y0 * y5);
	t_2 = (y * k) - (t * j);
	t_3 = (a * y5) - (c * y4);
	t_4 = y2 * (((x * ((c * y0) - (a * y1))) + (k * t_1)) + (t * t_3));
	t_5 = (z * t) - (x * y);
	t_6 = c * (((i * t_5) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	t_7 = (i * y1) - (b * y0);
	tmp = 0.0;
	if (y2 <= -90000000.0)
		tmp = t_4;
	elseif (y2 <= -1.26e-85)
		tmp = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	elseif (y2 <= -3e-166)
		tmp = k * (((y2 * t_1) - (z * t_7)) - (y * ((b * y4) - (i * y5))));
	elseif (y2 <= -8.5e-254)
		tmp = t_6;
	elseif (y2 <= 2e-219)
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * t_2) + (c * t_5)));
	elseif (y2 <= 1.35e-117)
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	elseif (y2 <= 5.6e-6)
		tmp = t_6;
	elseif (y2 <= 4.8e+50)
		tmp = t_4;
	elseif (y2 <= 9.2e+117)
		tmp = j * (x * t_7);
	elseif (y2 <= 5.8e+211)
		tmp = t_4;
	else
		tmp = t * (y2 * t_3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y2 * N[(N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(c * N[(N[(N[(i * t$95$5), $MachinePrecision] + N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -90000000.0], t$95$4, If[LessEqual[y2, -1.26e-85], N[(y5 * N[(N[(i * t$95$2), $MachinePrecision] + N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -3e-166], N[(k * N[(N[(N[(y2 * t$95$1), $MachinePrecision] - N[(z * t$95$7), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -8.5e-254], t$95$6, If[LessEqual[y2, 2e-219], N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y5 * t$95$2), $MachinePrecision] + N[(c * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.35e-117], N[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5.6e-6], t$95$6, If[LessEqual[y2, 4.8e+50], t$95$4, If[LessEqual[y2, 9.2e+117], N[(j * N[(x * t$95$7), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5.8e+211], t$95$4, N[(t * N[(y2 * t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y2 < -9e7 or 5.59999999999999975e-6 < y2 < 4.8000000000000004e50 or 9.19999999999999951e117 < y2 < 5.8000000000000001e211

   1. Initial program 24.0%

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

      1. associate-+l- 24.0%

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

   3. Simplified 24.0%

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

   4. Taylor expanded in y2 around inf 68.2%

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

   if -9e7 < y2 < -1.26e-85

   1. Initial program 14.3%

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

      1. associate-+l- 14.3%

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

   3. Simplified 14.3%

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

   4. Taylor expanded in y5 around -inf 60.6%

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

      1. mul-1-neg 60.6%

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

      2. associate--l+ 60.6%

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

      3. *-commutative 60.6%

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

   6. Simplified 60.6%

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

   if -1.26e-85 < y2 < -3.0000000000000003e-166

   1. Initial program 18.4%

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

      1. +-commutative 18.4%

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

      2. fma-def 18.4%

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

      3. *-commutative 18.4%

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

      4. *-commutative 18.4%

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

   3. Simplified 24.3%

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

   4. Taylor expanded in k around inf 65.2%

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

   if -3.0000000000000003e-166 < y2 < -8.49999999999999963e-254 or 1.35000000000000001e-117 < y2 < 5.59999999999999975e-6

   1. Initial program 28.0%

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

      1. associate-+l- 28.0%

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

   3. Simplified 28.0%

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

   4. Taylor expanded in c around inf 60.3%

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

   if -8.49999999999999963e-254 < y2 < 2.0000000000000001e-219

   1. Initial program 40.3%

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

      1. associate-+l- 40.3%

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

   3. Simplified 40.3%

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

   4. Taylor expanded in i around -inf 60.6%

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

   if 2.0000000000000001e-219 < y2 < 1.35000000000000001e-117

   1. Initial program 47.5%

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

      1. +-commutative 47.5%

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

      2. fma-def 47.5%

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

      3. *-commutative 47.5%

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

      4. *-commutative 47.5%

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

   3. Simplified 47.5%

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

   4. Taylor expanded in j around inf 43.7%

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

   5. Taylor expanded in y0 around inf 61.9%

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

   if 4.8000000000000004e50 < y2 < 9.19999999999999951e117

   1. Initial program 16.7%

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

      1. +-commutative 16.7%

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

      2. fma-def 25.0%

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

      3. *-commutative 25.0%

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

      4. *-commutative 25.0%

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

   3. Simplified 25.0%

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

   4. Taylor expanded in j around inf 42.0%

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

   5. Taylor expanded in x around inf 50.9%

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

   if 5.8000000000000001e211 < y2

   1. Initial program 9.5%

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

      1. associate-+l- 9.5%

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

   3. Simplified 9.5%

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

   4. Taylor expanded in y2 around inf 52.7%

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

   5. Taylor expanded in t around -inf 71.8%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 71.8%

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

      2. neg-mul-1 71.8%

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

      3. *-commutative 71.8%

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

   7. Simplified 71.8%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(y2 \cdot \left(y4 \cdot c - a \cdot y5\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -90000000:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -1.26 \cdot 10^{-85}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -3 \cdot 10^{-166}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - z \cdot \left(i \cdot y1 - b \cdot y0\right)\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -8.5 \cdot 10^{-254}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 2 \cdot 10^{-219}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.35 \cdot 10^{-117}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 5.6 \cdot 10^{-6}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 4.8 \cdot 10^{+50}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 9.2 \cdot 10^{+117}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 5.8 \cdot 10^{+211}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \]

Alternative 8: 30.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\\ t_2 := x \cdot a - k \cdot y4\\ \mathbf{if}\;y3 \leq -1.65 \cdot 10^{+116}:\\ \;\;\;\;y4 \cdot t_1\\ \mathbf{elif}\;y3 \leq -3900000000:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y3 \leq -1.08 \cdot 10^{-141}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq -4.4 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \left(y \cdot t_2\right)\\ \mathbf{elif}\;y3 \leq 4.2 \cdot 10^{-209}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 1.8 \cdot 10^{-83}:\\ \;\;\;\;t_2 \cdot \left(y \cdot b\right)\\ \mathbf{elif}\;y3 \leq 0.145:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;y3 \leq 1.22 \cdot 10^{+104}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;y3 \leq 6.8 \cdot 10^{+169}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + t_1\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (- (* k y2) (* j y3)))) (t_2 (- (* x a) (* k y4))))
   (if (<= y3 -1.65e+116)
     (* y4 t_1)
     (if (<= y3 -3900000000.0)
       (* c (* i (- (* z t) (* x y))))
       (if (<= y3 -1.08e-141)
         (* y2 (* a (- (* t y5) (* x y1))))
         (if (<= y3 -4.4e-224)
           (* b (* y t_2))
           (if (<= y3 4.2e-209)
             (* y4 (* t (- (* b j) (* c y2))))
             (if (<= y3 1.8e-83)
               (* t_2 (* y b))
               (if (<= y3 0.145)
                 (* i (* y (- (* k y5) (* x c))))
                 (if (<= y3 1.22e+104)
                   (* j (* y5 (- (* y0 y3) (* t i))))
                   (if (<= y3 6.8e+169)
                     (*
                      y4
                      (+
                       (+ (* b (- (* t j) (* y k))) t_1)
                       (* c (- (* y y3) (* t y2)))))
                     (* y0 (* j (- (* y3 y5) (* x b)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * ((k * y2) - (j * y3));
	double t_2 = (x * a) - (k * y4);
	double tmp;
	if (y3 <= -1.65e+116) {
		tmp = y4 * t_1;
	} else if (y3 <= -3900000000.0) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (y3 <= -1.08e-141) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else if (y3 <= -4.4e-224) {
		tmp = b * (y * t_2);
	} else if (y3 <= 4.2e-209) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (y3 <= 1.8e-83) {
		tmp = t_2 * (y * b);
	} else if (y3 <= 0.145) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (y3 <= 1.22e+104) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (y3 <= 6.8e+169) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + t_1) + (c * ((y * y3) - (t * y2))));
	} else {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y1 * ((k * y2) - (j * y3))
    t_2 = (x * a) - (k * y4)
    if (y3 <= (-1.65d+116)) then
        tmp = y4 * t_1
    else if (y3 <= (-3900000000.0d0)) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (y3 <= (-1.08d-141)) then
        tmp = y2 * (a * ((t * y5) - (x * y1)))
    else if (y3 <= (-4.4d-224)) then
        tmp = b * (y * t_2)
    else if (y3 <= 4.2d-209) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    else if (y3 <= 1.8d-83) then
        tmp = t_2 * (y * b)
    else if (y3 <= 0.145d0) then
        tmp = i * (y * ((k * y5) - (x * c)))
    else if (y3 <= 1.22d+104) then
        tmp = j * (y5 * ((y0 * y3) - (t * i)))
    else if (y3 <= 6.8d+169) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + t_1) + (c * ((y * y3) - (t * y2))))
    else
        tmp = y0 * (j * ((y3 * y5) - (x * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * ((k * y2) - (j * y3));
	double t_2 = (x * a) - (k * y4);
	double tmp;
	if (y3 <= -1.65e+116) {
		tmp = y4 * t_1;
	} else if (y3 <= -3900000000.0) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (y3 <= -1.08e-141) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else if (y3 <= -4.4e-224) {
		tmp = b * (y * t_2);
	} else if (y3 <= 4.2e-209) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (y3 <= 1.8e-83) {
		tmp = t_2 * (y * b);
	} else if (y3 <= 0.145) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (y3 <= 1.22e+104) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (y3 <= 6.8e+169) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + t_1) + (c * ((y * y3) - (t * y2))));
	} else {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y1 * ((k * y2) - (j * y3))
	t_2 = (x * a) - (k * y4)
	tmp = 0
	if y3 <= -1.65e+116:
		tmp = y4 * t_1
	elif y3 <= -3900000000.0:
		tmp = c * (i * ((z * t) - (x * y)))
	elif y3 <= -1.08e-141:
		tmp = y2 * (a * ((t * y5) - (x * y1)))
	elif y3 <= -4.4e-224:
		tmp = b * (y * t_2)
	elif y3 <= 4.2e-209:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	elif y3 <= 1.8e-83:
		tmp = t_2 * (y * b)
	elif y3 <= 0.145:
		tmp = i * (y * ((k * y5) - (x * c)))
	elif y3 <= 1.22e+104:
		tmp = j * (y5 * ((y0 * y3) - (t * i)))
	elif y3 <= 6.8e+169:
		tmp = y4 * (((b * ((t * j) - (y * k))) + t_1) + (c * ((y * y3) - (t * y2))))
	else:
		tmp = y0 * (j * ((y3 * y5) - (x * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))
	t_2 = Float64(Float64(x * a) - Float64(k * y4))
	tmp = 0.0
	if (y3 <= -1.65e+116)
		tmp = Float64(y4 * t_1);
	elseif (y3 <= -3900000000.0)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (y3 <= -1.08e-141)
		tmp = Float64(y2 * Float64(a * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (y3 <= -4.4e-224)
		tmp = Float64(b * Float64(y * t_2));
	elseif (y3 <= 4.2e-209)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (y3 <= 1.8e-83)
		tmp = Float64(t_2 * Float64(y * b));
	elseif (y3 <= 0.145)
		tmp = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))));
	elseif (y3 <= 1.22e+104)
		tmp = Float64(j * Float64(y5 * Float64(Float64(y0 * y3) - Float64(t * i))));
	elseif (y3 <= 6.8e+169)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + t_1) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	else
		tmp = Float64(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y1 * ((k * y2) - (j * y3));
	t_2 = (x * a) - (k * y4);
	tmp = 0.0;
	if (y3 <= -1.65e+116)
		tmp = y4 * t_1;
	elseif (y3 <= -3900000000.0)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (y3 <= -1.08e-141)
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	elseif (y3 <= -4.4e-224)
		tmp = b * (y * t_2);
	elseif (y3 <= 4.2e-209)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	elseif (y3 <= 1.8e-83)
		tmp = t_2 * (y * b);
	elseif (y3 <= 0.145)
		tmp = i * (y * ((k * y5) - (x * c)));
	elseif (y3 <= 1.22e+104)
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	elseif (y3 <= 6.8e+169)
		tmp = y4 * (((b * ((t * j) - (y * k))) + t_1) + (c * ((y * y3) - (t * y2))));
	else
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -1.65e+116], N[(y4 * t$95$1), $MachinePrecision], If[LessEqual[y3, -3900000000.0], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1.08e-141], N[(y2 * N[(a * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -4.4e-224], N[(b * N[(y * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 4.2e-209], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.8e-83], N[(t$95$2 * N[(y * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 0.145], N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.22e+104], N[(j * N[(y5 * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 6.8e+169], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y3 < -1.6499999999999999e116

   1. Initial program 11.8%

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

      1. associate-+l- 11.8%

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

   3. Simplified 11.8%

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

   4. Taylor expanded in y4 around inf 44.4%

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

   5. Taylor expanded in y1 around inf 59.2%

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

   if -1.6499999999999999e116 < y3 < -3.9e9

   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. Step-by-step derivation

      1. associate-+l- 30.4%

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

   3. Simplified 30.4%

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

   4. Taylor expanded in c around inf 71.3%

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

   5. Taylor expanded in i around inf 60.7%

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

      1. associate-*r* 60.7%

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

      2. neg-mul-1 60.7%

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

   7. Simplified 60.7%

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

   if -3.9e9 < y3 < -1.0799999999999999e-141

   1. Initial program 31.5%

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

      1. associate-+l- 31.5%

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

   3. Simplified 31.5%

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

   4. Taylor expanded in y2 around inf 48.7%

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

   5. Taylor expanded in a around -inf 55.3%

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

      1. mul-1-neg 55.3%

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

      2. associate-*r* 55.4%

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

      3. *-commutative 55.4%

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

   7. Simplified 55.4%

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

   if -1.0799999999999999e-141 < y3 < -4.4000000000000002e-224

   1. Initial program 33.2%

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

      1. associate-+l- 33.2%

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

   3. Simplified 33.2%

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

   4. Taylor expanded in b around inf 45.2%

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

   5. Taylor expanded in y around inf 51.6%

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

      1. associate-*r* 56.8%

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

      2. *-commutative 56.8%

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

      3. *-commutative 56.8%

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

      4. +-commutative 56.8%

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

      5. mul-1-neg 56.8%

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

      6. unsub-neg 56.8%

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

   7. Simplified 56.8%

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

   if -4.4000000000000002e-224 < y3 < 4.19999999999999991e-209

   1. Initial program 33.8%

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

      1. associate-+l- 33.8%

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

   3. Simplified 33.8%

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

   4. Taylor expanded in y4 around inf 42.0%

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

   5. Taylor expanded in t around inf 47.8%

      \[\leadsto y4 \cdot \color{blue}{\left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 47.8%

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

      2. *-commutative 47.8%

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

   7. Simplified 47.8%

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

   if 4.19999999999999991e-209 < y3 < 1.80000000000000006e-83

   1. Initial program 42.6%

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

      1. associate-+l- 42.6%

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

   3. Simplified 42.6%

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

   4. Taylor expanded in b around inf 31.3%

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

   5. Taylor expanded in y around inf 54.8%

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

   if 1.80000000000000006e-83 < y3 < 0.14499999999999999

   1. Initial program 15.8%

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

      1. associate-+l- 15.8%

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

   3. Simplified 15.8%

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

   4. Taylor expanded in i around -inf 42.5%

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

   5. Taylor expanded in y around inf 59.0%

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

      1. +-commutative 59.0%

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

      2. mul-1-neg 59.0%

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

      3. unsub-neg 59.0%

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

      4. *-commutative 59.0%

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

   7. Simplified 59.0%

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

   if 0.14499999999999999 < y3 < 1.22e104

   1. Initial program 17.3%

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

      1. +-commutative 17.3%

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

      2. fma-def 21.7%

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

      3. *-commutative 21.7%

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

      4. *-commutative 21.7%

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

   3. Simplified 21.7%

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

   4. Taylor expanded in j around inf 48.1%

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

   5. Taylor expanded in y5 around inf 53.0%

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

      1. *-commutative 53.0%

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

      2. mul-1-neg 53.0%

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

      3. unsub-neg 53.0%

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

      4. *-commutative 53.0%

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

   7. Simplified 53.0%

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

   if 1.22e104 < y3 < 6.80000000000000056e169

   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. Step-by-step derivation

      1. associate-+l- 31.8%

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

   3. Simplified 31.8%

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

   4. Taylor expanded in y4 around inf 62.5%

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

   if 6.80000000000000056e169 < y3

   1. Initial program 10.3%

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

      1. +-commutative 10.3%

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

      2. fma-def 10.3%

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

      3. *-commutative 10.3%

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

      4. *-commutative 10.3%

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

   3. Simplified 13.8%

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

   4. Taylor expanded in j around inf 35.2%

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

   5. Taylor expanded in y0 around inf 62.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(y3 \cdot y5 - b \cdot x\right) \cdot j\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.65 \cdot 10^{+116}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq -3900000000:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y3 \leq -1.08 \cdot 10^{-141}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq -4.4 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 4.2 \cdot 10^{-209}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 1.8 \cdot 10^{-83}:\\ \;\;\;\;\left(x \cdot a - k \cdot y4\right) \cdot \left(y \cdot b\right)\\ \mathbf{elif}\;y3 \leq 0.145:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;y3 \leq 1.22 \cdot 10^{+104}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;y3 \leq 6.8 \cdot 10^{+169}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \]

Alternative 9: 31.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\\ \mathbf{if}\;y3 \leq -8 \cdot 10^{+116}:\\ \;\;\;\;y4 \cdot t_1\\ \mathbf{elif}\;y3 \leq -2800000:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y3 \leq -2.35 \cdot 10^{-141}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq -9.6 \cdot 10^{-254}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 4.8 \cdot 10^{-208}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 1.15 \cdot 10^{-84}:\\ \;\;\;\;\left(x \cdot a - k \cdot y4\right) \cdot \left(y \cdot b\right)\\ \mathbf{elif}\;y3 \leq 3.2 \cdot 10^{-5}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;y3 \leq 4.5 \cdot 10^{+104}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;y3 \leq 10^{+171}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + t_1\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (- (* k y2) (* j y3)))))
   (if (<= y3 -8e+116)
     (* y4 t_1)
     (if (<= y3 -2800000.0)
       (* c (* i (- (* z t) (* x y))))
       (if (<= y3 -2.35e-141)
         (* y2 (* a (- (* t y5) (* x y1))))
         (if (<= y3 -9.6e-254)
           (*
            x
            (+
             (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
             (* j (- (* i y1) (* b y0)))))
           (if (<= y3 4.8e-208)
             (* y4 (* t (- (* b j) (* c y2))))
             (if (<= y3 1.15e-84)
               (* (- (* x a) (* k y4)) (* y b))
               (if (<= y3 3.2e-5)
                 (* i (* y (- (* k y5) (* x c))))
                 (if (<= y3 4.5e+104)
                   (* j (* y5 (- (* y0 y3) (* t i))))
                   (if (<= y3 1e+171)
                     (*
                      y4
                      (+
                       (+ (* b (- (* t j) (* y k))) t_1)
                       (* c (- (* y y3) (* t y2)))))
                     (* y0 (* j (- (* y3 y5) (* x b)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * ((k * y2) - (j * y3));
	double tmp;
	if (y3 <= -8e+116) {
		tmp = y4 * t_1;
	} else if (y3 <= -2800000.0) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (y3 <= -2.35e-141) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else if (y3 <= -9.6e-254) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else if (y3 <= 4.8e-208) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (y3 <= 1.15e-84) {
		tmp = ((x * a) - (k * y4)) * (y * b);
	} else if (y3 <= 3.2e-5) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (y3 <= 4.5e+104) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (y3 <= 1e+171) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + t_1) + (c * ((y * y3) - (t * y2))));
	} else {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y1 * ((k * y2) - (j * y3))
    if (y3 <= (-8d+116)) then
        tmp = y4 * t_1
    else if (y3 <= (-2800000.0d0)) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (y3 <= (-2.35d-141)) then
        tmp = y2 * (a * ((t * y5) - (x * y1)))
    else if (y3 <= (-9.6d-254)) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    else if (y3 <= 4.8d-208) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    else if (y3 <= 1.15d-84) then
        tmp = ((x * a) - (k * y4)) * (y * b)
    else if (y3 <= 3.2d-5) then
        tmp = i * (y * ((k * y5) - (x * c)))
    else if (y3 <= 4.5d+104) then
        tmp = j * (y5 * ((y0 * y3) - (t * i)))
    else if (y3 <= 1d+171) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + t_1) + (c * ((y * y3) - (t * y2))))
    else
        tmp = y0 * (j * ((y3 * y5) - (x * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * ((k * y2) - (j * y3));
	double tmp;
	if (y3 <= -8e+116) {
		tmp = y4 * t_1;
	} else if (y3 <= -2800000.0) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (y3 <= -2.35e-141) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else if (y3 <= -9.6e-254) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else if (y3 <= 4.8e-208) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (y3 <= 1.15e-84) {
		tmp = ((x * a) - (k * y4)) * (y * b);
	} else if (y3 <= 3.2e-5) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (y3 <= 4.5e+104) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (y3 <= 1e+171) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + t_1) + (c * ((y * y3) - (t * y2))));
	} else {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y1 * ((k * y2) - (j * y3))
	tmp = 0
	if y3 <= -8e+116:
		tmp = y4 * t_1
	elif y3 <= -2800000.0:
		tmp = c * (i * ((z * t) - (x * y)))
	elif y3 <= -2.35e-141:
		tmp = y2 * (a * ((t * y5) - (x * y1)))
	elif y3 <= -9.6e-254:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	elif y3 <= 4.8e-208:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	elif y3 <= 1.15e-84:
		tmp = ((x * a) - (k * y4)) * (y * b)
	elif y3 <= 3.2e-5:
		tmp = i * (y * ((k * y5) - (x * c)))
	elif y3 <= 4.5e+104:
		tmp = j * (y5 * ((y0 * y3) - (t * i)))
	elif y3 <= 1e+171:
		tmp = y4 * (((b * ((t * j) - (y * k))) + t_1) + (c * ((y * y3) - (t * y2))))
	else:
		tmp = y0 * (j * ((y3 * y5) - (x * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))
	tmp = 0.0
	if (y3 <= -8e+116)
		tmp = Float64(y4 * t_1);
	elseif (y3 <= -2800000.0)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (y3 <= -2.35e-141)
		tmp = Float64(y2 * Float64(a * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (y3 <= -9.6e-254)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y3 <= 4.8e-208)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (y3 <= 1.15e-84)
		tmp = Float64(Float64(Float64(x * a) - Float64(k * y4)) * Float64(y * b));
	elseif (y3 <= 3.2e-5)
		tmp = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))));
	elseif (y3 <= 4.5e+104)
		tmp = Float64(j * Float64(y5 * Float64(Float64(y0 * y3) - Float64(t * i))));
	elseif (y3 <= 1e+171)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + t_1) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	else
		tmp = Float64(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y1 * ((k * y2) - (j * y3));
	tmp = 0.0;
	if (y3 <= -8e+116)
		tmp = y4 * t_1;
	elseif (y3 <= -2800000.0)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (y3 <= -2.35e-141)
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	elseif (y3 <= -9.6e-254)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	elseif (y3 <= 4.8e-208)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	elseif (y3 <= 1.15e-84)
		tmp = ((x * a) - (k * y4)) * (y * b);
	elseif (y3 <= 3.2e-5)
		tmp = i * (y * ((k * y5) - (x * c)));
	elseif (y3 <= 4.5e+104)
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	elseif (y3 <= 1e+171)
		tmp = y4 * (((b * ((t * j) - (y * k))) + t_1) + (c * ((y * y3) - (t * y2))));
	else
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -8e+116], N[(y4 * t$95$1), $MachinePrecision], If[LessEqual[y3, -2800000.0], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -2.35e-141], N[(y2 * N[(a * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -9.6e-254], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 4.8e-208], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.15e-84], N[(N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision] * N[(y * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 3.2e-5], N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 4.5e+104], N[(j * N[(y5 * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1e+171], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y3 < -8.00000000000000012e116

   1. Initial program 11.8%

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

      1. associate-+l- 11.8%

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

   3. Simplified 11.8%

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

   4. Taylor expanded in y4 around inf 44.4%

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

   5. Taylor expanded in y1 around inf 59.2%

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

   if -8.00000000000000012e116 < y3 < -2.8e6

   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. Step-by-step derivation

      1. associate-+l- 30.4%

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

   3. Simplified 30.4%

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

   4. Taylor expanded in c around inf 71.3%

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

   5. Taylor expanded in i around inf 60.7%

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

      1. associate-*r* 60.7%

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

      2. neg-mul-1 60.7%

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

   7. Simplified 60.7%

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

   if -2.8e6 < y3 < -2.3499999999999999e-141

   1. Initial program 31.5%

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

      1. associate-+l- 31.5%

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

   3. Simplified 31.5%

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

   4. Taylor expanded in y2 around inf 48.7%

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

   5. Taylor expanded in a around -inf 55.3%

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

      1. mul-1-neg 55.3%

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

      2. associate-*r* 55.4%

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

      3. *-commutative 55.4%

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

   7. Simplified 55.4%

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

   if -2.3499999999999999e-141 < y3 < -9.60000000000000007e-254

   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. Step-by-step derivation

      1. associate-+l- 29.0%

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

   3. Simplified 29.0%

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

   4. Taylor expanded in x around inf 58.8%

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

   if -9.60000000000000007e-254 < y3 < 4.7999999999999998e-208

   1. Initial program 36.9%

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

      1. associate-+l- 36.9%

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

   3. Simplified 36.9%

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

   4. Taylor expanded in y4 around inf 43.2%

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

   5. Taylor expanded in t around inf 50.2%

      \[\leadsto y4 \cdot \color{blue}{\left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 50.2%

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

      2. *-commutative 50.2%

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

   7. Simplified 50.2%

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

   if 4.7999999999999998e-208 < y3 < 1.1499999999999999e-84

   1. Initial program 42.6%

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

      1. associate-+l- 42.6%

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

   3. Simplified 42.6%

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

   4. Taylor expanded in b around inf 31.3%

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

   5. Taylor expanded in y around inf 54.8%

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

   if 1.1499999999999999e-84 < y3 < 3.19999999999999986e-5

   1. Initial program 15.8%

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

      1. associate-+l- 15.8%

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

   3. Simplified 15.8%

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

   4. Taylor expanded in i around -inf 42.5%

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

   5. Taylor expanded in y around inf 59.0%

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

      1. +-commutative 59.0%

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

      2. mul-1-neg 59.0%

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

      3. unsub-neg 59.0%

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

      4. *-commutative 59.0%

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

   7. Simplified 59.0%

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

   if 3.19999999999999986e-5 < y3 < 4.4999999999999998e104

   1. Initial program 17.3%

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

      1. +-commutative 17.3%

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

      2. fma-def 21.7%

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

      3. *-commutative 21.7%

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

      4. *-commutative 21.7%

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

   3. Simplified 21.7%

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

   4. Taylor expanded in j around inf 48.1%

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

   5. Taylor expanded in y5 around inf 53.0%

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

      1. *-commutative 53.0%

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

      2. mul-1-neg 53.0%

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

      3. unsub-neg 53.0%

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

      4. *-commutative 53.0%

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

   7. Simplified 53.0%

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

   if 4.4999999999999998e104 < y3 < 9.99999999999999954e170

   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. Step-by-step derivation

      1. associate-+l- 31.8%

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

   3. Simplified 31.8%

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

   4. Taylor expanded in y4 around inf 62.5%

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

   if 9.99999999999999954e170 < y3

   1. Initial program 10.3%

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

      1. +-commutative 10.3%

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

      2. fma-def 10.3%

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

      3. *-commutative 10.3%

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

      4. *-commutative 10.3%

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

   3. Simplified 13.8%

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

   4. Taylor expanded in j around inf 35.2%

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

   5. Taylor expanded in y0 around inf 62.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(y3 \cdot y5 - b \cdot x\right) \cdot j\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -8 \cdot 10^{+116}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq -2800000:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y3 \leq -2.35 \cdot 10^{-141}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq -9.6 \cdot 10^{-254}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 4.8 \cdot 10^{-208}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 1.15 \cdot 10^{-84}:\\ \;\;\;\;\left(x \cdot a - k \cdot y4\right) \cdot \left(y \cdot b\right)\\ \mathbf{elif}\;y3 \leq 3.2 \cdot 10^{-5}:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;y3 \leq 4.5 \cdot 10^{+104}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;y3 \leq 10^{+171}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \]

Alternative 10: 39.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot y5 - c \cdot y4\\ t_2 := y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot t_1\right)\\ \mathbf{if}\;y2 \leq -9000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq -1.75 \cdot 10^{-249}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -3.6 \cdot 10^{-308}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 3.8 \cdot 10^{-225}:\\ \;\;\;\;\left(x \cdot b\right) \cdot \left(y \cdot a - j \cdot y0\right)\\ \mathbf{elif}\;y2 \leq 310000:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 4.8 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 8.6 \cdot 10^{+114}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 8 \cdot 10^{+211}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y2 \cdot t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a y5) (* c y4)))
        (t_2
         (*
          y2
          (+
           (+ (* x (- (* c y0) (* a y1))) (* k (- (* y1 y4) (* y0 y5))))
           (* t t_1)))))
   (if (<= y2 -9000000000.0)
     t_2
     (if (<= y2 -1.75e-249)
       (*
        y5
        (+
         (* i (- (* y k) (* t j)))
         (+ (* a (- (* t y2) (* y y3))) (* y0 (- (* j y3) (* k y2))))))
       (if (<= y2 -3.6e-308)
         (* k (* z (- (* b y0) (* i y1))))
         (if (<= y2 3.8e-225)
           (* (* x b) (- (* y a) (* j y0)))
           (if (<= y2 310000.0)
             (* y0 (* j (- (* y3 y5) (* x b))))
             (if (<= y2 4.8e+51)
               t_2
               (if (<= y2 8.6e+114)
                 (* j (* x (- (* i y1) (* b y0))))
                 (if (<= y2 8e+211) t_2 (* t (* y2 t_1))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y5) - (c * y4);
	double t_2 = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_1));
	double tmp;
	if (y2 <= -9000000000.0) {
		tmp = t_2;
	} else if (y2 <= -1.75e-249) {
		tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y2 <= -3.6e-308) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (y2 <= 3.8e-225) {
		tmp = (x * b) * ((y * a) - (j * y0));
	} else if (y2 <= 310000.0) {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	} else if (y2 <= 4.8e+51) {
		tmp = t_2;
	} else if (y2 <= 8.6e+114) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y2 <= 8e+211) {
		tmp = t_2;
	} else {
		tmp = t * (y2 * t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * y5) - (c * y4)
    t_2 = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_1))
    if (y2 <= (-9000000000.0d0)) then
        tmp = t_2
    else if (y2 <= (-1.75d-249)) then
        tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))))
    else if (y2 <= (-3.6d-308)) then
        tmp = k * (z * ((b * y0) - (i * y1)))
    else if (y2 <= 3.8d-225) then
        tmp = (x * b) * ((y * a) - (j * y0))
    else if (y2 <= 310000.0d0) then
        tmp = y0 * (j * ((y3 * y5) - (x * b)))
    else if (y2 <= 4.8d+51) then
        tmp = t_2
    else if (y2 <= 8.6d+114) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (y2 <= 8d+211) then
        tmp = t_2
    else
        tmp = t * (y2 * 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 * y5) - (c * y4);
	double t_2 = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_1));
	double tmp;
	if (y2 <= -9000000000.0) {
		tmp = t_2;
	} else if (y2 <= -1.75e-249) {
		tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y2 <= -3.6e-308) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (y2 <= 3.8e-225) {
		tmp = (x * b) * ((y * a) - (j * y0));
	} else if (y2 <= 310000.0) {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	} else if (y2 <= 4.8e+51) {
		tmp = t_2;
	} else if (y2 <= 8.6e+114) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y2 <= 8e+211) {
		tmp = t_2;
	} else {
		tmp = t * (y2 * 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 * y5) - (c * y4)
	t_2 = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_1))
	tmp = 0
	if y2 <= -9000000000.0:
		tmp = t_2
	elif y2 <= -1.75e-249:
		tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))))
	elif y2 <= -3.6e-308:
		tmp = k * (z * ((b * y0) - (i * y1)))
	elif y2 <= 3.8e-225:
		tmp = (x * b) * ((y * a) - (j * y0))
	elif y2 <= 310000.0:
		tmp = y0 * (j * ((y3 * y5) - (x * b)))
	elif y2 <= 4.8e+51:
		tmp = t_2
	elif y2 <= 8.6e+114:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif y2 <= 8e+211:
		tmp = t_2
	else:
		tmp = t * (y2 * 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(a * y5) - Float64(c * y4))
	t_2 = Float64(y2 * Float64(Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * t_1)))
	tmp = 0.0
	if (y2 <= -9000000000.0)
		tmp = t_2;
	elseif (y2 <= -1.75e-249)
		tmp = Float64(y5 * Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))));
	elseif (y2 <= -3.6e-308)
		tmp = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))));
	elseif (y2 <= 3.8e-225)
		tmp = Float64(Float64(x * b) * Float64(Float64(y * a) - Float64(j * y0)));
	elseif (y2 <= 310000.0)
		tmp = Float64(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (y2 <= 4.8e+51)
		tmp = t_2;
	elseif (y2 <= 8.6e+114)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (y2 <= 8e+211)
		tmp = t_2;
	else
		tmp = Float64(t * Float64(y2 * 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 * y5) - (c * y4);
	t_2 = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_1));
	tmp = 0.0;
	if (y2 <= -9000000000.0)
		tmp = t_2;
	elseif (y2 <= -1.75e-249)
		tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	elseif (y2 <= -3.6e-308)
		tmp = k * (z * ((b * y0) - (i * y1)));
	elseif (y2 <= 3.8e-225)
		tmp = (x * b) * ((y * a) - (j * y0));
	elseif (y2 <= 310000.0)
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	elseif (y2 <= 4.8e+51)
		tmp = t_2;
	elseif (y2 <= 8.6e+114)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (y2 <= 8e+211)
		tmp = t_2;
	else
		tmp = t * (y2 * 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[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y2 * N[(N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -9000000000.0], t$95$2, If[LessEqual[y2, -1.75e-249], N[(y5 * N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -3.6e-308], N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.8e-225], N[(N[(x * b), $MachinePrecision] * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 310000.0], N[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.8e+51], t$95$2, If[LessEqual[y2, 8.6e+114], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 8e+211], t$95$2, N[(t * N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y2 < -9e9 or 3.1e5 < y2 < 4.7999999999999997e51 or 8.6000000000000001e114 < y2 < 7.9999999999999997e211

   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. Step-by-step derivation

      1. associate-+l- 25.0%

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

   3. Simplified 25.0%

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

   4. Taylor expanded in y2 around inf 69.9%

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

   if -9e9 < y2 < -1.75000000000000006e-249

   1. Initial program 24.7%

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

      1. associate-+l- 24.7%

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

   3. Simplified 24.7%

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

   4. Taylor expanded in y5 around -inf 46.7%

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

      1. mul-1-neg 46.7%

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

      2. associate--l+ 46.7%

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

      3. *-commutative 46.7%

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

   6. Simplified 46.7%

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

   if -1.75000000000000006e-249 < y2 < -3.5999999999999999e-308

   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. Step-by-step derivation

      1. associate-+l- 23.5%

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

   3. Simplified 23.5%

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

   4. Taylor expanded in z around -inf 39.2%

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

      1. mul-1-neg 39.2%

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

      2. *-commutative 39.2%

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

      3. associate--l+ 39.2%

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

      4. *-commutative 39.2%

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

      5. *-commutative 39.2%

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

      6. *-commutative 39.2%

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

      7. *-commutative 39.2%

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

      8. *-commutative 39.2%

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

      9. *-commutative 39.2%

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

      10. *-commutative 39.2%

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

      11. *-commutative 39.2%

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

   6. Simplified 39.2%

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

   7. Taylor expanded in k around inf 62.3%

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

   if -3.5999999999999999e-308 < y2 < 3.8000000000000003e-225

   1. Initial program 63.3%

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

      1. associate-+l- 63.3%

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

   3. Simplified 63.3%

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

   4. Taylor expanded in b around inf 37.7%

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

   5. Taylor expanded in x around inf 50.8%

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

   if 3.8000000000000003e-225 < y2 < 3.1e5

   1. Initial program 30.7%

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

      1. +-commutative 30.7%

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

      2. fma-def 32.7%

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

      3. *-commutative 32.7%

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

      4. *-commutative 32.7%

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

   3. Simplified 36.5%

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

   4. Taylor expanded in j around inf 41.4%

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

   5. Taylor expanded in y0 around inf 50.7%

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

   if 4.7999999999999997e51 < y2 < 8.6000000000000001e114

   1. Initial program 16.7%

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

      1. +-commutative 16.7%

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

      2. fma-def 25.0%

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

      3. *-commutative 25.0%

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

      4. *-commutative 25.0%

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

   3. Simplified 25.0%

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

   4. Taylor expanded in j around inf 42.0%

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

   5. Taylor expanded in x around inf 50.9%

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

   if 7.9999999999999997e211 < y2

   1. Initial program 9.5%

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

      1. associate-+l- 9.5%

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

   3. Simplified 9.5%

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

   4. Taylor expanded in y2 around inf 52.7%

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

   5. Taylor expanded in t around -inf 71.8%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 71.8%

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

      2. neg-mul-1 71.8%

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

      3. *-commutative 71.8%

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

   7. Simplified 71.8%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(y2 \cdot \left(y4 \cdot c - a \cdot y5\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -9000000000:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -1.75 \cdot 10^{-249}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -3.6 \cdot 10^{-308}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 3.8 \cdot 10^{-225}:\\ \;\;\;\;\left(x \cdot b\right) \cdot \left(y \cdot a - j \cdot y0\right)\\ \mathbf{elif}\;y2 \leq 310000:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 4.8 \cdot 10^{+51}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 8.6 \cdot 10^{+114}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 8 \cdot 10^{+211}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \]

Alternative 11: 40.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot y5 - c \cdot y4\\ t_2 := y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot t_1\right)\\ t_3 := z \cdot t - x \cdot y\\ t_4 := c \cdot \left(\left(i \cdot t_3 + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;y2 \leq -7.4 \cdot 10^{-31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq -1.4 \cdot 10^{-253}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y2 \leq 1.3 \cdot 10^{-219}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot t_3\right)\right)\\ \mathbf{elif}\;y2 \leq 1.42 \cdot 10^{-117}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 5.6 \cdot 10^{-6}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y2 \leq 5 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y2 \leq 2.9 \cdot 10^{+112}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 2.45 \cdot 10^{+211}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y2 \cdot t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a y5) (* c y4)))
        (t_2
         (*
          y2
          (+
           (+ (* x (- (* c y0) (* a y1))) (* k (- (* y1 y4) (* y0 y5))))
           (* t t_1))))
        (t_3 (- (* z t) (* x y)))
        (t_4
         (*
          c
          (+
           (+ (* i t_3) (* y0 (- (* x y2) (* z y3))))
           (* y4 (- (* y y3) (* t y2)))))))
   (if (<= y2 -7.4e-31)
     t_2
     (if (<= y2 -1.4e-253)
       t_4
       (if (<= y2 1.3e-219)
         (*
          i
          (+
           (* y1 (- (* x j) (* z k)))
           (+ (* y5 (- (* y k) (* t j))) (* c t_3))))
         (if (<= y2 1.42e-117)
           (* y0 (* j (- (* y3 y5) (* x b))))
           (if (<= y2 5.6e-6)
             t_4
             (if (<= y2 5e+51)
               t_2
               (if (<= y2 2.9e+112)
                 (* j (* x (- (* i y1) (* b y0))))
                 (if (<= y2 2.45e+211) t_2 (* t (* y2 t_1))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y5) - (c * y4);
	double t_2 = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_1));
	double t_3 = (z * t) - (x * y);
	double t_4 = c * (((i * t_3) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	double tmp;
	if (y2 <= -7.4e-31) {
		tmp = t_2;
	} else if (y2 <= -1.4e-253) {
		tmp = t_4;
	} else if (y2 <= 1.3e-219) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) + (c * t_3)));
	} else if (y2 <= 1.42e-117) {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	} else if (y2 <= 5.6e-6) {
		tmp = t_4;
	} else if (y2 <= 5e+51) {
		tmp = t_2;
	} else if (y2 <= 2.9e+112) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y2 <= 2.45e+211) {
		tmp = t_2;
	} else {
		tmp = t * (y2 * t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (a * y5) - (c * y4)
    t_2 = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_1))
    t_3 = (z * t) - (x * y)
    t_4 = c * (((i * t_3) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
    if (y2 <= (-7.4d-31)) then
        tmp = t_2
    else if (y2 <= (-1.4d-253)) then
        tmp = t_4
    else if (y2 <= 1.3d-219) then
        tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) + (c * t_3)))
    else if (y2 <= 1.42d-117) then
        tmp = y0 * (j * ((y3 * y5) - (x * b)))
    else if (y2 <= 5.6d-6) then
        tmp = t_4
    else if (y2 <= 5d+51) then
        tmp = t_2
    else if (y2 <= 2.9d+112) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (y2 <= 2.45d+211) then
        tmp = t_2
    else
        tmp = t * (y2 * 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 * y5) - (c * y4);
	double t_2 = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_1));
	double t_3 = (z * t) - (x * y);
	double t_4 = c * (((i * t_3) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	double tmp;
	if (y2 <= -7.4e-31) {
		tmp = t_2;
	} else if (y2 <= -1.4e-253) {
		tmp = t_4;
	} else if (y2 <= 1.3e-219) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) + (c * t_3)));
	} else if (y2 <= 1.42e-117) {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	} else if (y2 <= 5.6e-6) {
		tmp = t_4;
	} else if (y2 <= 5e+51) {
		tmp = t_2;
	} else if (y2 <= 2.9e+112) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y2 <= 2.45e+211) {
		tmp = t_2;
	} else {
		tmp = t * (y2 * 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 * y5) - (c * y4)
	t_2 = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_1))
	t_3 = (z * t) - (x * y)
	t_4 = c * (((i * t_3) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
	tmp = 0
	if y2 <= -7.4e-31:
		tmp = t_2
	elif y2 <= -1.4e-253:
		tmp = t_4
	elif y2 <= 1.3e-219:
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) + (c * t_3)))
	elif y2 <= 1.42e-117:
		tmp = y0 * (j * ((y3 * y5) - (x * b)))
	elif y2 <= 5.6e-6:
		tmp = t_4
	elif y2 <= 5e+51:
		tmp = t_2
	elif y2 <= 2.9e+112:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif y2 <= 2.45e+211:
		tmp = t_2
	else:
		tmp = t * (y2 * 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(a * y5) - Float64(c * y4))
	t_2 = Float64(y2 * Float64(Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * t_1)))
	t_3 = Float64(Float64(z * t) - Float64(x * y))
	t_4 = Float64(c * Float64(Float64(Float64(i * t_3) + Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))))
	tmp = 0.0
	if (y2 <= -7.4e-31)
		tmp = t_2;
	elseif (y2 <= -1.4e-253)
		tmp = t_4;
	elseif (y2 <= 1.3e-219)
		tmp = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(y5 * Float64(Float64(y * k) - Float64(t * j))) + Float64(c * t_3))));
	elseif (y2 <= 1.42e-117)
		tmp = Float64(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (y2 <= 5.6e-6)
		tmp = t_4;
	elseif (y2 <= 5e+51)
		tmp = t_2;
	elseif (y2 <= 2.9e+112)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (y2 <= 2.45e+211)
		tmp = t_2;
	else
		tmp = Float64(t * Float64(y2 * 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 * y5) - (c * y4);
	t_2 = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_1));
	t_3 = (z * t) - (x * y);
	t_4 = c * (((i * t_3) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	tmp = 0.0;
	if (y2 <= -7.4e-31)
		tmp = t_2;
	elseif (y2 <= -1.4e-253)
		tmp = t_4;
	elseif (y2 <= 1.3e-219)
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) + (c * t_3)));
	elseif (y2 <= 1.42e-117)
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	elseif (y2 <= 5.6e-6)
		tmp = t_4;
	elseif (y2 <= 5e+51)
		tmp = t_2;
	elseif (y2 <= 2.9e+112)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (y2 <= 2.45e+211)
		tmp = t_2;
	else
		tmp = t * (y2 * 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[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y2 * N[(N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(c * N[(N[(N[(i * t$95$3), $MachinePrecision] + N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -7.4e-31], t$95$2, If[LessEqual[y2, -1.4e-253], t$95$4, If[LessEqual[y2, 1.3e-219], N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.42e-117], N[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5.6e-6], t$95$4, If[LessEqual[y2, 5e+51], t$95$2, If[LessEqual[y2, 2.9e+112], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.45e+211], t$95$2, N[(t * N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y2 < -7.3999999999999996e-31 or 5.59999999999999975e-6 < y2 < 5e51 or 2.9000000000000002e112 < y2 < 2.4500000000000002e211

   1. Initial program 23.2%

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

      1. associate-+l- 23.2%

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

   3. Simplified 23.2%

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

   4. Taylor expanded in y2 around inf 64.6%

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

   if -7.3999999999999996e-31 < y2 < -1.40000000000000003e-253 or 1.42000000000000001e-117 < y2 < 5.59999999999999975e-6

   1. Initial program 24.9%

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

      1. associate-+l- 24.9%

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

   3. Simplified 24.9%

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

   4. Taylor expanded in c around inf 56.6%

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

   if -1.40000000000000003e-253 < y2 < 1.30000000000000001e-219

   1. Initial program 40.3%

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

      1. associate-+l- 40.3%

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

   3. Simplified 40.3%

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

   4. Taylor expanded in i around -inf 60.6%

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

   if 1.30000000000000001e-219 < y2 < 1.42000000000000001e-117

   1. Initial program 47.5%

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

      1. +-commutative 47.5%

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

      2. fma-def 47.5%

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

      3. *-commutative 47.5%

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

      4. *-commutative 47.5%

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

   3. Simplified 47.5%

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

   4. Taylor expanded in j around inf 43.7%

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

   5. Taylor expanded in y0 around inf 61.9%

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

   if 5e51 < y2 < 2.9000000000000002e112

   1. Initial program 16.7%

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

      1. +-commutative 16.7%

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

      2. fma-def 25.0%

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

      3. *-commutative 25.0%

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

      4. *-commutative 25.0%

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

   3. Simplified 25.0%

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

   4. Taylor expanded in j around inf 42.0%

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

   5. Taylor expanded in x around inf 50.9%

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

   if 2.4500000000000002e211 < y2

   1. Initial program 9.5%

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

      1. associate-+l- 9.5%

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

   3. Simplified 9.5%

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

   4. Taylor expanded in y2 around inf 52.7%

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

   5. Taylor expanded in t around -inf 71.8%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 71.8%

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

      2. neg-mul-1 71.8%

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

      3. *-commutative 71.8%

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

   7. Simplified 71.8%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(y2 \cdot \left(y4 \cdot c - a \cdot y5\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -7.4 \cdot 10^{-31}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -1.4 \cdot 10^{-253}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 1.3 \cdot 10^{-219}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) + c \cdot \left(z \cdot t - x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.42 \cdot 10^{-117}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 5.6 \cdot 10^{-6}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 5 \cdot 10^{+51}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 2.9 \cdot 10^{+112}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 2.45 \cdot 10^{+211}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \]

Alternative 12: 31.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ t_2 := y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{if}\;j \leq -2.36 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.2 \cdot 10^{-162}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-178}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq -1.75 \cdot 10^{-194}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{-306}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{-254}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{-179}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 86000000000000:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 1.12 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{+206}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{+257}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* j (- (* y3 y5) (* x b)))))
        (t_2 (* y1 (* y2 (- (* k y4) (* x a))))))
   (if (<= j -2.36e+39)
     t_1
     (if (<= j -2.2e-162)
       (* (* c y4) (- (* y y3) (* t y2)))
       (if (<= j -6e-178)
         (* y4 (* y1 (- (* k y2) (* j y3))))
         (if (<= j -1.75e-194)
           (* c (* y2 (- (* x y0) (* t y4))))
           (if (<= j 7.2e-306)
             (* b (* y (- (* x a) (* k y4))))
             (if (<= j 3e-254)
               t_2
               (if (<= j 1.05e-179)
                 (* y0 (* y2 (* k (- y5))))
                 (if (<= j 86000000000000.0)
                   (* y4 (* y2 (- (* k y1) (* t c))))
                   (if (<= j 1.12e+77)
                     t_2
                     (if (<= j 3.5e+206)
                       (* j (* y5 (- (* y0 y3) (* t i))))
                       (if (<= j 1.2e+257)
                         (* j (* x (- (* i y1) (* b y0))))
                         t_1)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (j * ((y3 * y5) - (x * b)));
	double t_2 = y1 * (y2 * ((k * y4) - (x * a)));
	double tmp;
	if (j <= -2.36e+39) {
		tmp = t_1;
	} else if (j <= -2.2e-162) {
		tmp = (c * y4) * ((y * y3) - (t * y2));
	} else if (j <= -6e-178) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (j <= -1.75e-194) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (j <= 7.2e-306) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (j <= 3e-254) {
		tmp = t_2;
	} else if (j <= 1.05e-179) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (j <= 86000000000000.0) {
		tmp = y4 * (y2 * ((k * y1) - (t * c)));
	} else if (j <= 1.12e+77) {
		tmp = t_2;
	} else if (j <= 3.5e+206) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (j <= 1.2e+257) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y0 * (j * ((y3 * y5) - (x * b)))
    t_2 = y1 * (y2 * ((k * y4) - (x * a)))
    if (j <= (-2.36d+39)) then
        tmp = t_1
    else if (j <= (-2.2d-162)) then
        tmp = (c * y4) * ((y * y3) - (t * y2))
    else if (j <= (-6d-178)) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else if (j <= (-1.75d-194)) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (j <= 7.2d-306) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (j <= 3d-254) then
        tmp = t_2
    else if (j <= 1.05d-179) then
        tmp = y0 * (y2 * (k * -y5))
    else if (j <= 86000000000000.0d0) then
        tmp = y4 * (y2 * ((k * y1) - (t * c)))
    else if (j <= 1.12d+77) then
        tmp = t_2
    else if (j <= 3.5d+206) then
        tmp = j * (y5 * ((y0 * y3) - (t * i)))
    else if (j <= 1.2d+257) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (j * ((y3 * y5) - (x * b)));
	double t_2 = y1 * (y2 * ((k * y4) - (x * a)));
	double tmp;
	if (j <= -2.36e+39) {
		tmp = t_1;
	} else if (j <= -2.2e-162) {
		tmp = (c * y4) * ((y * y3) - (t * y2));
	} else if (j <= -6e-178) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (j <= -1.75e-194) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (j <= 7.2e-306) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (j <= 3e-254) {
		tmp = t_2;
	} else if (j <= 1.05e-179) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (j <= 86000000000000.0) {
		tmp = y4 * (y2 * ((k * y1) - (t * c)));
	} else if (j <= 1.12e+77) {
		tmp = t_2;
	} else if (j <= 3.5e+206) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (j <= 1.2e+257) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * (j * ((y3 * y5) - (x * b)))
	t_2 = y1 * (y2 * ((k * y4) - (x * a)))
	tmp = 0
	if j <= -2.36e+39:
		tmp = t_1
	elif j <= -2.2e-162:
		tmp = (c * y4) * ((y * y3) - (t * y2))
	elif j <= -6e-178:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	elif j <= -1.75e-194:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif j <= 7.2e-306:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif j <= 3e-254:
		tmp = t_2
	elif j <= 1.05e-179:
		tmp = y0 * (y2 * (k * -y5))
	elif j <= 86000000000000.0:
		tmp = y4 * (y2 * ((k * y1) - (t * c)))
	elif j <= 1.12e+77:
		tmp = t_2
	elif j <= 3.5e+206:
		tmp = j * (y5 * ((y0 * y3) - (t * i)))
	elif j <= 1.2e+257:
		tmp = j * (x * ((i * y1) - (b * y0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))))
	t_2 = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))))
	tmp = 0.0
	if (j <= -2.36e+39)
		tmp = t_1;
	elseif (j <= -2.2e-162)
		tmp = Float64(Float64(c * y4) * Float64(Float64(y * y3) - Float64(t * y2)));
	elseif (j <= -6e-178)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (j <= -1.75e-194)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (j <= 7.2e-306)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (j <= 3e-254)
		tmp = t_2;
	elseif (j <= 1.05e-179)
		tmp = Float64(y0 * Float64(y2 * Float64(k * Float64(-y5))));
	elseif (j <= 86000000000000.0)
		tmp = Float64(y4 * Float64(y2 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (j <= 1.12e+77)
		tmp = t_2;
	elseif (j <= 3.5e+206)
		tmp = Float64(j * Float64(y5 * Float64(Float64(y0 * y3) - Float64(t * i))));
	elseif (j <= 1.2e+257)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y0 * (j * ((y3 * y5) - (x * b)));
	t_2 = y1 * (y2 * ((k * y4) - (x * a)));
	tmp = 0.0;
	if (j <= -2.36e+39)
		tmp = t_1;
	elseif (j <= -2.2e-162)
		tmp = (c * y4) * ((y * y3) - (t * y2));
	elseif (j <= -6e-178)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	elseif (j <= -1.75e-194)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (j <= 7.2e-306)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (j <= 3e-254)
		tmp = t_2;
	elseif (j <= 1.05e-179)
		tmp = y0 * (y2 * (k * -y5));
	elseif (j <= 86000000000000.0)
		tmp = y4 * (y2 * ((k * y1) - (t * c)));
	elseif (j <= 1.12e+77)
		tmp = t_2;
	elseif (j <= 3.5e+206)
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	elseif (j <= 1.2e+257)
		tmp = j * (x * ((i * y1) - (b * y0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.36e+39], t$95$1, If[LessEqual[j, -2.2e-162], N[(N[(c * y4), $MachinePrecision] * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6e-178], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.75e-194], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.2e-306], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3e-254], t$95$2, If[LessEqual[j, 1.05e-179], N[(y0 * N[(y2 * N[(k * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 86000000000000.0], N[(y4 * N[(y2 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.12e+77], t$95$2, If[LessEqual[j, 3.5e+206], N[(j * N[(y5 * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.2e+257], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if j < -2.35999999999999992e39 or 1.2e257 < j

   1. Initial program 24.8%

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

      1. +-commutative 24.8%

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

      2. fma-def 27.7%

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

      3. *-commutative 27.7%

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

      4. *-commutative 27.7%

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

   3. Simplified 32.1%

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

   4. Taylor expanded in j around inf 51.3%

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

   5. Taylor expanded in y0 around inf 51.3%

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

   if -2.35999999999999992e39 < j < -2.1999999999999999e-162

   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. Step-by-step derivation

      1. associate-+l- 30.2%

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

   3. Simplified 30.2%

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

   4. Taylor expanded in y4 around inf 49.4%

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

   5. Taylor expanded in c around inf 46.8%

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

      1. associate-*r* 44.2%

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

      2. *-commutative 44.2%

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

      3. *-commutative 44.2%

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

   7. Simplified 44.2%

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

   if -2.1999999999999999e-162 < j < -5.9999999999999997e-178

   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. Step-by-step derivation

      1. associate-+l- 22.2%

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

   3. Simplified 22.2%

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

   4. Taylor expanded in y4 around inf 66.9%

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

   5. Taylor expanded in y1 around inf 78.0%

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

   if -5.9999999999999997e-178 < j < -1.7500000000000001e-194

   1. Initial program 2.2%

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

      1. associate-+l- 2.2%

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

   3. Simplified 2.2%

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

   4. Taylor expanded in y2 around inf 52.2%

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

   5. Taylor expanded in c around inf 77.2%

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

   if -1.7500000000000001e-194 < j < 7.19999999999999982e-306

   1. Initial program 5.9%

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

      1. associate-+l- 5.9%

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

   3. Simplified 5.9%

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

   4. Taylor expanded in b around inf 52.6%

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

   5. Taylor expanded in y around inf 58.7%

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

      1. associate-*r* 58.7%

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

      2. *-commutative 58.7%

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

      3. *-commutative 58.7%

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

      4. +-commutative 58.7%

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

      5. mul-1-neg 58.7%

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

      6. unsub-neg 58.7%

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

   7. Simplified 58.7%

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

   if 7.19999999999999982e-306 < j < 3.00000000000000012e-254 or 8.6e13 < j < 1.1199999999999999e77

   1. Initial program 35.0%

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

      1. associate-+l- 35.0%

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

   3. Simplified 35.0%

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

   4. Taylor expanded in y2 around inf 36.1%

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

   5. Taylor expanded in y1 around inf 47.1%

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

      1. *-commutative 47.1%

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

      2. +-commutative 47.1%

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

      3. mul-1-neg 47.1%

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

      4. unsub-neg 47.1%

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

   7. Simplified 47.1%

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

   if 3.00000000000000012e-254 < j < 1.0499999999999999e-179

   1. Initial program 11.5%

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

      1. associate-+l- 11.5%

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

   3. Simplified 11.5%

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

   4. Taylor expanded in y2 around inf 61.1%

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

   5. Taylor expanded in y0 around -inf 44.9%

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

      1. associate-*r* 44.9%

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

      2. neg-mul-1 44.9%

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

      3. *-commutative 44.9%

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

      4. mul-1-neg 44.9%

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

      5. unsub-neg 44.9%

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

      6. *-commutative 44.9%

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

   7. Simplified 44.9%

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

   8. Taylor expanded in k around inf 50.8%

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

   if 1.0499999999999999e-179 < j < 8.6e13

   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. Step-by-step derivation

      1. associate-+l- 35.2%

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

   3. Simplified 35.2%

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

   4. Taylor expanded in y2 around inf 45.8%

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

   5. Taylor expanded in y4 around inf 45.4%

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

   if 1.1199999999999999e77 < j < 3.50000000000000014e206

   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. Step-by-step derivation

      1. +-commutative 23.1%

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

      2. fma-def 27.6%

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

      3. *-commutative 27.6%

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

      4. *-commutative 27.6%

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

   3. Simplified 32.1%

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

   4. Taylor expanded in j around inf 59.3%

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

   5. Taylor expanded in y5 around inf 68.7%

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

      1. *-commutative 68.7%

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

      2. mul-1-neg 68.7%

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

      3. unsub-neg 68.7%

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

      4. *-commutative 68.7%

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

   7. Simplified 68.7%

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

   if 3.50000000000000014e206 < j < 1.2e257

   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. Step-by-step derivation

      1. +-commutative 22.2%

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

      2. fma-def 22.2%

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

      3. *-commutative 22.2%

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

      4. *-commutative 22.2%

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

   3. Simplified 22.2%

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

   4. Taylor expanded in j around inf 66.7%

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

   5. Taylor expanded in x around inf 77.8%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]
3. Recombined 10 regimes into one program.

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.36 \cdot 10^{+39}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;j \leq -2.2 \cdot 10^{-162}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-178}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq -1.75 \cdot 10^{-194}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{-306}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{-254}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{-179}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 86000000000000:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 1.12 \cdot 10^{+77}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{+206}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{+257}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \]

Alternative 13: 31.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{if}\;j \leq -3.5 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.6 \cdot 10^{-161}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-181}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq -2.7 \cdot 10^{-194}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 2.25 \cdot 10^{-304}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 2.85 \cdot 10^{-133}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 85000000000000:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{+27}:\\ \;\;\;\;z \cdot \left(\left(c \cdot y0\right) \cdot \left(-y3\right)\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{+77}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{+206}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;j \leq 1.02 \cdot 10^{+259}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* j (- (* y3 y5) (* x b))))))
   (if (<= j -3.5e+39)
     t_1
     (if (<= j -1.6e-161)
       (* (* c y4) (- (* y y3) (* t y2)))
       (if (<= j -3.7e-181)
         (* y4 (* y1 (- (* k y2) (* j y3))))
         (if (<= j -2.7e-194)
           (* c (* y2 (- (* x y0) (* t y4))))
           (if (<= j 2.25e-304)
             (* b (* y (- (* x a) (* k y4))))
             (if (<= j 2.85e-133)
               (* k (* y5 (- (* y i) (* y0 y2))))
               (if (<= j 85000000000000.0)
                 (* y4 (* y2 (- (* k y1) (* t c))))
                 (if (<= j 5e+27)
                   (* z (* (* c y0) (- y3)))
                   (if (<= j 1.5e+77)
                     (* y1 (* y2 (- (* k y4) (* x a))))
                     (if (<= j 1.7e+206)
                       (* j (* y5 (- (* y0 y3) (* t i))))
                       (if (<= j 1.02e+259)
                         (* j (* x (- (* i y1) (* b y0))))
                         t_1)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (j * ((y3 * y5) - (x * b)));
	double tmp;
	if (j <= -3.5e+39) {
		tmp = t_1;
	} else if (j <= -1.6e-161) {
		tmp = (c * y4) * ((y * y3) - (t * y2));
	} else if (j <= -3.7e-181) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (j <= -2.7e-194) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (j <= 2.25e-304) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (j <= 2.85e-133) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (j <= 85000000000000.0) {
		tmp = y4 * (y2 * ((k * y1) - (t * c)));
	} else if (j <= 5e+27) {
		tmp = z * ((c * y0) * -y3);
	} else if (j <= 1.5e+77) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (j <= 1.7e+206) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (j <= 1.02e+259) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y0 * (j * ((y3 * y5) - (x * b)))
    if (j <= (-3.5d+39)) then
        tmp = t_1
    else if (j <= (-1.6d-161)) then
        tmp = (c * y4) * ((y * y3) - (t * y2))
    else if (j <= (-3.7d-181)) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else if (j <= (-2.7d-194)) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (j <= 2.25d-304) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (j <= 2.85d-133) then
        tmp = k * (y5 * ((y * i) - (y0 * y2)))
    else if (j <= 85000000000000.0d0) then
        tmp = y4 * (y2 * ((k * y1) - (t * c)))
    else if (j <= 5d+27) then
        tmp = z * ((c * y0) * -y3)
    else if (j <= 1.5d+77) then
        tmp = y1 * (y2 * ((k * y4) - (x * a)))
    else if (j <= 1.7d+206) then
        tmp = j * (y5 * ((y0 * y3) - (t * i)))
    else if (j <= 1.02d+259) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (j * ((y3 * y5) - (x * b)));
	double tmp;
	if (j <= -3.5e+39) {
		tmp = t_1;
	} else if (j <= -1.6e-161) {
		tmp = (c * y4) * ((y * y3) - (t * y2));
	} else if (j <= -3.7e-181) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (j <= -2.7e-194) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (j <= 2.25e-304) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (j <= 2.85e-133) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (j <= 85000000000000.0) {
		tmp = y4 * (y2 * ((k * y1) - (t * c)));
	} else if (j <= 5e+27) {
		tmp = z * ((c * y0) * -y3);
	} else if (j <= 1.5e+77) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (j <= 1.7e+206) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (j <= 1.02e+259) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * (j * ((y3 * y5) - (x * b)))
	tmp = 0
	if j <= -3.5e+39:
		tmp = t_1
	elif j <= -1.6e-161:
		tmp = (c * y4) * ((y * y3) - (t * y2))
	elif j <= -3.7e-181:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	elif j <= -2.7e-194:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif j <= 2.25e-304:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif j <= 2.85e-133:
		tmp = k * (y5 * ((y * i) - (y0 * y2)))
	elif j <= 85000000000000.0:
		tmp = y4 * (y2 * ((k * y1) - (t * c)))
	elif j <= 5e+27:
		tmp = z * ((c * y0) * -y3)
	elif j <= 1.5e+77:
		tmp = y1 * (y2 * ((k * y4) - (x * a)))
	elif j <= 1.7e+206:
		tmp = j * (y5 * ((y0 * y3) - (t * i)))
	elif j <= 1.02e+259:
		tmp = j * (x * ((i * y1) - (b * y0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))))
	tmp = 0.0
	if (j <= -3.5e+39)
		tmp = t_1;
	elseif (j <= -1.6e-161)
		tmp = Float64(Float64(c * y4) * Float64(Float64(y * y3) - Float64(t * y2)));
	elseif (j <= -3.7e-181)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (j <= -2.7e-194)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (j <= 2.25e-304)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (j <= 2.85e-133)
		tmp = Float64(k * Float64(y5 * Float64(Float64(y * i) - Float64(y0 * y2))));
	elseif (j <= 85000000000000.0)
		tmp = Float64(y4 * Float64(y2 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (j <= 5e+27)
		tmp = Float64(z * Float64(Float64(c * y0) * Float64(-y3)));
	elseif (j <= 1.5e+77)
		tmp = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (j <= 1.7e+206)
		tmp = Float64(j * Float64(y5 * Float64(Float64(y0 * y3) - Float64(t * i))));
	elseif (j <= 1.02e+259)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y0 * (j * ((y3 * y5) - (x * b)));
	tmp = 0.0;
	if (j <= -3.5e+39)
		tmp = t_1;
	elseif (j <= -1.6e-161)
		tmp = (c * y4) * ((y * y3) - (t * y2));
	elseif (j <= -3.7e-181)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	elseif (j <= -2.7e-194)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (j <= 2.25e-304)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (j <= 2.85e-133)
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	elseif (j <= 85000000000000.0)
		tmp = y4 * (y2 * ((k * y1) - (t * c)));
	elseif (j <= 5e+27)
		tmp = z * ((c * y0) * -y3);
	elseif (j <= 1.5e+77)
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	elseif (j <= 1.7e+206)
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	elseif (j <= 1.02e+259)
		tmp = j * (x * ((i * y1) - (b * y0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.5e+39], t$95$1, If[LessEqual[j, -1.6e-161], N[(N[(c * y4), $MachinePrecision] * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.7e-181], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.7e-194], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.25e-304], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.85e-133], N[(k * N[(y5 * N[(N[(y * i), $MachinePrecision] - N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 85000000000000.0], N[(y4 * N[(y2 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5e+27], N[(z * N[(N[(c * y0), $MachinePrecision] * (-y3)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.5e+77], N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.7e+206], N[(j * N[(y5 * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.02e+259], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if j < -3.5000000000000002e39 or 1.02000000000000007e259 < j

   1. Initial program 24.8%

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

      1. +-commutative 24.8%

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

      2. fma-def 27.7%

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

      3. *-commutative 27.7%

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

      4. *-commutative 27.7%

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

   3. Simplified 32.1%

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

   4. Taylor expanded in j around inf 51.3%

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

   5. Taylor expanded in y0 around inf 51.3%

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

   if -3.5000000000000002e39 < j < -1.59999999999999993e-161

   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. Step-by-step derivation

      1. associate-+l- 30.2%

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

   3. Simplified 30.2%

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

   4. Taylor expanded in y4 around inf 49.4%

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

   5. Taylor expanded in c around inf 46.8%

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

      1. associate-*r* 44.2%

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

      2. *-commutative 44.2%

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

      3. *-commutative 44.2%

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

   7. Simplified 44.2%

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

   if -1.59999999999999993e-161 < j < -3.69999999999999984e-181

   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. Step-by-step derivation

      1. associate-+l- 22.2%

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

   3. Simplified 22.2%

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

   4. Taylor expanded in y4 around inf 66.9%

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

   5. Taylor expanded in y1 around inf 78.0%

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

   if -3.69999999999999984e-181 < j < -2.7e-194

   1. Initial program 2.2%

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

      1. associate-+l- 2.2%

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

   3. Simplified 2.2%

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

   4. Taylor expanded in y2 around inf 52.2%

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

   5. Taylor expanded in c around inf 77.2%

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

   if -2.7e-194 < j < 2.2499999999999999e-304

   1. Initial program 5.9%

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

      1. associate-+l- 5.9%

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

   3. Simplified 5.9%

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

   4. Taylor expanded in b around inf 52.6%

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

   5. Taylor expanded in y around inf 58.7%

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

      1. associate-*r* 58.7%

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

      2. *-commutative 58.7%

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

      3. *-commutative 58.7%

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

      4. +-commutative 58.7%

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

      5. mul-1-neg 58.7%

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

      6. unsub-neg 58.7%

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

   7. Simplified 58.7%

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

   if 2.2499999999999999e-304 < j < 2.84999999999999985e-133

   1. Initial program 25.1%

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

      1. associate-+l- 25.1%

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

   3. Simplified 25.1%

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

   4. Taylor expanded in y5 around -inf 43.8%

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

      1. mul-1-neg 43.8%

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

      2. associate--l+ 43.8%

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

      3. *-commutative 43.8%

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

   6. Simplified 43.8%

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

   7. Taylor expanded in k around inf 37.5%

      \[\leadsto -\color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)} \]
   8. Step-by-step derivation

      1. *-commutative 37.5%

         \[\leadsto -k \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right)\right)} \]

      2. +-commutative 37.5%

         \[\leadsto -k \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(y \cdot i\right)\right)}\right) \]

      3. mul-1-neg 37.5%

         \[\leadsto -k \cdot \left(y5 \cdot \left(y0 \cdot y2 + \color{blue}{\left(-y \cdot i\right)}\right)\right) \]

      4. unsub-neg 37.5%

         \[\leadsto -k \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 - y \cdot i\right)}\right) \]

      5. *-commutative 37.5%

         \[\leadsto -k \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot y0} - y \cdot i\right)\right) \]

   9. Simplified 37.5%

      \[\leadsto -\color{blue}{k \cdot \left(y5 \cdot \left(y2 \cdot y0 - y \cdot i\right)\right)} \]

   if 2.84999999999999985e-133 < j < 8.5e13

   1. Initial program 35.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 35.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 35.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 42.1%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y4 around inf 53.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(k \cdot y1 - c \cdot t\right) \cdot y2\right)} \]

   if 8.5e13 < j < 4.99999999999999979e27

   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. Step-by-step derivation

      1. associate-+l- 0.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 42.9%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.9%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. *-commutative 42.9%

         \[\leadsto -\color{blue}{z \cdot \left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \]

      3. associate--l+ 42.9%

         \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \]

      4. *-commutative 42.9%

         \[\leadsto -z \cdot \left(\color{blue}{y3 \cdot \left(c \cdot y0 - a \cdot y1\right)} + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      5. *-commutative 42.9%

         \[\leadsto -z \cdot \left(y3 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      6. *-commutative 42.9%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      7. *-commutative 42.9%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      8. *-commutative 42.9%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - \color{blue}{i \cdot c}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      9. *-commutative 42.9%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - \color{blue}{k \cdot \left(y0 \cdot b - y1 \cdot i\right)}\right)\right) \]

      10. *-commutative 42.9%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(\color{blue}{b \cdot y0} - y1 \cdot i\right)\right)\right) \]

      11. *-commutative 42.9%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right)\right) \]

   6. Simplified 42.9%

      \[\leadsto \color{blue}{-z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in y3 around inf 85.9%

      \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3\right)} \]
   8. Step-by-step derivation

      1. *-commutative 85.9%

         \[\leadsto -z \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y3\right) \]

   9. Simplified 85.9%

      \[\leadsto -z \cdot \color{blue}{\left(\left(y0 \cdot c - a \cdot y1\right) \cdot y3\right)} \]

   10. Taylor expanded in y0 around inf 85.9%

       \[\leadsto -z \cdot \left(\color{blue}{\left(c \cdot y0\right)} \cdot y3\right) \]
   11. Step-by-step derivation

       1. *-commutative 85.9%

          \[\leadsto -z \cdot \left(\color{blue}{\left(y0 \cdot c\right)} \cdot y3\right) \]

   12. Simplified 85.9%

       \[\leadsto -z \cdot \left(\color{blue}{\left(y0 \cdot c\right)} \cdot y3\right) \]

   if 4.99999999999999979e27 < j < 1.4999999999999999e77

   1. Initial program 53.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 53.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 53.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 54.4%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y1 around inf 61.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right) \cdot y2\right)} \]
   6. Step-by-step derivation

      1. *-commutative 61.9%

         \[\leadsto y1 \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]

      2. +-commutative 61.9%

         \[\leadsto y1 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y4 + -1 \cdot \left(a \cdot x\right)\right)}\right) \]

      3. mul-1-neg 61.9%

         \[\leadsto y1 \cdot \left(y2 \cdot \left(k \cdot y4 + \color{blue}{\left(-a \cdot x\right)}\right)\right) \]

      4. unsub-neg 61.9%

         \[\leadsto y1 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y4 - a \cdot x\right)}\right) \]

   7. Simplified 61.9%

      \[\leadsto \color{blue}{y1 \cdot \left(y2 \cdot \left(k \cdot y4 - a \cdot x\right)\right)} \]

   if 1.4999999999999999e77 < j < 1.69999999999999999e206

   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. Step-by-step derivation

      1. +-commutative 23.1%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 27.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 27.6%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 27.6%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 32.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 59.3%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y5 around inf 68.7%

      \[\leadsto \color{blue}{\left(\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot y5\right)} \cdot j \]
   6. Step-by-step derivation

      1. *-commutative 68.7%

         \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)\right)} \cdot j \]

      2. mul-1-neg 68.7%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \cdot j \]

      3. unsub-neg 68.7%

         \[\leadsto \left(y5 \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \cdot j \]

      4. *-commutative 68.7%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 - \color{blue}{t \cdot i}\right)\right) \cdot j \]

   7. Simplified 68.7%

      \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)} \cdot j \]

   if 1.69999999999999999e206 < j < 1.02000000000000007e259

   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. Step-by-step derivation

      1. +-commutative 22.2%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 22.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 22.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 22.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 22.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 66.7%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in x around inf 77.8%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]
3. Recombined 11 regimes into one program.

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.5 \cdot 10^{+39}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;j \leq -1.6 \cdot 10^{-161}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-181}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq -2.7 \cdot 10^{-194}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 2.25 \cdot 10^{-304}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 2.85 \cdot 10^{-133}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 85000000000000:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{+27}:\\ \;\;\;\;z \cdot \left(\left(c \cdot y0\right) \cdot \left(-y3\right)\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{+77}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{+206}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;j \leq 1.02 \cdot 10^{+259}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \]

Alternative 14: 31.7% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ t_2 := y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{if}\;j \leq -4.6 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{-108}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq -1.85 \cdot 10^{-183}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.75 \cdot 10^{-246}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-254}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-179}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.15 \cdot 10^{-40}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 70000000000000:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* j (- (* y3 y5) (* x b)))))
        (t_2 (* y1 (* y2 (- (* k y4) (* x a))))))
   (if (<= j -4.6e+38)
     t_1
     (if (<= j -4.2e-108)
       (* y4 (* t (- (* b j) (* c y2))))
       (if (<= j -1.85e-183)
         t_2
         (if (<= j -1.75e-246)
           (* c (* y2 (- (* x y0) (* t y4))))
           (if (<= j 4.4e-254)
             t_2
             (if (<= j 1.5e-179)
               (* y0 (* y2 (* k (- y5))))
               (if (<= j 2.15e-40)
                 (* y2 (* k (- (* y1 y4) (* y0 y5))))
                 (if (<= j 70000000000000.0)
                   (* c (* y4 (* t (- y2))))
                   (if (<= j 8e+76) 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 = y0 * (j * ((y3 * y5) - (x * b)));
	double t_2 = y1 * (y2 * ((k * y4) - (x * a)));
	double tmp;
	if (j <= -4.6e+38) {
		tmp = t_1;
	} else if (j <= -4.2e-108) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (j <= -1.85e-183) {
		tmp = t_2;
	} else if (j <= -1.75e-246) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (j <= 4.4e-254) {
		tmp = t_2;
	} else if (j <= 1.5e-179) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (j <= 2.15e-40) {
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)));
	} else if (j <= 70000000000000.0) {
		tmp = c * (y4 * (t * -y2));
	} else if (j <= 8e+76) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y0 * (j * ((y3 * y5) - (x * b)))
    t_2 = y1 * (y2 * ((k * y4) - (x * a)))
    if (j <= (-4.6d+38)) then
        tmp = t_1
    else if (j <= (-4.2d-108)) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    else if (j <= (-1.85d-183)) then
        tmp = t_2
    else if (j <= (-1.75d-246)) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (j <= 4.4d-254) then
        tmp = t_2
    else if (j <= 1.5d-179) then
        tmp = y0 * (y2 * (k * -y5))
    else if (j <= 2.15d-40) then
        tmp = y2 * (k * ((y1 * y4) - (y0 * y5)))
    else if (j <= 70000000000000.0d0) then
        tmp = c * (y4 * (t * -y2))
    else if (j <= 8d+76) 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 = y0 * (j * ((y3 * y5) - (x * b)));
	double t_2 = y1 * (y2 * ((k * y4) - (x * a)));
	double tmp;
	if (j <= -4.6e+38) {
		tmp = t_1;
	} else if (j <= -4.2e-108) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (j <= -1.85e-183) {
		tmp = t_2;
	} else if (j <= -1.75e-246) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (j <= 4.4e-254) {
		tmp = t_2;
	} else if (j <= 1.5e-179) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (j <= 2.15e-40) {
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)));
	} else if (j <= 70000000000000.0) {
		tmp = c * (y4 * (t * -y2));
	} else if (j <= 8e+76) {
		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 = y0 * (j * ((y3 * y5) - (x * b)))
	t_2 = y1 * (y2 * ((k * y4) - (x * a)))
	tmp = 0
	if j <= -4.6e+38:
		tmp = t_1
	elif j <= -4.2e-108:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	elif j <= -1.85e-183:
		tmp = t_2
	elif j <= -1.75e-246:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif j <= 4.4e-254:
		tmp = t_2
	elif j <= 1.5e-179:
		tmp = y0 * (y2 * (k * -y5))
	elif j <= 2.15e-40:
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)))
	elif j <= 70000000000000.0:
		tmp = c * (y4 * (t * -y2))
	elif j <= 8e+76:
		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(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))))
	t_2 = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))))
	tmp = 0.0
	if (j <= -4.6e+38)
		tmp = t_1;
	elseif (j <= -4.2e-108)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (j <= -1.85e-183)
		tmp = t_2;
	elseif (j <= -1.75e-246)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (j <= 4.4e-254)
		tmp = t_2;
	elseif (j <= 1.5e-179)
		tmp = Float64(y0 * Float64(y2 * Float64(k * Float64(-y5))));
	elseif (j <= 2.15e-40)
		tmp = Float64(y2 * Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (j <= 70000000000000.0)
		tmp = Float64(c * Float64(y4 * Float64(t * Float64(-y2))));
	elseif (j <= 8e+76)
		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 = y0 * (j * ((y3 * y5) - (x * b)));
	t_2 = y1 * (y2 * ((k * y4) - (x * a)));
	tmp = 0.0;
	if (j <= -4.6e+38)
		tmp = t_1;
	elseif (j <= -4.2e-108)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	elseif (j <= -1.85e-183)
		tmp = t_2;
	elseif (j <= -1.75e-246)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (j <= 4.4e-254)
		tmp = t_2;
	elseif (j <= 1.5e-179)
		tmp = y0 * (y2 * (k * -y5));
	elseif (j <= 2.15e-40)
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)));
	elseif (j <= 70000000000000.0)
		tmp = c * (y4 * (t * -y2));
	elseif (j <= 8e+76)
		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[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4.6e+38], t$95$1, If[LessEqual[j, -4.2e-108], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.85e-183], t$95$2, If[LessEqual[j, -1.75e-246], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.4e-254], t$95$2, If[LessEqual[j, 1.5e-179], N[(y0 * N[(y2 * N[(k * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.15e-40], N[(y2 * N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 70000000000000.0], N[(c * N[(y4 * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8e+76], t$95$2, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -4.6000000000000002e38 or 8.0000000000000004e76 < j

   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. Step-by-step derivation

      1. +-commutative 24.2%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 27.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 27.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 27.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 31.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 54.5%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y0 around inf 53.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(y3 \cdot y5 - b \cdot x\right) \cdot j\right)} \]

   if -4.6000000000000002e38 < j < -4.1999999999999998e-108

   1. Initial program 26.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 26.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 26.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 48.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 42.3%

      \[\leadsto y4 \cdot \color{blue}{\left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 42.3%

         \[\leadsto y4 \cdot \left(t \cdot \left(\color{blue}{j \cdot b} - c \cdot y2\right)\right) \]

      2. *-commutative 42.3%

         \[\leadsto y4 \cdot \left(t \cdot \left(j \cdot b - \color{blue}{y2 \cdot c}\right)\right) \]

   7. Simplified 42.3%

      \[\leadsto y4 \cdot \color{blue}{\left(t \cdot \left(j \cdot b - y2 \cdot c\right)\right)} \]

   if -4.1999999999999998e-108 < j < -1.8499999999999999e-183 or -1.7500000000000001e-246 < j < 4.4000000000000002e-254 or 7e13 < j < 8.0000000000000004e76

   1. Initial program 29.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 29.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 29.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 42.3%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y1 around inf 49.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right) \cdot y2\right)} \]
   6. Step-by-step derivation

      1. *-commutative 49.8%

         \[\leadsto y1 \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]

      2. +-commutative 49.8%

         \[\leadsto y1 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y4 + -1 \cdot \left(a \cdot x\right)\right)}\right) \]

      3. mul-1-neg 49.8%

         \[\leadsto y1 \cdot \left(y2 \cdot \left(k \cdot y4 + \color{blue}{\left(-a \cdot x\right)}\right)\right) \]

      4. unsub-neg 49.8%

         \[\leadsto y1 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y4 - a \cdot x\right)}\right) \]

   7. Simplified 49.8%

      \[\leadsto \color{blue}{y1 \cdot \left(y2 \cdot \left(k \cdot y4 - a \cdot x\right)\right)} \]

   if -1.8499999999999999e-183 < j < -1.7500000000000001e-246

   1. Initial program 8.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 8.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 8.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 31.6%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 40.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   if 4.4000000000000002e-254 < j < 1.50000000000000003e-179

   1. Initial program 11.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 11.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 11.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 61.1%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y0 around -inf 44.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 44.9%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right)} \]

      2. neg-mul-1 44.9%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right) \]

      3. *-commutative 44.9%

         \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(y2 \cdot \left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right)\right)} \]

      4. mul-1-neg 44.9%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 + \color{blue}{\left(-c \cdot x\right)}\right)\right) \]

      5. unsub-neg 44.9%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \]

      6. *-commutative 44.9%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 - \color{blue}{x \cdot c}\right)\right) \]

   7. Simplified 44.9%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 - x \cdot c\right)\right)} \]

   8. Taylor expanded in k around inf 50.8%

      \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y5\right)}\right) \]

   if 1.50000000000000003e-179 < j < 2.1500000000000001e-40

   1. Initial program 31.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 31.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 31.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 44.6%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in k around inf 42.1%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 42.1%

         \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)} \]

      2. *-commutative 42.1%

         \[\leadsto \left(k \cdot y2\right) \cdot \left(\color{blue}{y1 \cdot y4} - y0 \cdot y5\right) \]

   7. Simplified 42.1%

      \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]

   8. Taylor expanded in k around 0 42.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(y4 \cdot y1 - y0 \cdot y5\right) \cdot y2\right)} \]
   9. Step-by-step derivation

      1. *-commutative 42.1%

         \[\leadsto k \cdot \left(\left(y4 \cdot y1 - \color{blue}{y5 \cdot y0}\right) \cdot y2\right) \]

      2. associate-*r* 42.1%

         \[\leadsto \color{blue}{\left(k \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right) \cdot y2} \]

      3. *-commutative 42.1%

         \[\leadsto \color{blue}{y2 \cdot \left(k \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   10. Simplified 42.1%

       \[\leadsto \color{blue}{y2 \cdot \left(k \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   if 2.1500000000000001e-40 < j < 7e13

   1. Initial program 44.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 44.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 44.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 49.3%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 56.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   6. Taylor expanded in y0 around 0 67.0%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 67.0%

         \[\leadsto c \cdot \color{blue}{\left(-y4 \cdot \left(t \cdot y2\right)\right)} \]

      2. *-commutative 67.0%

         \[\leadsto c \cdot \left(-\color{blue}{\left(t \cdot y2\right) \cdot y4}\right) \]

      3. distribute-rgt-neg-in 67.0%

         \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot y2\right) \cdot \left(-y4\right)\right)} \]

   8. Simplified 67.0%

      \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot y2\right) \cdot \left(-y4\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.6 \cdot 10^{+38}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{-108}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq -1.85 \cdot 10^{-183}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;j \leq -1.75 \cdot 10^{-246}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-254}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-179}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.15 \cdot 10^{-40}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 70000000000000:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+76}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \]

Alternative 15: 31.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ t_2 := y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{if}\;j \leq -2.75 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{-129}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-181}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq -8.2 \cdot 10^{-247}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-254}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 10^{-179}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.8 \cdot 10^{-42}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 70000000000000:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* j (- (* y3 y5) (* x b)))))
        (t_2 (* y1 (* y2 (- (* k y4) (* x a))))))
   (if (<= j -2.75e+39)
     t_1
     (if (<= j -4.2e-129)
       (* y4 (* t (- (* b j) (* c y2))))
       (if (<= j -3.7e-181)
         (* y4 (* y1 (- (* k y2) (* j y3))))
         (if (<= j -8.2e-247)
           (* c (* y2 (- (* x y0) (* t y4))))
           (if (<= j 4.4e-254)
             t_2
             (if (<= j 1e-179)
               (* y0 (* y2 (* k (- y5))))
               (if (<= j 1.8e-42)
                 (* y2 (* k (- (* y1 y4) (* y0 y5))))
                 (if (<= j 70000000000000.0)
                   (* c (* y4 (* t (- y2))))
                   (if (<= j 1.1e+77) 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 = y0 * (j * ((y3 * y5) - (x * b)));
	double t_2 = y1 * (y2 * ((k * y4) - (x * a)));
	double tmp;
	if (j <= -2.75e+39) {
		tmp = t_1;
	} else if (j <= -4.2e-129) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (j <= -3.7e-181) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (j <= -8.2e-247) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (j <= 4.4e-254) {
		tmp = t_2;
	} else if (j <= 1e-179) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (j <= 1.8e-42) {
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)));
	} else if (j <= 70000000000000.0) {
		tmp = c * (y4 * (t * -y2));
	} else if (j <= 1.1e+77) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y0 * (j * ((y3 * y5) - (x * b)))
    t_2 = y1 * (y2 * ((k * y4) - (x * a)))
    if (j <= (-2.75d+39)) then
        tmp = t_1
    else if (j <= (-4.2d-129)) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    else if (j <= (-3.7d-181)) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else if (j <= (-8.2d-247)) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (j <= 4.4d-254) then
        tmp = t_2
    else if (j <= 1d-179) then
        tmp = y0 * (y2 * (k * -y5))
    else if (j <= 1.8d-42) then
        tmp = y2 * (k * ((y1 * y4) - (y0 * y5)))
    else if (j <= 70000000000000.0d0) then
        tmp = c * (y4 * (t * -y2))
    else if (j <= 1.1d+77) 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 = y0 * (j * ((y3 * y5) - (x * b)));
	double t_2 = y1 * (y2 * ((k * y4) - (x * a)));
	double tmp;
	if (j <= -2.75e+39) {
		tmp = t_1;
	} else if (j <= -4.2e-129) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (j <= -3.7e-181) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (j <= -8.2e-247) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (j <= 4.4e-254) {
		tmp = t_2;
	} else if (j <= 1e-179) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (j <= 1.8e-42) {
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)));
	} else if (j <= 70000000000000.0) {
		tmp = c * (y4 * (t * -y2));
	} else if (j <= 1.1e+77) {
		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 = y0 * (j * ((y3 * y5) - (x * b)))
	t_2 = y1 * (y2 * ((k * y4) - (x * a)))
	tmp = 0
	if j <= -2.75e+39:
		tmp = t_1
	elif j <= -4.2e-129:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	elif j <= -3.7e-181:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	elif j <= -8.2e-247:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif j <= 4.4e-254:
		tmp = t_2
	elif j <= 1e-179:
		tmp = y0 * (y2 * (k * -y5))
	elif j <= 1.8e-42:
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)))
	elif j <= 70000000000000.0:
		tmp = c * (y4 * (t * -y2))
	elif j <= 1.1e+77:
		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(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))))
	t_2 = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))))
	tmp = 0.0
	if (j <= -2.75e+39)
		tmp = t_1;
	elseif (j <= -4.2e-129)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (j <= -3.7e-181)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (j <= -8.2e-247)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (j <= 4.4e-254)
		tmp = t_2;
	elseif (j <= 1e-179)
		tmp = Float64(y0 * Float64(y2 * Float64(k * Float64(-y5))));
	elseif (j <= 1.8e-42)
		tmp = Float64(y2 * Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (j <= 70000000000000.0)
		tmp = Float64(c * Float64(y4 * Float64(t * Float64(-y2))));
	elseif (j <= 1.1e+77)
		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 = y0 * (j * ((y3 * y5) - (x * b)));
	t_2 = y1 * (y2 * ((k * y4) - (x * a)));
	tmp = 0.0;
	if (j <= -2.75e+39)
		tmp = t_1;
	elseif (j <= -4.2e-129)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	elseif (j <= -3.7e-181)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	elseif (j <= -8.2e-247)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (j <= 4.4e-254)
		tmp = t_2;
	elseif (j <= 1e-179)
		tmp = y0 * (y2 * (k * -y5));
	elseif (j <= 1.8e-42)
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)));
	elseif (j <= 70000000000000.0)
		tmp = c * (y4 * (t * -y2));
	elseif (j <= 1.1e+77)
		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[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.75e+39], t$95$1, If[LessEqual[j, -4.2e-129], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.7e-181], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -8.2e-247], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.4e-254], t$95$2, If[LessEqual[j, 1e-179], N[(y0 * N[(y2 * N[(k * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.8e-42], N[(y2 * N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 70000000000000.0], N[(c * N[(y4 * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.1e+77], t$95$2, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if j < -2.7499999999999999e39 or 1.1e77 < j

   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. Step-by-step derivation

      1. +-commutative 24.2%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 27.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 27.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 27.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 31.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 54.5%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y0 around inf 53.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(y3 \cdot y5 - b \cdot x\right) \cdot j\right)} \]

   if -2.7499999999999999e39 < j < -4.2e-129

   1. Initial program 26.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 26.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 26.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 49.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 43.4%

      \[\leadsto y4 \cdot \color{blue}{\left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 43.4%

         \[\leadsto y4 \cdot \left(t \cdot \left(\color{blue}{j \cdot b} - c \cdot y2\right)\right) \]

      2. *-commutative 43.4%

         \[\leadsto y4 \cdot \left(t \cdot \left(j \cdot b - \color{blue}{y2 \cdot c}\right)\right) \]

   7. Simplified 43.4%

      \[\leadsto y4 \cdot \color{blue}{\left(t \cdot \left(j \cdot b - y2 \cdot c\right)\right)} \]

   if -4.2e-129 < j < -3.69999999999999984e-181

   1. Initial program 33.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 33.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 33.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 60.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 61.1%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]

   if -3.69999999999999984e-181 < j < -8.1999999999999997e-247

   1. Initial program 8.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 8.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 8.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 31.6%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 40.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   if -8.1999999999999997e-247 < j < 4.4000000000000002e-254 or 7e13 < j < 1.1e77

   1. Initial program 28.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 28.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 28.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 43.2%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y1 around inf 47.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right) \cdot y2\right)} \]
   6. Step-by-step derivation

      1. *-commutative 47.9%

         \[\leadsto y1 \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]

      2. +-commutative 47.9%

         \[\leadsto y1 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y4 + -1 \cdot \left(a \cdot x\right)\right)}\right) \]

      3. mul-1-neg 47.9%

         \[\leadsto y1 \cdot \left(y2 \cdot \left(k \cdot y4 + \color{blue}{\left(-a \cdot x\right)}\right)\right) \]

      4. unsub-neg 47.9%

         \[\leadsto y1 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y4 - a \cdot x\right)}\right) \]

   7. Simplified 47.9%

      \[\leadsto \color{blue}{y1 \cdot \left(y2 \cdot \left(k \cdot y4 - a \cdot x\right)\right)} \]

   if 4.4000000000000002e-254 < j < 1e-179

   1. Initial program 11.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 11.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 11.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 61.1%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y0 around -inf 44.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 44.9%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right)} \]

      2. neg-mul-1 44.9%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right) \]

      3. *-commutative 44.9%

         \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(y2 \cdot \left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right)\right)} \]

      4. mul-1-neg 44.9%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 + \color{blue}{\left(-c \cdot x\right)}\right)\right) \]

      5. unsub-neg 44.9%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \]

      6. *-commutative 44.9%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 - \color{blue}{x \cdot c}\right)\right) \]

   7. Simplified 44.9%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 - x \cdot c\right)\right)} \]

   8. Taylor expanded in k around inf 50.8%

      \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y5\right)}\right) \]

   if 1e-179 < j < 1.8000000000000001e-42

   1. Initial program 31.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 31.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 31.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 44.6%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in k around inf 42.1%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 42.1%

         \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)} \]

      2. *-commutative 42.1%

         \[\leadsto \left(k \cdot y2\right) \cdot \left(\color{blue}{y1 \cdot y4} - y0 \cdot y5\right) \]

   7. Simplified 42.1%

      \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]

   8. Taylor expanded in k around 0 42.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(y4 \cdot y1 - y0 \cdot y5\right) \cdot y2\right)} \]
   9. Step-by-step derivation

      1. *-commutative 42.1%

         \[\leadsto k \cdot \left(\left(y4 \cdot y1 - \color{blue}{y5 \cdot y0}\right) \cdot y2\right) \]

      2. associate-*r* 42.1%

         \[\leadsto \color{blue}{\left(k \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right) \cdot y2} \]

      3. *-commutative 42.1%

         \[\leadsto \color{blue}{y2 \cdot \left(k \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   10. Simplified 42.1%

       \[\leadsto \color{blue}{y2 \cdot \left(k \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   if 1.8000000000000001e-42 < j < 7e13

   1. Initial program 44.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 44.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 44.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 49.3%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 56.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   6. Taylor expanded in y0 around 0 67.0%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 67.0%

         \[\leadsto c \cdot \color{blue}{\left(-y4 \cdot \left(t \cdot y2\right)\right)} \]

      2. *-commutative 67.0%

         \[\leadsto c \cdot \left(-\color{blue}{\left(t \cdot y2\right) \cdot y4}\right) \]

      3. distribute-rgt-neg-in 67.0%

         \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot y2\right) \cdot \left(-y4\right)\right)} \]

   8. Simplified 67.0%

      \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot y2\right) \cdot \left(-y4\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.75 \cdot 10^{+39}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{-129}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-181}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq -8.2 \cdot 10^{-247}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-254}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;j \leq 10^{-179}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.8 \cdot 10^{-42}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 70000000000000:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{+77}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \]

Alternative 16: 31.9% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ t_2 := y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{if}\;j \leq -3.2 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.9 \cdot 10^{-129}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq -2.1 \cdot 10^{-183}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq -2.8 \cdot 10^{-194}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-305}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-255}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{-179}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 80000000000000:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 1.02 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* j (- (* y3 y5) (* x b)))))
        (t_2 (* y1 (* y2 (- (* k y4) (* x a))))))
   (if (<= j -3.2e+39)
     t_1
     (if (<= j -1.9e-129)
       (* y4 (* t (- (* b j) (* c y2))))
       (if (<= j -2.1e-183)
         (* y4 (* y1 (- (* k y2) (* j y3))))
         (if (<= j -2.8e-194)
           (* c (* y2 (- (* x y0) (* t y4))))
           (if (<= j 3.8e-305)
             (* b (* y (- (* x a) (* k y4))))
             (if (<= j 6e-255)
               t_2
               (if (<= j 1.35e-179)
                 (* y0 (* y2 (* k (- y5))))
                 (if (<= j 80000000000000.0)
                   (* y4 (* y2 (- (* k y1) (* t c))))
                   (if (<= j 1.02e+77) 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 = y0 * (j * ((y3 * y5) - (x * b)));
	double t_2 = y1 * (y2 * ((k * y4) - (x * a)));
	double tmp;
	if (j <= -3.2e+39) {
		tmp = t_1;
	} else if (j <= -1.9e-129) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (j <= -2.1e-183) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (j <= -2.8e-194) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (j <= 3.8e-305) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (j <= 6e-255) {
		tmp = t_2;
	} else if (j <= 1.35e-179) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (j <= 80000000000000.0) {
		tmp = y4 * (y2 * ((k * y1) - (t * c)));
	} else if (j <= 1.02e+77) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y0 * (j * ((y3 * y5) - (x * b)))
    t_2 = y1 * (y2 * ((k * y4) - (x * a)))
    if (j <= (-3.2d+39)) then
        tmp = t_1
    else if (j <= (-1.9d-129)) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    else if (j <= (-2.1d-183)) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else if (j <= (-2.8d-194)) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (j <= 3.8d-305) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (j <= 6d-255) then
        tmp = t_2
    else if (j <= 1.35d-179) then
        tmp = y0 * (y2 * (k * -y5))
    else if (j <= 80000000000000.0d0) then
        tmp = y4 * (y2 * ((k * y1) - (t * c)))
    else if (j <= 1.02d+77) 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 = y0 * (j * ((y3 * y5) - (x * b)));
	double t_2 = y1 * (y2 * ((k * y4) - (x * a)));
	double tmp;
	if (j <= -3.2e+39) {
		tmp = t_1;
	} else if (j <= -1.9e-129) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (j <= -2.1e-183) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (j <= -2.8e-194) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (j <= 3.8e-305) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (j <= 6e-255) {
		tmp = t_2;
	} else if (j <= 1.35e-179) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (j <= 80000000000000.0) {
		tmp = y4 * (y2 * ((k * y1) - (t * c)));
	} else if (j <= 1.02e+77) {
		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 = y0 * (j * ((y3 * y5) - (x * b)))
	t_2 = y1 * (y2 * ((k * y4) - (x * a)))
	tmp = 0
	if j <= -3.2e+39:
		tmp = t_1
	elif j <= -1.9e-129:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	elif j <= -2.1e-183:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	elif j <= -2.8e-194:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif j <= 3.8e-305:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif j <= 6e-255:
		tmp = t_2
	elif j <= 1.35e-179:
		tmp = y0 * (y2 * (k * -y5))
	elif j <= 80000000000000.0:
		tmp = y4 * (y2 * ((k * y1) - (t * c)))
	elif j <= 1.02e+77:
		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(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))))
	t_2 = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))))
	tmp = 0.0
	if (j <= -3.2e+39)
		tmp = t_1;
	elseif (j <= -1.9e-129)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (j <= -2.1e-183)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (j <= -2.8e-194)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (j <= 3.8e-305)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (j <= 6e-255)
		tmp = t_2;
	elseif (j <= 1.35e-179)
		tmp = Float64(y0 * Float64(y2 * Float64(k * Float64(-y5))));
	elseif (j <= 80000000000000.0)
		tmp = Float64(y4 * Float64(y2 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (j <= 1.02e+77)
		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 = y0 * (j * ((y3 * y5) - (x * b)));
	t_2 = y1 * (y2 * ((k * y4) - (x * a)));
	tmp = 0.0;
	if (j <= -3.2e+39)
		tmp = t_1;
	elseif (j <= -1.9e-129)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	elseif (j <= -2.1e-183)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	elseif (j <= -2.8e-194)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (j <= 3.8e-305)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (j <= 6e-255)
		tmp = t_2;
	elseif (j <= 1.35e-179)
		tmp = y0 * (y2 * (k * -y5));
	elseif (j <= 80000000000000.0)
		tmp = y4 * (y2 * ((k * y1) - (t * c)));
	elseif (j <= 1.02e+77)
		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[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.2e+39], t$95$1, If[LessEqual[j, -1.9e-129], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.1e-183], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.8e-194], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.8e-305], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6e-255], t$95$2, If[LessEqual[j, 1.35e-179], N[(y0 * N[(y2 * N[(k * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 80000000000000.0], N[(y4 * N[(y2 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.02e+77], t$95$2, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if j < -3.19999999999999993e39 or 1.02e77 < j

   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. Step-by-step derivation

      1. +-commutative 24.2%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 27.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 27.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 27.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 31.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 54.5%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y0 around inf 53.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(y3 \cdot y5 - b \cdot x\right) \cdot j\right)} \]

   if -3.19999999999999993e39 < j < -1.89999999999999992e-129

   1. Initial program 26.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 26.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 26.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 49.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 43.4%

      \[\leadsto y4 \cdot \color{blue}{\left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 43.4%

         \[\leadsto y4 \cdot \left(t \cdot \left(\color{blue}{j \cdot b} - c \cdot y2\right)\right) \]

      2. *-commutative 43.4%

         \[\leadsto y4 \cdot \left(t \cdot \left(j \cdot b - \color{blue}{y2 \cdot c}\right)\right) \]

   7. Simplified 43.4%

      \[\leadsto y4 \cdot \color{blue}{\left(t \cdot \left(j \cdot b - y2 \cdot c\right)\right)} \]

   if -1.89999999999999992e-129 < j < -2.1000000000000002e-183

   1. Initial program 33.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 33.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 33.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 60.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 61.1%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]

   if -2.1000000000000002e-183 < j < -2.80000000000000011e-194

   1. Initial program 2.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 2.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 2.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 52.2%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 77.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   if -2.80000000000000011e-194 < j < 3.8e-305

   1. Initial program 5.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 5.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 5.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 52.6%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot b} \]

   5. Taylor expanded in y around inf 58.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot \left(y \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 58.7%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot y\right) \cdot b} \]

      2. *-commutative 58.7%

         \[\leadsto \color{blue}{b \cdot \left(\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot y\right)} \]

      3. *-commutative 58.7%

         \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]

      4. +-commutative 58.7%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      5. mul-1-neg 58.7%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      6. unsub-neg 58.7%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   7. Simplified 58.7%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   if 3.8e-305 < j < 6.00000000000000004e-255 or 8e13 < j < 1.02e77

   1. Initial program 35.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 35.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 35.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 36.1%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y1 around inf 47.1%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right) \cdot y2\right)} \]
   6. Step-by-step derivation

      1. *-commutative 47.1%

         \[\leadsto y1 \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]

      2. +-commutative 47.1%

         \[\leadsto y1 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y4 + -1 \cdot \left(a \cdot x\right)\right)}\right) \]

      3. mul-1-neg 47.1%

         \[\leadsto y1 \cdot \left(y2 \cdot \left(k \cdot y4 + \color{blue}{\left(-a \cdot x\right)}\right)\right) \]

      4. unsub-neg 47.1%

         \[\leadsto y1 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y4 - a \cdot x\right)}\right) \]

   7. Simplified 47.1%

      \[\leadsto \color{blue}{y1 \cdot \left(y2 \cdot \left(k \cdot y4 - a \cdot x\right)\right)} \]

   if 6.00000000000000004e-255 < j < 1.34999999999999994e-179

   1. Initial program 11.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 11.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 11.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 61.1%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y0 around -inf 44.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 44.9%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right)} \]

      2. neg-mul-1 44.9%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right) \]

      3. *-commutative 44.9%

         \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(y2 \cdot \left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right)\right)} \]

      4. mul-1-neg 44.9%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 + \color{blue}{\left(-c \cdot x\right)}\right)\right) \]

      5. unsub-neg 44.9%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \]

      6. *-commutative 44.9%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 - \color{blue}{x \cdot c}\right)\right) \]

   7. Simplified 44.9%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 - x \cdot c\right)\right)} \]

   8. Taylor expanded in k around inf 50.8%

      \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y5\right)}\right) \]

   if 1.34999999999999994e-179 < j < 8e13

   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. Step-by-step derivation

      1. associate-+l- 35.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 35.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 45.8%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y4 around inf 45.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(k \cdot y1 - c \cdot t\right) \cdot y2\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.2 \cdot 10^{+39}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;j \leq -1.9 \cdot 10^{-129}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq -2.1 \cdot 10^{-183}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq -2.8 \cdot 10^{-194}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-305}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-255}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{-179}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 80000000000000:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 1.02 \cdot 10^{+77}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \]

Alternative 17: 32.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ t_2 := y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{if}\;j \leq -6 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.2 \cdot 10^{-162}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-178}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq -9 \cdot 10^{-195}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{-304}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 3.1 \cdot 10^{-254}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-179}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 70000000000000:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* j (- (* y3 y5) (* x b)))))
        (t_2 (* y1 (* y2 (- (* k y4) (* x a))))))
   (if (<= j -6e+38)
     t_1
     (if (<= j -2.2e-162)
       (* (* c y4) (- (* y y3) (* t y2)))
       (if (<= j -3.5e-178)
         (* y4 (* y1 (- (* k y2) (* j y3))))
         (if (<= j -9e-195)
           (* c (* y2 (- (* x y0) (* t y4))))
           (if (<= j 7e-304)
             (* b (* y (- (* x a) (* k y4))))
             (if (<= j 3.1e-254)
               t_2
               (if (<= j 1.7e-179)
                 (* y0 (* y2 (* k (- y5))))
                 (if (<= j 70000000000000.0)
                   (* y4 (* y2 (- (* k y1) (* t c))))
                   (if (<= j 8.5e+76) 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 = y0 * (j * ((y3 * y5) - (x * b)));
	double t_2 = y1 * (y2 * ((k * y4) - (x * a)));
	double tmp;
	if (j <= -6e+38) {
		tmp = t_1;
	} else if (j <= -2.2e-162) {
		tmp = (c * y4) * ((y * y3) - (t * y2));
	} else if (j <= -3.5e-178) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (j <= -9e-195) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (j <= 7e-304) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (j <= 3.1e-254) {
		tmp = t_2;
	} else if (j <= 1.7e-179) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (j <= 70000000000000.0) {
		tmp = y4 * (y2 * ((k * y1) - (t * c)));
	} else if (j <= 8.5e+76) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y0 * (j * ((y3 * y5) - (x * b)))
    t_2 = y1 * (y2 * ((k * y4) - (x * a)))
    if (j <= (-6d+38)) then
        tmp = t_1
    else if (j <= (-2.2d-162)) then
        tmp = (c * y4) * ((y * y3) - (t * y2))
    else if (j <= (-3.5d-178)) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else if (j <= (-9d-195)) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (j <= 7d-304) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (j <= 3.1d-254) then
        tmp = t_2
    else if (j <= 1.7d-179) then
        tmp = y0 * (y2 * (k * -y5))
    else if (j <= 70000000000000.0d0) then
        tmp = y4 * (y2 * ((k * y1) - (t * c)))
    else if (j <= 8.5d+76) 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 = y0 * (j * ((y3 * y5) - (x * b)));
	double t_2 = y1 * (y2 * ((k * y4) - (x * a)));
	double tmp;
	if (j <= -6e+38) {
		tmp = t_1;
	} else if (j <= -2.2e-162) {
		tmp = (c * y4) * ((y * y3) - (t * y2));
	} else if (j <= -3.5e-178) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (j <= -9e-195) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (j <= 7e-304) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (j <= 3.1e-254) {
		tmp = t_2;
	} else if (j <= 1.7e-179) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (j <= 70000000000000.0) {
		tmp = y4 * (y2 * ((k * y1) - (t * c)));
	} else if (j <= 8.5e+76) {
		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 = y0 * (j * ((y3 * y5) - (x * b)))
	t_2 = y1 * (y2 * ((k * y4) - (x * a)))
	tmp = 0
	if j <= -6e+38:
		tmp = t_1
	elif j <= -2.2e-162:
		tmp = (c * y4) * ((y * y3) - (t * y2))
	elif j <= -3.5e-178:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	elif j <= -9e-195:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif j <= 7e-304:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif j <= 3.1e-254:
		tmp = t_2
	elif j <= 1.7e-179:
		tmp = y0 * (y2 * (k * -y5))
	elif j <= 70000000000000.0:
		tmp = y4 * (y2 * ((k * y1) - (t * c)))
	elif j <= 8.5e+76:
		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(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))))
	t_2 = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))))
	tmp = 0.0
	if (j <= -6e+38)
		tmp = t_1;
	elseif (j <= -2.2e-162)
		tmp = Float64(Float64(c * y4) * Float64(Float64(y * y3) - Float64(t * y2)));
	elseif (j <= -3.5e-178)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (j <= -9e-195)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (j <= 7e-304)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (j <= 3.1e-254)
		tmp = t_2;
	elseif (j <= 1.7e-179)
		tmp = Float64(y0 * Float64(y2 * Float64(k * Float64(-y5))));
	elseif (j <= 70000000000000.0)
		tmp = Float64(y4 * Float64(y2 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (j <= 8.5e+76)
		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 = y0 * (j * ((y3 * y5) - (x * b)));
	t_2 = y1 * (y2 * ((k * y4) - (x * a)));
	tmp = 0.0;
	if (j <= -6e+38)
		tmp = t_1;
	elseif (j <= -2.2e-162)
		tmp = (c * y4) * ((y * y3) - (t * y2));
	elseif (j <= -3.5e-178)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	elseif (j <= -9e-195)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (j <= 7e-304)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (j <= 3.1e-254)
		tmp = t_2;
	elseif (j <= 1.7e-179)
		tmp = y0 * (y2 * (k * -y5));
	elseif (j <= 70000000000000.0)
		tmp = y4 * (y2 * ((k * y1) - (t * c)));
	elseif (j <= 8.5e+76)
		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[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6e+38], t$95$1, If[LessEqual[j, -2.2e-162], N[(N[(c * y4), $MachinePrecision] * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.5e-178], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -9e-195], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7e-304], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.1e-254], t$95$2, If[LessEqual[j, 1.7e-179], N[(y0 * N[(y2 * N[(k * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 70000000000000.0], N[(y4 * N[(y2 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.5e+76], t$95$2, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if j < -6.0000000000000002e38 or 8.49999999999999992e76 < j

   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. Step-by-step derivation

      1. +-commutative 24.2%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 27.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 27.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 27.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 31.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 54.5%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y0 around inf 53.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(y3 \cdot y5 - b \cdot x\right) \cdot j\right)} \]

   if -6.0000000000000002e38 < j < -2.1999999999999999e-162

   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. Step-by-step derivation

      1. associate-+l- 30.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 30.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 49.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 46.8%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 44.2%

         \[\leadsto \color{blue}{\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)} \]

      2. *-commutative 44.2%

         \[\leadsto \color{blue}{\left(y4 \cdot c\right)} \cdot \left(y \cdot y3 - t \cdot y2\right) \]

      3. *-commutative 44.2%

         \[\leadsto \left(y4 \cdot c\right) \cdot \left(\color{blue}{y3 \cdot y} - t \cdot y2\right) \]

   7. Simplified 44.2%

      \[\leadsto \color{blue}{\left(y4 \cdot c\right) \cdot \left(y3 \cdot y - t \cdot y2\right)} \]

   if -2.1999999999999999e-162 < j < -3.49999999999999983e-178

   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. Step-by-step derivation

      1. associate-+l- 22.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 22.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 66.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 78.0%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]

   if -3.49999999999999983e-178 < j < -9e-195

   1. Initial program 2.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 2.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 2.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 52.2%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 77.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   if -9e-195 < j < 7e-304

   1. Initial program 5.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 5.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 5.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 52.6%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot b} \]

   5. Taylor expanded in y around inf 58.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot \left(y \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 58.7%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot y\right) \cdot b} \]

      2. *-commutative 58.7%

         \[\leadsto \color{blue}{b \cdot \left(\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot y\right)} \]

      3. *-commutative 58.7%

         \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]

      4. +-commutative 58.7%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      5. mul-1-neg 58.7%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      6. unsub-neg 58.7%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   7. Simplified 58.7%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   if 7e-304 < j < 3.09999999999999988e-254 or 7e13 < j < 8.49999999999999992e76

   1. Initial program 35.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 35.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 35.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 36.1%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y1 around inf 47.1%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right) \cdot y2\right)} \]
   6. Step-by-step derivation

      1. *-commutative 47.1%

         \[\leadsto y1 \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]

      2. +-commutative 47.1%

         \[\leadsto y1 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y4 + -1 \cdot \left(a \cdot x\right)\right)}\right) \]

      3. mul-1-neg 47.1%

         \[\leadsto y1 \cdot \left(y2 \cdot \left(k \cdot y4 + \color{blue}{\left(-a \cdot x\right)}\right)\right) \]

      4. unsub-neg 47.1%

         \[\leadsto y1 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y4 - a \cdot x\right)}\right) \]

   7. Simplified 47.1%

      \[\leadsto \color{blue}{y1 \cdot \left(y2 \cdot \left(k \cdot y4 - a \cdot x\right)\right)} \]

   if 3.09999999999999988e-254 < j < 1.6999999999999999e-179

   1. Initial program 11.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 11.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 11.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 61.1%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y0 around -inf 44.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 44.9%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right)} \]

      2. neg-mul-1 44.9%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right) \]

      3. *-commutative 44.9%

         \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(y2 \cdot \left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right)\right)} \]

      4. mul-1-neg 44.9%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 + \color{blue}{\left(-c \cdot x\right)}\right)\right) \]

      5. unsub-neg 44.9%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \]

      6. *-commutative 44.9%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 - \color{blue}{x \cdot c}\right)\right) \]

   7. Simplified 44.9%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 - x \cdot c\right)\right)} \]

   8. Taylor expanded in k around inf 50.8%

      \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y5\right)}\right) \]

   if 1.6999999999999999e-179 < j < 7e13

   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. Step-by-step derivation

      1. associate-+l- 35.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 35.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 45.8%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y4 around inf 45.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(k \cdot y1 - c \cdot t\right) \cdot y2\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6 \cdot 10^{+38}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;j \leq -2.2 \cdot 10^{-162}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-178}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq -9 \cdot 10^{-195}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{-304}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 3.1 \cdot 10^{-254}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-179}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 70000000000000:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+76}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \]

Alternative 18: 32.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ t_2 := y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{if}\;j \leq -3.25 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -2.4 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.02 \cdot 10^{-166}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq -5 \cdot 10^{-236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{-116}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 68000000000000:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 1.16 \cdot 10^{+77}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{+209}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;j \leq 1.12 \cdot 10^{+250}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* c y4) (- (* y y3) (* t y2))))
        (t_2 (* y0 (* j (- (* y3 y5) (* x b))))))
   (if (<= j -3.25e+38)
     t_2
     (if (<= j -2.4e-162)
       t_1
       (if (<= j -1.02e-166)
         (* y4 (* y1 (- (* k y2) (* j y3))))
         (if (<= j -5e-236)
           t_1
           (if (<= j 2.2e-116)
             (* y2 (* a (- (* t y5) (* x y1))))
             (if (<= j 68000000000000.0)
               (* y4 (* y2 (- (* k y1) (* t c))))
               (if (<= j 1.16e+77)
                 (* y1 (* y2 (- (* k y4) (* x a))))
                 (if (<= j 2e+209)
                   (* j (* y5 (- (* y0 y3) (* t i))))
                   (if (<= j 1.12e+250)
                     (* j (* x (- (* i y1) (* b y0))))
                     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 * y4) * ((y * y3) - (t * y2));
	double t_2 = y0 * (j * ((y3 * y5) - (x * b)));
	double tmp;
	if (j <= -3.25e+38) {
		tmp = t_2;
	} else if (j <= -2.4e-162) {
		tmp = t_1;
	} else if (j <= -1.02e-166) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (j <= -5e-236) {
		tmp = t_1;
	} else if (j <= 2.2e-116) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else if (j <= 68000000000000.0) {
		tmp = y4 * (y2 * ((k * y1) - (t * c)));
	} else if (j <= 1.16e+77) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (j <= 2e+209) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (j <= 1.12e+250) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (c * y4) * ((y * y3) - (t * y2))
    t_2 = y0 * (j * ((y3 * y5) - (x * b)))
    if (j <= (-3.25d+38)) then
        tmp = t_2
    else if (j <= (-2.4d-162)) then
        tmp = t_1
    else if (j <= (-1.02d-166)) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else if (j <= (-5d-236)) then
        tmp = t_1
    else if (j <= 2.2d-116) then
        tmp = y2 * (a * ((t * y5) - (x * y1)))
    else if (j <= 68000000000000.0d0) then
        tmp = y4 * (y2 * ((k * y1) - (t * c)))
    else if (j <= 1.16d+77) then
        tmp = y1 * (y2 * ((k * y4) - (x * a)))
    else if (j <= 2d+209) then
        tmp = j * (y5 * ((y0 * y3) - (t * i)))
    else if (j <= 1.12d+250) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y4) * ((y * y3) - (t * y2));
	double t_2 = y0 * (j * ((y3 * y5) - (x * b)));
	double tmp;
	if (j <= -3.25e+38) {
		tmp = t_2;
	} else if (j <= -2.4e-162) {
		tmp = t_1;
	} else if (j <= -1.02e-166) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (j <= -5e-236) {
		tmp = t_1;
	} else if (j <= 2.2e-116) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else if (j <= 68000000000000.0) {
		tmp = y4 * (y2 * ((k * y1) - (t * c)));
	} else if (j <= 1.16e+77) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (j <= 2e+209) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (j <= 1.12e+250) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * y4) * ((y * y3) - (t * y2))
	t_2 = y0 * (j * ((y3 * y5) - (x * b)))
	tmp = 0
	if j <= -3.25e+38:
		tmp = t_2
	elif j <= -2.4e-162:
		tmp = t_1
	elif j <= -1.02e-166:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	elif j <= -5e-236:
		tmp = t_1
	elif j <= 2.2e-116:
		tmp = y2 * (a * ((t * y5) - (x * y1)))
	elif j <= 68000000000000.0:
		tmp = y4 * (y2 * ((k * y1) - (t * c)))
	elif j <= 1.16e+77:
		tmp = y1 * (y2 * ((k * y4) - (x * a)))
	elif j <= 2e+209:
		tmp = j * (y5 * ((y0 * y3) - (t * i)))
	elif j <= 1.12e+250:
		tmp = j * (x * ((i * y1) - (b * y0)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y4) * Float64(Float64(y * y3) - Float64(t * y2)))
	t_2 = Float64(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))))
	tmp = 0.0
	if (j <= -3.25e+38)
		tmp = t_2;
	elseif (j <= -2.4e-162)
		tmp = t_1;
	elseif (j <= -1.02e-166)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (j <= -5e-236)
		tmp = t_1;
	elseif (j <= 2.2e-116)
		tmp = Float64(y2 * Float64(a * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (j <= 68000000000000.0)
		tmp = Float64(y4 * Float64(y2 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (j <= 1.16e+77)
		tmp = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (j <= 2e+209)
		tmp = Float64(j * Float64(y5 * Float64(Float64(y0 * y3) - Float64(t * i))));
	elseif (j <= 1.12e+250)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (c * y4) * ((y * y3) - (t * y2));
	t_2 = y0 * (j * ((y3 * y5) - (x * b)));
	tmp = 0.0;
	if (j <= -3.25e+38)
		tmp = t_2;
	elseif (j <= -2.4e-162)
		tmp = t_1;
	elseif (j <= -1.02e-166)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	elseif (j <= -5e-236)
		tmp = t_1;
	elseif (j <= 2.2e-116)
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	elseif (j <= 68000000000000.0)
		tmp = y4 * (y2 * ((k * y1) - (t * c)));
	elseif (j <= 1.16e+77)
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	elseif (j <= 2e+209)
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	elseif (j <= 1.12e+250)
		tmp = j * (x * ((i * y1) - (b * y0)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(c * y4), $MachinePrecision] * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.25e+38], t$95$2, If[LessEqual[j, -2.4e-162], t$95$1, If[LessEqual[j, -1.02e-166], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -5e-236], t$95$1, If[LessEqual[j, 2.2e-116], N[(y2 * N[(a * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 68000000000000.0], N[(y4 * N[(y2 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.16e+77], N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2e+209], N[(j * N[(y5 * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.12e+250], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if j < -3.25e38 or 1.12000000000000007e250 < j

   1. Initial program 24.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 24.8%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 27.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 27.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 27.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 32.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 51.3%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y0 around inf 51.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(y3 \cdot y5 - b \cdot x\right) \cdot j\right)} \]

   if -3.25e38 < j < -2.4000000000000002e-162 or -1.02000000000000007e-166 < j < -4.9999999999999998e-236

   1. Initial program 28.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 28.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 28.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 50.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 48.8%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 46.8%

         \[\leadsto \color{blue}{\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)} \]

      2. *-commutative 46.8%

         \[\leadsto \color{blue}{\left(y4 \cdot c\right)} \cdot \left(y \cdot y3 - t \cdot y2\right) \]

      3. *-commutative 46.8%

         \[\leadsto \left(y4 \cdot c\right) \cdot \left(\color{blue}{y3 \cdot y} - t \cdot y2\right) \]

   7. Simplified 46.8%

      \[\leadsto \color{blue}{\left(y4 \cdot c\right) \cdot \left(y3 \cdot y - t \cdot y2\right)} \]

   if -2.4000000000000002e-162 < j < -1.02000000000000007e-166

   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. Step-by-step derivation

      1. associate-+l- 0.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 80.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 100.0%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]

   if -4.9999999999999998e-236 < j < 2.2000000000000001e-116

   1. Initial program 19.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 19.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 19.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 51.7%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in a around -inf 45.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(y1 \cdot x - t \cdot y5\right) \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 45.0%

         \[\leadsto \color{blue}{-a \cdot \left(\left(y1 \cdot x - t \cdot y5\right) \cdot y2\right)} \]

      2. associate-*r* 45.0%

         \[\leadsto -\color{blue}{\left(a \cdot \left(y1 \cdot x - t \cdot y5\right)\right) \cdot y2} \]

      3. *-commutative 45.0%

         \[\leadsto -\left(a \cdot \left(y1 \cdot x - \color{blue}{y5 \cdot t}\right)\right) \cdot y2 \]

   7. Simplified 45.0%

      \[\leadsto \color{blue}{-\left(a \cdot \left(y1 \cdot x - y5 \cdot t\right)\right) \cdot y2} \]

   if 2.2000000000000001e-116 < j < 6.8e13

   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. Step-by-step derivation

      1. associate-+l- 37.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 37.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 43.9%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y4 around inf 55.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(k \cdot y1 - c \cdot t\right) \cdot y2\right)} \]

   if 6.8e13 < j < 1.1600000000000001e77

   1. Initial program 34.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 34.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 34.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 40.4%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y1 around inf 55.7%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right) \cdot y2\right)} \]
   6. Step-by-step derivation

      1. *-commutative 55.7%

         \[\leadsto y1 \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]

      2. +-commutative 55.7%

         \[\leadsto y1 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y4 + -1 \cdot \left(a \cdot x\right)\right)}\right) \]

      3. mul-1-neg 55.7%

         \[\leadsto y1 \cdot \left(y2 \cdot \left(k \cdot y4 + \color{blue}{\left(-a \cdot x\right)}\right)\right) \]

      4. unsub-neg 55.7%

         \[\leadsto y1 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y4 - a \cdot x\right)}\right) \]

   7. Simplified 55.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y2 \cdot \left(k \cdot y4 - a \cdot x\right)\right)} \]

   if 1.1600000000000001e77 < j < 2.0000000000000001e209

   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. Step-by-step derivation

      1. +-commutative 23.1%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 27.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 27.6%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 27.6%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 32.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 59.3%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y5 around inf 68.7%

      \[\leadsto \color{blue}{\left(\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot y5\right)} \cdot j \]
   6. Step-by-step derivation

      1. *-commutative 68.7%

         \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)\right)} \cdot j \]

      2. mul-1-neg 68.7%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \cdot j \]

      3. unsub-neg 68.7%

         \[\leadsto \left(y5 \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \cdot j \]

      4. *-commutative 68.7%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 - \color{blue}{t \cdot i}\right)\right) \cdot j \]

   7. Simplified 68.7%

      \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)} \cdot j \]

   if 2.0000000000000001e209 < j < 1.12000000000000007e250

   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. Step-by-step derivation

      1. +-commutative 22.2%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 22.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 22.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 22.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 22.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 66.7%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in x around inf 77.8%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]
3. Recombined 8 regimes into one program.

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.25 \cdot 10^{+38}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;j \leq -2.4 \cdot 10^{-162}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{elif}\;j \leq -1.02 \cdot 10^{-166}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq -5 \cdot 10^{-236}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{-116}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 68000000000000:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 1.16 \cdot 10^{+77}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{+209}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;j \leq 1.12 \cdot 10^{+250}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \]

Alternative 19: 30.7% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{if}\;y3 \leq -8.5 \cdot 10^{+116}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq -58000:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y3 \leq -1.82 \cdot 10^{-141}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq -7 \cdot 10^{-225}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq 1.7 \cdot 10^{-211}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 7 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq 1.35 \cdot 10^{+84}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq 5.6 \cdot 10^{+119}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq 3.4 \cdot 10^{+160}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y (- (* x a) (* k y4))))))
   (if (<= y3 -8.5e+116)
     (* y4 (* y1 (- (* k y2) (* j y3))))
     (if (<= y3 -58000.0)
       (* c (* i (- (* z t) (* x y))))
       (if (<= y3 -1.82e-141)
         (* y2 (* a (- (* t y5) (* x y1))))
         (if (<= y3 -7e-225)
           t_1
           (if (<= y3 1.7e-211)
             (* y4 (* t (- (* b j) (* c y2))))
             (if (<= y3 7e-84)
               t_1
               (if (<= y3 1.35e+84)
                 (* i (* y5 (- (* y k) (* t j))))
                 (if (<= y3 5.6e+119)
                   (* k (* z (- (* b y0) (* i y1))))
                   (if (<= y3 3.4e+160)
                     (* (* c y4) (- (* y y3) (* t y2)))
                     (* y0 (* j (- (* y3 y5) (* x b)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y * ((x * a) - (k * y4)));
	double tmp;
	if (y3 <= -8.5e+116) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (y3 <= -58000.0) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (y3 <= -1.82e-141) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else if (y3 <= -7e-225) {
		tmp = t_1;
	} else if (y3 <= 1.7e-211) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (y3 <= 7e-84) {
		tmp = t_1;
	} else if (y3 <= 1.35e+84) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y3 <= 5.6e+119) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (y3 <= 3.4e+160) {
		tmp = (c * y4) * ((y * y3) - (t * y2));
	} else {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (y * ((x * a) - (k * y4)))
    if (y3 <= (-8.5d+116)) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else if (y3 <= (-58000.0d0)) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (y3 <= (-1.82d-141)) then
        tmp = y2 * (a * ((t * y5) - (x * y1)))
    else if (y3 <= (-7d-225)) then
        tmp = t_1
    else if (y3 <= 1.7d-211) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    else if (y3 <= 7d-84) then
        tmp = t_1
    else if (y3 <= 1.35d+84) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (y3 <= 5.6d+119) then
        tmp = k * (z * ((b * y0) - (i * y1)))
    else if (y3 <= 3.4d+160) then
        tmp = (c * y4) * ((y * y3) - (t * y2))
    else
        tmp = y0 * (j * ((y3 * y5) - (x * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y * ((x * a) - (k * y4)));
	double tmp;
	if (y3 <= -8.5e+116) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (y3 <= -58000.0) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (y3 <= -1.82e-141) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else if (y3 <= -7e-225) {
		tmp = t_1;
	} else if (y3 <= 1.7e-211) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (y3 <= 7e-84) {
		tmp = t_1;
	} else if (y3 <= 1.35e+84) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y3 <= 5.6e+119) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (y3 <= 3.4e+160) {
		tmp = (c * y4) * ((y * y3) - (t * y2));
	} else {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (y * ((x * a) - (k * y4)))
	tmp = 0
	if y3 <= -8.5e+116:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	elif y3 <= -58000.0:
		tmp = c * (i * ((z * t) - (x * y)))
	elif y3 <= -1.82e-141:
		tmp = y2 * (a * ((t * y5) - (x * y1)))
	elif y3 <= -7e-225:
		tmp = t_1
	elif y3 <= 1.7e-211:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	elif y3 <= 7e-84:
		tmp = t_1
	elif y3 <= 1.35e+84:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif y3 <= 5.6e+119:
		tmp = k * (z * ((b * y0) - (i * y1)))
	elif y3 <= 3.4e+160:
		tmp = (c * y4) * ((y * y3) - (t * y2))
	else:
		tmp = y0 * (j * ((y3 * y5) - (x * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))))
	tmp = 0.0
	if (y3 <= -8.5e+116)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (y3 <= -58000.0)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (y3 <= -1.82e-141)
		tmp = Float64(y2 * Float64(a * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (y3 <= -7e-225)
		tmp = t_1;
	elseif (y3 <= 1.7e-211)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (y3 <= 7e-84)
		tmp = t_1;
	elseif (y3 <= 1.35e+84)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (y3 <= 5.6e+119)
		tmp = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))));
	elseif (y3 <= 3.4e+160)
		tmp = Float64(Float64(c * y4) * Float64(Float64(y * y3) - Float64(t * y2)));
	else
		tmp = Float64(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (y * ((x * a) - (k * y4)));
	tmp = 0.0;
	if (y3 <= -8.5e+116)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	elseif (y3 <= -58000.0)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (y3 <= -1.82e-141)
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	elseif (y3 <= -7e-225)
		tmp = t_1;
	elseif (y3 <= 1.7e-211)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	elseif (y3 <= 7e-84)
		tmp = t_1;
	elseif (y3 <= 1.35e+84)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (y3 <= 5.6e+119)
		tmp = k * (z * ((b * y0) - (i * y1)));
	elseif (y3 <= 3.4e+160)
		tmp = (c * y4) * ((y * y3) - (t * y2));
	else
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -8.5e+116], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -58000.0], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1.82e-141], N[(y2 * N[(a * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -7e-225], t$95$1, If[LessEqual[y3, 1.7e-211], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 7e-84], t$95$1, If[LessEqual[y3, 1.35e+84], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 5.6e+119], N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 3.4e+160], N[(N[(c * y4), $MachinePrecision] * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y3 < -8.5000000000000002e116

   1. Initial program 11.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 11.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 11.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 44.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 59.2%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]

   if -8.5000000000000002e116 < y3 < -58000

   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. Step-by-step derivation

      1. associate-+l- 30.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 30.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 71.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in i around inf 60.7%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 60.7%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

      2. neg-mul-1 60.7%

         \[\leadsto \color{blue}{\left(-c\right)} \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) \]

   7. Simplified 60.7%

      \[\leadsto \color{blue}{\left(-c\right) \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   if -58000 < y3 < -1.82000000000000005e-141

   1. Initial program 31.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 31.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 31.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 48.7%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in a around -inf 55.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(y1 \cdot x - t \cdot y5\right) \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 55.3%

         \[\leadsto \color{blue}{-a \cdot \left(\left(y1 \cdot x - t \cdot y5\right) \cdot y2\right)} \]

      2. associate-*r* 55.4%

         \[\leadsto -\color{blue}{\left(a \cdot \left(y1 \cdot x - t \cdot y5\right)\right) \cdot y2} \]

      3. *-commutative 55.4%

         \[\leadsto -\left(a \cdot \left(y1 \cdot x - \color{blue}{y5 \cdot t}\right)\right) \cdot y2 \]

   7. Simplified 55.4%

      \[\leadsto \color{blue}{-\left(a \cdot \left(y1 \cdot x - y5 \cdot t\right)\right) \cdot y2} \]

   if -1.82000000000000005e-141 < y3 < -6.9999999999999994e-225 or 1.7e-211 < y3 < 7.0000000000000002e-84

   1. Initial program 38.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 38.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 38.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 36.4%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot b} \]

   5. Taylor expanded in y around inf 52.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot \left(y \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 50.4%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot y\right) \cdot b} \]

      2. *-commutative 50.4%

         \[\leadsto \color{blue}{b \cdot \left(\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot y\right)} \]

      3. *-commutative 50.4%

         \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]

      4. +-commutative 50.4%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      5. mul-1-neg 50.4%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      6. unsub-neg 50.4%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   7. Simplified 50.4%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   if -6.9999999999999994e-225 < y3 < 1.7e-211

   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. Step-by-step derivation

      1. associate-+l- 34.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 34.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 43.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 49.0%

      \[\leadsto y4 \cdot \color{blue}{\left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 49.0%

         \[\leadsto y4 \cdot \left(t \cdot \left(\color{blue}{j \cdot b} - c \cdot y2\right)\right) \]

      2. *-commutative 49.0%

         \[\leadsto y4 \cdot \left(t \cdot \left(j \cdot b - \color{blue}{y2 \cdot c}\right)\right) \]

   7. Simplified 49.0%

      \[\leadsto y4 \cdot \color{blue}{\left(t \cdot \left(j \cdot b - y2 \cdot c\right)\right)} \]

   if 7.0000000000000002e-84 < y3 < 1.35e84

   1. Initial program 18.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 18.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 18.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in i around -inf 45.7%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(y \cdot x - t \cdot z\right) + \left(t \cdot j - k \cdot y\right) \cdot y5\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in y5 around inf 46.3%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot y5\right)\right)} \]

   if 1.35e84 < y3 < 5.60000000000000026e119

   1. Initial program 8.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 8.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 8.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 41.5%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 41.5%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. *-commutative 41.5%

         \[\leadsto -\color{blue}{z \cdot \left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \]

      3. associate--l+ 41.5%

         \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \]

      4. *-commutative 41.5%

         \[\leadsto -z \cdot \left(\color{blue}{y3 \cdot \left(c \cdot y0 - a \cdot y1\right)} + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      5. *-commutative 41.5%

         \[\leadsto -z \cdot \left(y3 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      6. *-commutative 41.5%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      7. *-commutative 41.5%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      8. *-commutative 41.5%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - \color{blue}{i \cdot c}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      9. *-commutative 41.5%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - \color{blue}{k \cdot \left(y0 \cdot b - y1 \cdot i\right)}\right)\right) \]

      10. *-commutative 41.5%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(\color{blue}{b \cdot y0} - y1 \cdot i\right)\right)\right) \]

      11. *-commutative 41.5%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right)\right) \]

   6. Simplified 41.5%

      \[\leadsto \color{blue}{-z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in k around inf 67.1%

      \[\leadsto -\color{blue}{k \cdot \left(\left(i \cdot y1 - y0 \cdot b\right) \cdot z\right)} \]

   if 5.60000000000000026e119 < y3 < 3.4000000000000003e160

   1. Initial program 50.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 50.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 50.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 59.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 50.7%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 60.4%

         \[\leadsto \color{blue}{\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)} \]

      2. *-commutative 60.4%

         \[\leadsto \color{blue}{\left(y4 \cdot c\right)} \cdot \left(y \cdot y3 - t \cdot y2\right) \]

      3. *-commutative 60.4%

         \[\leadsto \left(y4 \cdot c\right) \cdot \left(\color{blue}{y3 \cdot y} - t \cdot y2\right) \]

   7. Simplified 60.4%

      \[\leadsto \color{blue}{\left(y4 \cdot c\right) \cdot \left(y3 \cdot y - t \cdot y2\right)} \]

   if 3.4000000000000003e160 < y3

   1. Initial program 9.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 9.4%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 9.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 9.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 9.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 12.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 31.9%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y0 around inf 62.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(y3 \cdot y5 - b \cdot x\right) \cdot j\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -8.5 \cdot 10^{+116}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq -58000:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y3 \leq -1.82 \cdot 10^{-141}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq -7 \cdot 10^{-225}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 1.7 \cdot 10^{-211}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 7 \cdot 10^{-84}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 1.35 \cdot 10^{+84}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq 5.6 \cdot 10^{+119}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq 3.4 \cdot 10^{+160}:\\ \;\;\;\;\left(c \cdot y4\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \]

Alternative 20: 31.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{if}\;y3 \leq -2.7 \cdot 10^{+116}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq -58000:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y3 \leq -1.12 \cdot 10^{-141}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq -1.85 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq 8.5 \cdot 10^{-211}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 1.6 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq 0.0078:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;y3 \leq 9 \cdot 10^{+103}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;y3 \leq 2.6 \cdot 10^{+198}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y (- (* x a) (* k y4))))))
   (if (<= y3 -2.7e+116)
     (* y4 (* y1 (- (* k y2) (* j y3))))
     (if (<= y3 -58000.0)
       (* c (* i (- (* z t) (* x y))))
       (if (<= y3 -1.12e-141)
         (* y2 (* a (- (* t y5) (* x y1))))
         (if (<= y3 -1.85e-224)
           t_1
           (if (<= y3 8.5e-211)
             (* y4 (* t (- (* b j) (* c y2))))
             (if (<= y3 1.6e-86)
               t_1
               (if (<= y3 0.0078)
                 (* i (* y (- (* k y5) (* x c))))
                 (if (<= y3 9e+103)
                   (* j (* y5 (- (* y0 y3) (* t i))))
                   (if (<= y3 2.6e+198)
                     (* j (* y4 (- (* t b) (* y1 y3))))
                     (* y0 (* j (- (* y3 y5) (* x b)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y * ((x * a) - (k * y4)));
	double tmp;
	if (y3 <= -2.7e+116) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (y3 <= -58000.0) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (y3 <= -1.12e-141) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else if (y3 <= -1.85e-224) {
		tmp = t_1;
	} else if (y3 <= 8.5e-211) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (y3 <= 1.6e-86) {
		tmp = t_1;
	} else if (y3 <= 0.0078) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (y3 <= 9e+103) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (y3 <= 2.6e+198) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (y * ((x * a) - (k * y4)))
    if (y3 <= (-2.7d+116)) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else if (y3 <= (-58000.0d0)) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (y3 <= (-1.12d-141)) then
        tmp = y2 * (a * ((t * y5) - (x * y1)))
    else if (y3 <= (-1.85d-224)) then
        tmp = t_1
    else if (y3 <= 8.5d-211) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    else if (y3 <= 1.6d-86) then
        tmp = t_1
    else if (y3 <= 0.0078d0) then
        tmp = i * (y * ((k * y5) - (x * c)))
    else if (y3 <= 9d+103) then
        tmp = j * (y5 * ((y0 * y3) - (t * i)))
    else if (y3 <= 2.6d+198) then
        tmp = j * (y4 * ((t * b) - (y1 * y3)))
    else
        tmp = y0 * (j * ((y3 * y5) - (x * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y * ((x * a) - (k * y4)));
	double tmp;
	if (y3 <= -2.7e+116) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (y3 <= -58000.0) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (y3 <= -1.12e-141) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else if (y3 <= -1.85e-224) {
		tmp = t_1;
	} else if (y3 <= 8.5e-211) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (y3 <= 1.6e-86) {
		tmp = t_1;
	} else if (y3 <= 0.0078) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (y3 <= 9e+103) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (y3 <= 2.6e+198) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (y * ((x * a) - (k * y4)))
	tmp = 0
	if y3 <= -2.7e+116:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	elif y3 <= -58000.0:
		tmp = c * (i * ((z * t) - (x * y)))
	elif y3 <= -1.12e-141:
		tmp = y2 * (a * ((t * y5) - (x * y1)))
	elif y3 <= -1.85e-224:
		tmp = t_1
	elif y3 <= 8.5e-211:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	elif y3 <= 1.6e-86:
		tmp = t_1
	elif y3 <= 0.0078:
		tmp = i * (y * ((k * y5) - (x * c)))
	elif y3 <= 9e+103:
		tmp = j * (y5 * ((y0 * y3) - (t * i)))
	elif y3 <= 2.6e+198:
		tmp = j * (y4 * ((t * b) - (y1 * y3)))
	else:
		tmp = y0 * (j * ((y3 * y5) - (x * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))))
	tmp = 0.0
	if (y3 <= -2.7e+116)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (y3 <= -58000.0)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (y3 <= -1.12e-141)
		tmp = Float64(y2 * Float64(a * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (y3 <= -1.85e-224)
		tmp = t_1;
	elseif (y3 <= 8.5e-211)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (y3 <= 1.6e-86)
		tmp = t_1;
	elseif (y3 <= 0.0078)
		tmp = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))));
	elseif (y3 <= 9e+103)
		tmp = Float64(j * Float64(y5 * Float64(Float64(y0 * y3) - Float64(t * i))));
	elseif (y3 <= 2.6e+198)
		tmp = Float64(j * Float64(y4 * Float64(Float64(t * b) - Float64(y1 * y3))));
	else
		tmp = Float64(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (y * ((x * a) - (k * y4)));
	tmp = 0.0;
	if (y3 <= -2.7e+116)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	elseif (y3 <= -58000.0)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (y3 <= -1.12e-141)
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	elseif (y3 <= -1.85e-224)
		tmp = t_1;
	elseif (y3 <= 8.5e-211)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	elseif (y3 <= 1.6e-86)
		tmp = t_1;
	elseif (y3 <= 0.0078)
		tmp = i * (y * ((k * y5) - (x * c)));
	elseif (y3 <= 9e+103)
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	elseif (y3 <= 2.6e+198)
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	else
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -2.7e+116], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -58000.0], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1.12e-141], N[(y2 * N[(a * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1.85e-224], t$95$1, If[LessEqual[y3, 8.5e-211], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.6e-86], t$95$1, If[LessEqual[y3, 0.0078], N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 9e+103], N[(j * N[(y5 * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.6e+198], N[(j * N[(y4 * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y3 < -2.7e116

   1. Initial program 11.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 11.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 11.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 44.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 59.2%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]

   if -2.7e116 < y3 < -58000

   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. Step-by-step derivation

      1. associate-+l- 30.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 30.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 71.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in i around inf 60.7%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 60.7%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

      2. neg-mul-1 60.7%

         \[\leadsto \color{blue}{\left(-c\right)} \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) \]

   7. Simplified 60.7%

      \[\leadsto \color{blue}{\left(-c\right) \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   if -58000 < y3 < -1.12000000000000002e-141

   1. Initial program 31.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 31.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 31.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 48.7%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in a around -inf 55.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(y1 \cdot x - t \cdot y5\right) \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 55.3%

         \[\leadsto \color{blue}{-a \cdot \left(\left(y1 \cdot x - t \cdot y5\right) \cdot y2\right)} \]

      2. associate-*r* 55.4%

         \[\leadsto -\color{blue}{\left(a \cdot \left(y1 \cdot x - t \cdot y5\right)\right) \cdot y2} \]

      3. *-commutative 55.4%

         \[\leadsto -\left(a \cdot \left(y1 \cdot x - \color{blue}{y5 \cdot t}\right)\right) \cdot y2 \]

   7. Simplified 55.4%

      \[\leadsto \color{blue}{-\left(a \cdot \left(y1 \cdot x - y5 \cdot t\right)\right) \cdot y2} \]

   if -1.12000000000000002e-141 < y3 < -1.8500000000000001e-224 or 8.49999999999999936e-211 < y3 < 1.60000000000000003e-86

   1. Initial program 38.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 38.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 38.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 36.4%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot b} \]

   5. Taylor expanded in y around inf 52.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot \left(y \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 50.4%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot y\right) \cdot b} \]

      2. *-commutative 50.4%

         \[\leadsto \color{blue}{b \cdot \left(\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot y\right)} \]

      3. *-commutative 50.4%

         \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]

      4. +-commutative 50.4%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      5. mul-1-neg 50.4%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      6. unsub-neg 50.4%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   7. Simplified 50.4%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   if -1.8500000000000001e-224 < y3 < 8.49999999999999936e-211

   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. Step-by-step derivation

      1. associate-+l- 34.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 34.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 43.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 49.0%

      \[\leadsto y4 \cdot \color{blue}{\left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 49.0%

         \[\leadsto y4 \cdot \left(t \cdot \left(\color{blue}{j \cdot b} - c \cdot y2\right)\right) \]

      2. *-commutative 49.0%

         \[\leadsto y4 \cdot \left(t \cdot \left(j \cdot b - \color{blue}{y2 \cdot c}\right)\right) \]

   7. Simplified 49.0%

      \[\leadsto y4 \cdot \color{blue}{\left(t \cdot \left(j \cdot b - y2 \cdot c\right)\right)} \]

   if 1.60000000000000003e-86 < y3 < 0.0077999999999999996

   1. Initial program 15.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 15.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 15.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in i around -inf 42.5%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(y \cdot x - t \cdot z\right) + \left(t \cdot j - k \cdot y\right) \cdot y5\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in y around inf 59.0%

      \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right) \cdot y\right)}\right) \]
   6. Step-by-step derivation

      1. +-commutative 59.0%

         \[\leadsto -1 \cdot \left(i \cdot \left(\color{blue}{\left(c \cdot x + -1 \cdot \left(k \cdot y5\right)\right)} \cdot y\right)\right) \]

      2. mul-1-neg 59.0%

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot x + \color{blue}{\left(-k \cdot y5\right)}\right) \cdot y\right)\right) \]

      3. unsub-neg 59.0%

         \[\leadsto -1 \cdot \left(i \cdot \left(\color{blue}{\left(c \cdot x - k \cdot y5\right)} \cdot y\right)\right) \]

      4. *-commutative 59.0%

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(\color{blue}{x \cdot c} - k \cdot y5\right) \cdot y\right)\right) \]

   7. Simplified 59.0%

      \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(x \cdot c - k \cdot y5\right) \cdot y\right)}\right) \]

   if 0.0077999999999999996 < y3 < 9.00000000000000002e103

   1. Initial program 17.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 17.3%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 21.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 21.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 21.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 21.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 48.1%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y5 around inf 53.0%

      \[\leadsto \color{blue}{\left(\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot y5\right)} \cdot j \]
   6. Step-by-step derivation

      1. *-commutative 53.0%

         \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)\right)} \cdot j \]

      2. mul-1-neg 53.0%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \cdot j \]

      3. unsub-neg 53.0%

         \[\leadsto \left(y5 \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \cdot j \]

      4. *-commutative 53.0%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 - \color{blue}{t \cdot i}\right)\right) \cdot j \]

   7. Simplified 53.0%

      \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)} \cdot j \]

   if 9.00000000000000002e103 < y3 < 2.59999999999999981e198

   1. Initial program 26.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 26.8%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 42.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 42.6%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 42.6%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 42.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 47.8%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y4 around inf 53.1%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot b + -1 \cdot \left(y1 \cdot y3\right)\right)\right)} \cdot j \]
   6. Step-by-step derivation

      1. mul-1-neg 53.1%

         \[\leadsto \left(y4 \cdot \left(t \cdot b + \color{blue}{\left(-y1 \cdot y3\right)}\right)\right) \cdot j \]

      2. unsub-neg 53.1%

         \[\leadsto \left(y4 \cdot \color{blue}{\left(t \cdot b - y1 \cdot y3\right)}\right) \cdot j \]

   7. Simplified 53.1%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)} \cdot j \]

   if 2.59999999999999981e198 < y3

   1. Initial program 11.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 11.5%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 11.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 11.5%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 11.5%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 15.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 27.8%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y0 around inf 65.6%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(y3 \cdot y5 - b \cdot x\right) \cdot j\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -2.7 \cdot 10^{+116}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq -58000:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y3 \leq -1.12 \cdot 10^{-141}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq -1.85 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 8.5 \cdot 10^{-211}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 1.6 \cdot 10^{-86}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 0.0078:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;y3 \leq 9 \cdot 10^{+103}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;y3 \leq 2.6 \cdot 10^{+198}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \]

Alternative 21: 30.8% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot a - k \cdot y4\\ \mathbf{if}\;y3 \leq -3 \cdot 10^{+116}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq -6800000000:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y3 \leq -6.4 \cdot 10^{-142}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq -1.1 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \left(y \cdot t_1\right)\\ \mathbf{elif}\;y3 \leq 1.7 \cdot 10^{-208}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 8.4 \cdot 10^{-85}:\\ \;\;\;\;t_1 \cdot \left(y \cdot b\right)\\ \mathbf{elif}\;y3 \leq 300:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;y3 \leq 2.5 \cdot 10^{+104}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;y3 \leq 3.1 \cdot 10^{+191}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x a) (* k y4))))
   (if (<= y3 -3e+116)
     (* y4 (* y1 (- (* k y2) (* j y3))))
     (if (<= y3 -6800000000.0)
       (* c (* i (- (* z t) (* x y))))
       (if (<= y3 -6.4e-142)
         (* y2 (* a (- (* t y5) (* x y1))))
         (if (<= y3 -1.1e-224)
           (* b (* y t_1))
           (if (<= y3 1.7e-208)
             (* y4 (* t (- (* b j) (* c y2))))
             (if (<= y3 8.4e-85)
               (* t_1 (* y b))
               (if (<= y3 300.0)
                 (* i (* y (- (* k y5) (* x c))))
                 (if (<= y3 2.5e+104)
                   (* j (* y5 (- (* y0 y3) (* t i))))
                   (if (<= y3 3.1e+191)
                     (* j (* y4 (- (* t b) (* y1 y3))))
                     (* y0 (* j (- (* y3 y5) (* x b)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * a) - (k * y4);
	double tmp;
	if (y3 <= -3e+116) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (y3 <= -6800000000.0) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (y3 <= -6.4e-142) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else if (y3 <= -1.1e-224) {
		tmp = b * (y * t_1);
	} else if (y3 <= 1.7e-208) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (y3 <= 8.4e-85) {
		tmp = t_1 * (y * b);
	} else if (y3 <= 300.0) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (y3 <= 2.5e+104) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (y3 <= 3.1e+191) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * a) - (k * y4)
    if (y3 <= (-3d+116)) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else if (y3 <= (-6800000000.0d0)) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (y3 <= (-6.4d-142)) then
        tmp = y2 * (a * ((t * y5) - (x * y1)))
    else if (y3 <= (-1.1d-224)) then
        tmp = b * (y * t_1)
    else if (y3 <= 1.7d-208) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    else if (y3 <= 8.4d-85) then
        tmp = t_1 * (y * b)
    else if (y3 <= 300.0d0) then
        tmp = i * (y * ((k * y5) - (x * c)))
    else if (y3 <= 2.5d+104) then
        tmp = j * (y5 * ((y0 * y3) - (t * i)))
    else if (y3 <= 3.1d+191) then
        tmp = j * (y4 * ((t * b) - (y1 * y3)))
    else
        tmp = y0 * (j * ((y3 * y5) - (x * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * a) - (k * y4);
	double tmp;
	if (y3 <= -3e+116) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else if (y3 <= -6800000000.0) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (y3 <= -6.4e-142) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else if (y3 <= -1.1e-224) {
		tmp = b * (y * t_1);
	} else if (y3 <= 1.7e-208) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (y3 <= 8.4e-85) {
		tmp = t_1 * (y * b);
	} else if (y3 <= 300.0) {
		tmp = i * (y * ((k * y5) - (x * c)));
	} else if (y3 <= 2.5e+104) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (y3 <= 3.1e+191) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else {
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (x * a) - (k * y4)
	tmp = 0
	if y3 <= -3e+116:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	elif y3 <= -6800000000.0:
		tmp = c * (i * ((z * t) - (x * y)))
	elif y3 <= -6.4e-142:
		tmp = y2 * (a * ((t * y5) - (x * y1)))
	elif y3 <= -1.1e-224:
		tmp = b * (y * t_1)
	elif y3 <= 1.7e-208:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	elif y3 <= 8.4e-85:
		tmp = t_1 * (y * b)
	elif y3 <= 300.0:
		tmp = i * (y * ((k * y5) - (x * c)))
	elif y3 <= 2.5e+104:
		tmp = j * (y5 * ((y0 * y3) - (t * i)))
	elif y3 <= 3.1e+191:
		tmp = j * (y4 * ((t * b) - (y1 * y3)))
	else:
		tmp = y0 * (j * ((y3 * y5) - (x * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(x * a) - Float64(k * y4))
	tmp = 0.0
	if (y3 <= -3e+116)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (y3 <= -6800000000.0)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (y3 <= -6.4e-142)
		tmp = Float64(y2 * Float64(a * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (y3 <= -1.1e-224)
		tmp = Float64(b * Float64(y * t_1));
	elseif (y3 <= 1.7e-208)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (y3 <= 8.4e-85)
		tmp = Float64(t_1 * Float64(y * b));
	elseif (y3 <= 300.0)
		tmp = Float64(i * Float64(y * Float64(Float64(k * y5) - Float64(x * c))));
	elseif (y3 <= 2.5e+104)
		tmp = Float64(j * Float64(y5 * Float64(Float64(y0 * y3) - Float64(t * i))));
	elseif (y3 <= 3.1e+191)
		tmp = Float64(j * Float64(y4 * Float64(Float64(t * b) - Float64(y1 * y3))));
	else
		tmp = Float64(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (x * a) - (k * y4);
	tmp = 0.0;
	if (y3 <= -3e+116)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	elseif (y3 <= -6800000000.0)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (y3 <= -6.4e-142)
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	elseif (y3 <= -1.1e-224)
		tmp = b * (y * t_1);
	elseif (y3 <= 1.7e-208)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	elseif (y3 <= 8.4e-85)
		tmp = t_1 * (y * b);
	elseif (y3 <= 300.0)
		tmp = i * (y * ((k * y5) - (x * c)));
	elseif (y3 <= 2.5e+104)
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	elseif (y3 <= 3.1e+191)
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	else
		tmp = y0 * (j * ((y3 * y5) - (x * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -3e+116], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -6800000000.0], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -6.4e-142], N[(y2 * N[(a * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1.1e-224], N[(b * N[(y * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.7e-208], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 8.4e-85], N[(t$95$1 * N[(y * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 300.0], N[(i * N[(y * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.5e+104], N[(j * N[(y5 * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 3.1e+191], N[(j * N[(y4 * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y3 < -2.9999999999999999e116

   1. Initial program 11.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 11.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 11.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 44.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y1 around inf 59.2%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \]

   if -2.9999999999999999e116 < y3 < -6.8e9

   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. Step-by-step derivation

      1. associate-+l- 30.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 30.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 71.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in i around inf 60.7%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 60.7%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

      2. neg-mul-1 60.7%

         \[\leadsto \color{blue}{\left(-c\right)} \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) \]

   7. Simplified 60.7%

      \[\leadsto \color{blue}{\left(-c\right) \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   if -6.8e9 < y3 < -6.3999999999999997e-142

   1. Initial program 31.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 31.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 31.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 48.7%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in a around -inf 55.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(y1 \cdot x - t \cdot y5\right) \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 55.3%

         \[\leadsto \color{blue}{-a \cdot \left(\left(y1 \cdot x - t \cdot y5\right) \cdot y2\right)} \]

      2. associate-*r* 55.4%

         \[\leadsto -\color{blue}{\left(a \cdot \left(y1 \cdot x - t \cdot y5\right)\right) \cdot y2} \]

      3. *-commutative 55.4%

         \[\leadsto -\left(a \cdot \left(y1 \cdot x - \color{blue}{y5 \cdot t}\right)\right) \cdot y2 \]

   7. Simplified 55.4%

      \[\leadsto \color{blue}{-\left(a \cdot \left(y1 \cdot x - y5 \cdot t\right)\right) \cdot y2} \]

   if -6.3999999999999997e-142 < y3 < -1.1e-224

   1. Initial program 33.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 33.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 33.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 45.2%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot b} \]

   5. Taylor expanded in y around inf 51.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot \left(y \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 56.8%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot y\right) \cdot b} \]

      2. *-commutative 56.8%

         \[\leadsto \color{blue}{b \cdot \left(\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot y\right)} \]

      3. *-commutative 56.8%

         \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]

      4. +-commutative 56.8%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      5. mul-1-neg 56.8%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      6. unsub-neg 56.8%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   7. Simplified 56.8%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   if -1.1e-224 < y3 < 1.7e-208

   1. Initial program 33.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 33.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 33.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 42.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 47.8%

      \[\leadsto y4 \cdot \color{blue}{\left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 47.8%

         \[\leadsto y4 \cdot \left(t \cdot \left(\color{blue}{j \cdot b} - c \cdot y2\right)\right) \]

      2. *-commutative 47.8%

         \[\leadsto y4 \cdot \left(t \cdot \left(j \cdot b - \color{blue}{y2 \cdot c}\right)\right) \]

   7. Simplified 47.8%

      \[\leadsto y4 \cdot \color{blue}{\left(t \cdot \left(j \cdot b - y2 \cdot c\right)\right)} \]

   if 1.7e-208 < y3 < 8.3999999999999999e-85

   1. Initial program 42.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 42.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 42.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 31.3%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot b} \]

   5. Taylor expanded in y around inf 54.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot \left(y \cdot b\right)} \]

   if 8.3999999999999999e-85 < y3 < 300

   1. Initial program 15.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 15.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 15.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in i around -inf 42.5%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(y \cdot x - t \cdot z\right) + \left(t \cdot j - k \cdot y\right) \cdot y5\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in y around inf 59.0%

      \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right) \cdot y\right)}\right) \]
   6. Step-by-step derivation

      1. +-commutative 59.0%

         \[\leadsto -1 \cdot \left(i \cdot \left(\color{blue}{\left(c \cdot x + -1 \cdot \left(k \cdot y5\right)\right)} \cdot y\right)\right) \]

      2. mul-1-neg 59.0%

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot x + \color{blue}{\left(-k \cdot y5\right)}\right) \cdot y\right)\right) \]

      3. unsub-neg 59.0%

         \[\leadsto -1 \cdot \left(i \cdot \left(\color{blue}{\left(c \cdot x - k \cdot y5\right)} \cdot y\right)\right) \]

      4. *-commutative 59.0%

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(\color{blue}{x \cdot c} - k \cdot y5\right) \cdot y\right)\right) \]

   7. Simplified 59.0%

      \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(x \cdot c - k \cdot y5\right) \cdot y\right)}\right) \]

   if 300 < y3 < 2.4999999999999998e104

   1. Initial program 17.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 17.3%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 21.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 21.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 21.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 21.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 48.1%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y5 around inf 53.0%

      \[\leadsto \color{blue}{\left(\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot y5\right)} \cdot j \]
   6. Step-by-step derivation

      1. *-commutative 53.0%

         \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)\right)} \cdot j \]

      2. mul-1-neg 53.0%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \cdot j \]

      3. unsub-neg 53.0%

         \[\leadsto \left(y5 \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \cdot j \]

      4. *-commutative 53.0%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 - \color{blue}{t \cdot i}\right)\right) \cdot j \]

   7. Simplified 53.0%

      \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)} \cdot j \]

   if 2.4999999999999998e104 < y3 < 3.09999999999999999e191

   1. Initial program 26.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 26.8%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 42.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 42.6%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 42.6%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 42.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 47.8%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y4 around inf 53.1%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot b + -1 \cdot \left(y1 \cdot y3\right)\right)\right)} \cdot j \]
   6. Step-by-step derivation

      1. mul-1-neg 53.1%

         \[\leadsto \left(y4 \cdot \left(t \cdot b + \color{blue}{\left(-y1 \cdot y3\right)}\right)\right) \cdot j \]

      2. unsub-neg 53.1%

         \[\leadsto \left(y4 \cdot \color{blue}{\left(t \cdot b - y1 \cdot y3\right)}\right) \cdot j \]

   7. Simplified 53.1%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)} \cdot j \]

   if 3.09999999999999999e191 < y3

   1. Initial program 11.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 11.5%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 11.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 11.5%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 11.5%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 15.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 27.8%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y0 around inf 65.6%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(y3 \cdot y5 - b \cdot x\right) \cdot j\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -3 \cdot 10^{+116}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq -6800000000:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y3 \leq -6.4 \cdot 10^{-142}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq -1.1 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 1.7 \cdot 10^{-208}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 8.4 \cdot 10^{-85}:\\ \;\;\;\;\left(x \cdot a - k \cdot y4\right) \cdot \left(y \cdot b\right)\\ \mathbf{elif}\;y3 \leq 300:\\ \;\;\;\;i \cdot \left(y \cdot \left(k \cdot y5 - x \cdot c\right)\right)\\ \mathbf{elif}\;y3 \leq 2.5 \cdot 10^{+104}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;y3 \leq 3.1 \cdot 10^{+191}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \]

Alternative 22: 28.8% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ t_2 := b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{if}\;y0 \leq -4 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -1.15 \cdot 10^{-84}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 3.5 \cdot 10^{-151}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y0 \leq 1.7 \cdot 10^{+20}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y0 \leq 1.95 \cdot 10^{+114}:\\ \;\;\;\;\left(k \cdot y0\right) \cdot \left(y2 \cdot \left(-y5\right)\right)\\ \mathbf{elif}\;y0 \leq 8 \cdot 10^{+250}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 4.7 \cdot 10^{+285}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* j (- (* y3 y5) (* x b)))))
        (t_2 (* b (* y (- (* x a) (* k y4))))))
   (if (<= y0 -4e+36)
     t_1
     (if (<= y0 -1.15e-84)
       (* z (* y3 (* a y1)))
       (if (<= y0 3.5e-151)
         t_2
         (if (<= y0 1.7e+20)
           (* y1 (* y2 (- (* k y4) (* x a))))
           (if (<= y0 1.95e+114)
             (* (* k y0) (* y2 (- y5)))
             (if (<= y0 8e+250)
               (* c (* y2 (- (* x y0) (* t y4))))
               (if (<= y0 4.7e+285) 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 = y0 * (j * ((y3 * y5) - (x * b)));
	double t_2 = b * (y * ((x * a) - (k * y4)));
	double tmp;
	if (y0 <= -4e+36) {
		tmp = t_1;
	} else if (y0 <= -1.15e-84) {
		tmp = z * (y3 * (a * y1));
	} else if (y0 <= 3.5e-151) {
		tmp = t_2;
	} else if (y0 <= 1.7e+20) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (y0 <= 1.95e+114) {
		tmp = (k * y0) * (y2 * -y5);
	} else if (y0 <= 8e+250) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y0 <= 4.7e+285) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y0 * (j * ((y3 * y5) - (x * b)))
    t_2 = b * (y * ((x * a) - (k * y4)))
    if (y0 <= (-4d+36)) then
        tmp = t_1
    else if (y0 <= (-1.15d-84)) then
        tmp = z * (y3 * (a * y1))
    else if (y0 <= 3.5d-151) then
        tmp = t_2
    else if (y0 <= 1.7d+20) then
        tmp = y1 * (y2 * ((k * y4) - (x * a)))
    else if (y0 <= 1.95d+114) then
        tmp = (k * y0) * (y2 * -y5)
    else if (y0 <= 8d+250) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (y0 <= 4.7d+285) 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 = y0 * (j * ((y3 * y5) - (x * b)));
	double t_2 = b * (y * ((x * a) - (k * y4)));
	double tmp;
	if (y0 <= -4e+36) {
		tmp = t_1;
	} else if (y0 <= -1.15e-84) {
		tmp = z * (y3 * (a * y1));
	} else if (y0 <= 3.5e-151) {
		tmp = t_2;
	} else if (y0 <= 1.7e+20) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (y0 <= 1.95e+114) {
		tmp = (k * y0) * (y2 * -y5);
	} else if (y0 <= 8e+250) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y0 <= 4.7e+285) {
		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 = y0 * (j * ((y3 * y5) - (x * b)))
	t_2 = b * (y * ((x * a) - (k * y4)))
	tmp = 0
	if y0 <= -4e+36:
		tmp = t_1
	elif y0 <= -1.15e-84:
		tmp = z * (y3 * (a * y1))
	elif y0 <= 3.5e-151:
		tmp = t_2
	elif y0 <= 1.7e+20:
		tmp = y1 * (y2 * ((k * y4) - (x * a)))
	elif y0 <= 1.95e+114:
		tmp = (k * y0) * (y2 * -y5)
	elif y0 <= 8e+250:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif y0 <= 4.7e+285:
		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(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))))
	t_2 = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))))
	tmp = 0.0
	if (y0 <= -4e+36)
		tmp = t_1;
	elseif (y0 <= -1.15e-84)
		tmp = Float64(z * Float64(y3 * Float64(a * y1)));
	elseif (y0 <= 3.5e-151)
		tmp = t_2;
	elseif (y0 <= 1.7e+20)
		tmp = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (y0 <= 1.95e+114)
		tmp = Float64(Float64(k * y0) * Float64(y2 * Float64(-y5)));
	elseif (y0 <= 8e+250)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (y0 <= 4.7e+285)
		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 = y0 * (j * ((y3 * y5) - (x * b)));
	t_2 = b * (y * ((x * a) - (k * y4)));
	tmp = 0.0;
	if (y0 <= -4e+36)
		tmp = t_1;
	elseif (y0 <= -1.15e-84)
		tmp = z * (y3 * (a * y1));
	elseif (y0 <= 3.5e-151)
		tmp = t_2;
	elseif (y0 <= 1.7e+20)
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	elseif (y0 <= 1.95e+114)
		tmp = (k * y0) * (y2 * -y5);
	elseif (y0 <= 8e+250)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (y0 <= 4.7e+285)
		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[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -4e+36], t$95$1, If[LessEqual[y0, -1.15e-84], N[(z * N[(y3 * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 3.5e-151], t$95$2, If[LessEqual[y0, 1.7e+20], N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.95e+114], N[(N[(k * y0), $MachinePrecision] * N[(y2 * (-y5)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 8e+250], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.7e+285], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y0 < -4.00000000000000017e36 or 4.7000000000000001e285 < y0

   1. Initial program 16.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 16.0%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 19.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 19.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 19.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 20.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 29.1%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y0 around inf 52.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(y3 \cdot y5 - b \cdot x\right) \cdot j\right)} \]

   if -4.00000000000000017e36 < y0 < -1.1499999999999999e-84

   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. Step-by-step derivation

      1. associate-+l- 27.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 27.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 37.6%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 37.6%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. *-commutative 37.6%

         \[\leadsto -\color{blue}{z \cdot \left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \]

      3. associate--l+ 37.6%

         \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \]

      4. *-commutative 37.6%

         \[\leadsto -z \cdot \left(\color{blue}{y3 \cdot \left(c \cdot y0 - a \cdot y1\right)} + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      5. *-commutative 37.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      6. *-commutative 37.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      7. *-commutative 37.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      8. *-commutative 37.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - \color{blue}{i \cdot c}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      9. *-commutative 37.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - \color{blue}{k \cdot \left(y0 \cdot b - y1 \cdot i\right)}\right)\right) \]

      10. *-commutative 37.6%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(\color{blue}{b \cdot y0} - y1 \cdot i\right)\right)\right) \]

      11. *-commutative 37.6%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right)\right) \]

   6. Simplified 37.6%

      \[\leadsto \color{blue}{-z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in y3 around inf 38.1%

      \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3\right)} \]
   8. Step-by-step derivation

      1. *-commutative 38.1%

         \[\leadsto -z \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y3\right) \]

   9. Simplified 38.1%

      \[\leadsto -z \cdot \color{blue}{\left(\left(y0 \cdot c - a \cdot y1\right) \cdot y3\right)} \]

   10. Taylor expanded in y0 around 0 34.7%

       \[\leadsto -z \cdot \left(\color{blue}{\left(-1 \cdot \left(y1 \cdot a\right)\right)} \cdot y3\right) \]
   11. Step-by-step derivation

       1. mul-1-neg 34.7%

          \[\leadsto -z \cdot \left(\color{blue}{\left(-y1 \cdot a\right)} \cdot y3\right) \]

       2. *-commutative 34.7%

          \[\leadsto -z \cdot \left(\left(-\color{blue}{a \cdot y1}\right) \cdot y3\right) \]

       3. distribute-rgt-neg-in 34.7%

          \[\leadsto -z \cdot \left(\color{blue}{\left(a \cdot \left(-y1\right)\right)} \cdot y3\right) \]

   12. Simplified 34.7%

       \[\leadsto -z \cdot \left(\color{blue}{\left(a \cdot \left(-y1\right)\right)} \cdot y3\right) \]

   if -1.1499999999999999e-84 < y0 < 3.49999999999999995e-151 or 7.9999999999999994e250 < y0 < 4.7000000000000001e285

   1. Initial program 34.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 34.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 34.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 42.7%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot b} \]

   5. Taylor expanded in y around inf 39.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot \left(y \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 41.7%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot y\right) \cdot b} \]

      2. *-commutative 41.7%

         \[\leadsto \color{blue}{b \cdot \left(\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot y\right)} \]

      3. *-commutative 41.7%

         \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]

      4. +-commutative 41.7%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      5. mul-1-neg 41.7%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      6. unsub-neg 41.7%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   7. Simplified 41.7%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   if 3.49999999999999995e-151 < y0 < 1.7e20

   1. Initial program 18.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 18.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 18.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 49.4%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y1 around inf 46.4%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right) \cdot y2\right)} \]
   6. Step-by-step derivation

      1. *-commutative 46.4%

         \[\leadsto y1 \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]

      2. +-commutative 46.4%

         \[\leadsto y1 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y4 + -1 \cdot \left(a \cdot x\right)\right)}\right) \]

      3. mul-1-neg 46.4%

         \[\leadsto y1 \cdot \left(y2 \cdot \left(k \cdot y4 + \color{blue}{\left(-a \cdot x\right)}\right)\right) \]

      4. unsub-neg 46.4%

         \[\leadsto y1 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y4 - a \cdot x\right)}\right) \]

   7. Simplified 46.4%

      \[\leadsto \color{blue}{y1 \cdot \left(y2 \cdot \left(k \cdot y4 - a \cdot x\right)\right)} \]

   if 1.7e20 < y0 < 1.95e114

   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. Step-by-step derivation

      1. associate-+l- 35.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 35.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 43.4%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in k around inf 51.1%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 51.1%

         \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)} \]

      2. *-commutative 51.1%

         \[\leadsto \left(k \cdot y2\right) \cdot \left(\color{blue}{y1 \cdot y4} - y0 \cdot y5\right) \]

   7. Simplified 51.1%

      \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]

   8. Taylor expanded in y1 around 0 51.0%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(y5 \cdot y2\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 51.0%

         \[\leadsto \color{blue}{-k \cdot \left(y0 \cdot \left(y5 \cdot y2\right)\right)} \]

      2. associate-*r* 57.8%

         \[\leadsto -\color{blue}{\left(k \cdot y0\right) \cdot \left(y5 \cdot y2\right)} \]

      3. distribute-rgt-neg-in 57.8%

         \[\leadsto \color{blue}{\left(k \cdot y0\right) \cdot \left(-y5 \cdot y2\right)} \]

      4. *-commutative 57.8%

         \[\leadsto \left(k \cdot y0\right) \cdot \left(-\color{blue}{y2 \cdot y5}\right) \]

   10. Simplified 57.8%

       \[\leadsto \color{blue}{\left(k \cdot y0\right) \cdot \left(-y2 \cdot y5\right)} \]

   if 1.95e114 < y0 < 7.9999999999999994e250

   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. Step-by-step derivation

      1. associate-+l- 20.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 20.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 32.4%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 52.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -4 \cdot 10^{+36}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq -1.15 \cdot 10^{-84}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 3.5 \cdot 10^{-151}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.7 \cdot 10^{+20}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;y0 \leq 1.95 \cdot 10^{+114}:\\ \;\;\;\;\left(k \cdot y0\right) \cdot \left(y2 \cdot \left(-y5\right)\right)\\ \mathbf{elif}\;y0 \leq 8 \cdot 10^{+250}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 4.7 \cdot 10^{+285}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \]

Alternative 23: 32.1% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ t_2 := y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{if}\;j \leq -2.5 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-108}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 4.6 \cdot 10^{-255}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 9.6 \cdot 10^{-180}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 60000000000000:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 1.86 \cdot 10^{+27}:\\ \;\;\;\;z \cdot \left(\left(c \cdot y0\right) \cdot \left(-y3\right)\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* j (- (* y3 y5) (* x b)))))
        (t_2 (* y1 (* y2 (- (* k y4) (* x a))))))
   (if (<= j -2.5e+50)
     t_1
     (if (<= j -1.05e-108)
       (* c (* y2 (- (* x y0) (* t y4))))
       (if (<= j 4.6e-255)
         t_2
         (if (<= j 9.6e-180)
           (* y0 (* y2 (* k (- y5))))
           (if (<= j 60000000000000.0)
             (* y2 (* k (- (* y1 y4) (* y0 y5))))
             (if (<= j 1.86e+27)
               (* z (* (* c y0) (- y3)))
               (if (<= j 5.5e+76) 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 = y0 * (j * ((y3 * y5) - (x * b)));
	double t_2 = y1 * (y2 * ((k * y4) - (x * a)));
	double tmp;
	if (j <= -2.5e+50) {
		tmp = t_1;
	} else if (j <= -1.05e-108) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (j <= 4.6e-255) {
		tmp = t_2;
	} else if (j <= 9.6e-180) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (j <= 60000000000000.0) {
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)));
	} else if (j <= 1.86e+27) {
		tmp = z * ((c * y0) * -y3);
	} else if (j <= 5.5e+76) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y0 * (j * ((y3 * y5) - (x * b)))
    t_2 = y1 * (y2 * ((k * y4) - (x * a)))
    if (j <= (-2.5d+50)) then
        tmp = t_1
    else if (j <= (-1.05d-108)) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (j <= 4.6d-255) then
        tmp = t_2
    else if (j <= 9.6d-180) then
        tmp = y0 * (y2 * (k * -y5))
    else if (j <= 60000000000000.0d0) then
        tmp = y2 * (k * ((y1 * y4) - (y0 * y5)))
    else if (j <= 1.86d+27) then
        tmp = z * ((c * y0) * -y3)
    else if (j <= 5.5d+76) 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 = y0 * (j * ((y3 * y5) - (x * b)));
	double t_2 = y1 * (y2 * ((k * y4) - (x * a)));
	double tmp;
	if (j <= -2.5e+50) {
		tmp = t_1;
	} else if (j <= -1.05e-108) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (j <= 4.6e-255) {
		tmp = t_2;
	} else if (j <= 9.6e-180) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (j <= 60000000000000.0) {
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)));
	} else if (j <= 1.86e+27) {
		tmp = z * ((c * y0) * -y3);
	} else if (j <= 5.5e+76) {
		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 = y0 * (j * ((y3 * y5) - (x * b)))
	t_2 = y1 * (y2 * ((k * y4) - (x * a)))
	tmp = 0
	if j <= -2.5e+50:
		tmp = t_1
	elif j <= -1.05e-108:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif j <= 4.6e-255:
		tmp = t_2
	elif j <= 9.6e-180:
		tmp = y0 * (y2 * (k * -y5))
	elif j <= 60000000000000.0:
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)))
	elif j <= 1.86e+27:
		tmp = z * ((c * y0) * -y3)
	elif j <= 5.5e+76:
		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(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))))
	t_2 = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))))
	tmp = 0.0
	if (j <= -2.5e+50)
		tmp = t_1;
	elseif (j <= -1.05e-108)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (j <= 4.6e-255)
		tmp = t_2;
	elseif (j <= 9.6e-180)
		tmp = Float64(y0 * Float64(y2 * Float64(k * Float64(-y5))));
	elseif (j <= 60000000000000.0)
		tmp = Float64(y2 * Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (j <= 1.86e+27)
		tmp = Float64(z * Float64(Float64(c * y0) * Float64(-y3)));
	elseif (j <= 5.5e+76)
		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 = y0 * (j * ((y3 * y5) - (x * b)));
	t_2 = y1 * (y2 * ((k * y4) - (x * a)));
	tmp = 0.0;
	if (j <= -2.5e+50)
		tmp = t_1;
	elseif (j <= -1.05e-108)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (j <= 4.6e-255)
		tmp = t_2;
	elseif (j <= 9.6e-180)
		tmp = y0 * (y2 * (k * -y5));
	elseif (j <= 60000000000000.0)
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)));
	elseif (j <= 1.86e+27)
		tmp = z * ((c * y0) * -y3);
	elseif (j <= 5.5e+76)
		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[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.5e+50], t$95$1, If[LessEqual[j, -1.05e-108], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.6e-255], t$95$2, If[LessEqual[j, 9.6e-180], N[(y0 * N[(y2 * N[(k * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 60000000000000.0], N[(y2 * N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.86e+27], N[(z * N[(N[(c * y0), $MachinePrecision] * (-y3)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.5e+76], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -2.5e50 or 5.5000000000000001e76 < j

   1. Initial program 23.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 23.7%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 26.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 26.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 26.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 30.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 55.6%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y0 around inf 53.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(y3 \cdot y5 - b \cdot x\right) \cdot j\right)} \]

   if -2.5e50 < j < -1.05e-108

   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. Step-by-step derivation

      1. associate-+l- 28.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 28.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 52.1%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 35.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   if -1.05e-108 < j < 4.5999999999999997e-255 or 1.86e27 < j < 5.5000000000000001e76

   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. Step-by-step derivation

      1. associate-+l- 28.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 28.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 43.1%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y1 around inf 42.7%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right) \cdot y2\right)} \]
   6. Step-by-step derivation

      1. *-commutative 42.7%

         \[\leadsto y1 \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]

      2. +-commutative 42.7%

         \[\leadsto y1 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y4 + -1 \cdot \left(a \cdot x\right)\right)}\right) \]

      3. mul-1-neg 42.7%

         \[\leadsto y1 \cdot \left(y2 \cdot \left(k \cdot y4 + \color{blue}{\left(-a \cdot x\right)}\right)\right) \]

      4. unsub-neg 42.7%

         \[\leadsto y1 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y4 - a \cdot x\right)}\right) \]

   7. Simplified 42.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y2 \cdot \left(k \cdot y4 - a \cdot x\right)\right)} \]

   if 4.5999999999999997e-255 < j < 9.59999999999999917e-180

   1. Initial program 11.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 11.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 11.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 61.1%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y0 around -inf 44.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 44.9%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right)} \]

      2. neg-mul-1 44.9%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right) \]

      3. *-commutative 44.9%

         \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(y2 \cdot \left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right)\right)} \]

      4. mul-1-neg 44.9%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 + \color{blue}{\left(-c \cdot x\right)}\right)\right) \]

      5. unsub-neg 44.9%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \]

      6. *-commutative 44.9%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 - \color{blue}{x \cdot c}\right)\right) \]

   7. Simplified 44.9%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 - x \cdot c\right)\right)} \]

   8. Taylor expanded in k around inf 50.8%

      \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y5\right)}\right) \]

   if 9.59999999999999917e-180 < j < 6e13

   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. Step-by-step derivation

      1. associate-+l- 37.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 37.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 48.7%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in k around inf 42.5%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 42.5%

         \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)} \]

      2. *-commutative 42.5%

         \[\leadsto \left(k \cdot y2\right) \cdot \left(\color{blue}{y1 \cdot y4} - y0 \cdot y5\right) \]

   7. Simplified 42.5%

      \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]

   8. Taylor expanded in k around 0 42.5%

      \[\leadsto \color{blue}{k \cdot \left(\left(y4 \cdot y1 - y0 \cdot y5\right) \cdot y2\right)} \]
   9. Step-by-step derivation

      1. *-commutative 42.5%

         \[\leadsto k \cdot \left(\left(y4 \cdot y1 - \color{blue}{y5 \cdot y0}\right) \cdot y2\right) \]

      2. associate-*r* 42.5%

         \[\leadsto \color{blue}{\left(k \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right) \cdot y2} \]

      3. *-commutative 42.5%

         \[\leadsto \color{blue}{y2 \cdot \left(k \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   10. Simplified 42.5%

       \[\leadsto \color{blue}{y2 \cdot \left(k \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   if 6e13 < j < 1.86e27

   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. Step-by-step derivation

      1. associate-+l- 0.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 44.6%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.6%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. *-commutative 44.6%

         \[\leadsto -\color{blue}{z \cdot \left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \]

      3. associate--l+ 44.6%

         \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \]

      4. *-commutative 44.6%

         \[\leadsto -z \cdot \left(\color{blue}{y3 \cdot \left(c \cdot y0 - a \cdot y1\right)} + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      5. *-commutative 44.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      6. *-commutative 44.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      7. *-commutative 44.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      8. *-commutative 44.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - \color{blue}{i \cdot c}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      9. *-commutative 44.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - \color{blue}{k \cdot \left(y0 \cdot b - y1 \cdot i\right)}\right)\right) \]

      10. *-commutative 44.6%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(\color{blue}{b \cdot y0} - y1 \cdot i\right)\right)\right) \]

      11. *-commutative 44.6%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right)\right) \]

   6. Simplified 44.6%

      \[\leadsto \color{blue}{-z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in y3 around inf 78.1%

      \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3\right)} \]
   8. Step-by-step derivation

      1. *-commutative 78.1%

         \[\leadsto -z \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y3\right) \]

   9. Simplified 78.1%

      \[\leadsto -z \cdot \color{blue}{\left(\left(y0 \cdot c - a \cdot y1\right) \cdot y3\right)} \]

   10. Taylor expanded in y0 around inf 78.1%

       \[\leadsto -z \cdot \left(\color{blue}{\left(c \cdot y0\right)} \cdot y3\right) \]
   11. Step-by-step derivation

       1. *-commutative 78.1%

          \[\leadsto -z \cdot \left(\color{blue}{\left(y0 \cdot c\right)} \cdot y3\right) \]

   12. Simplified 78.1%

       \[\leadsto -z \cdot \left(\color{blue}{\left(y0 \cdot c\right)} \cdot y3\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.5 \cdot 10^{+50}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-108}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 4.6 \cdot 10^{-255}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;j \leq 9.6 \cdot 10^{-180}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 60000000000000:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 1.86 \cdot 10^{+27}:\\ \;\;\;\;z \cdot \left(\left(c \cdot y0\right) \cdot \left(-y3\right)\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{+76}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \]

Alternative 24: 21.4% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y5 \cdot \left(t \cdot \left(-i\right)\right)\right)\\ \mathbf{if}\;y3 \leq -4.4 \cdot 10^{-12}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y3 \leq -2.3 \cdot 10^{-161}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y3 \leq -1.5 \cdot 10^{-240}:\\ \;\;\;\;\left(-i\right) \cdot \left(t \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq 8.2 \cdot 10^{-249}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 8 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq 410000000000:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y0 \cdot \left(-y5\right)\right)\\ \mathbf{elif}\;y3 \leq 9 \cdot 10^{+43}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 1.7 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y5 (* t (- i))))))
   (if (<= y3 -4.4e-12)
     (* c (* y0 (* z (- y3))))
     (if (<= y3 -2.3e-161)
       (* y0 (* y2 (* k (- y5))))
       (if (<= y3 -1.5e-240)
         (* (- i) (* t (* j y5)))
         (if (<= y3 8.2e-249)
           (* c (* y4 (* t (- y2))))
           (if (<= y3 8e-116)
             t_1
             (if (<= y3 410000000000.0)
               (* (* k y2) (* y0 (- y5)))
               (if (<= y3 9e+43)
                 (* c (* x (* y0 y2)))
                 (if (<= y3 1.7e+81) t_1 (* y0 (* y3 (* j y5)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y5 * (t * -i));
	double tmp;
	if (y3 <= -4.4e-12) {
		tmp = c * (y0 * (z * -y3));
	} else if (y3 <= -2.3e-161) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (y3 <= -1.5e-240) {
		tmp = -i * (t * (j * y5));
	} else if (y3 <= 8.2e-249) {
		tmp = c * (y4 * (t * -y2));
	} else if (y3 <= 8e-116) {
		tmp = t_1;
	} else if (y3 <= 410000000000.0) {
		tmp = (k * y2) * (y0 * -y5);
	} else if (y3 <= 9e+43) {
		tmp = c * (x * (y0 * y2));
	} else if (y3 <= 1.7e+81) {
		tmp = t_1;
	} else {
		tmp = y0 * (y3 * (j * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (y5 * (t * -i))
    if (y3 <= (-4.4d-12)) then
        tmp = c * (y0 * (z * -y3))
    else if (y3 <= (-2.3d-161)) then
        tmp = y0 * (y2 * (k * -y5))
    else if (y3 <= (-1.5d-240)) then
        tmp = -i * (t * (j * y5))
    else if (y3 <= 8.2d-249) then
        tmp = c * (y4 * (t * -y2))
    else if (y3 <= 8d-116) then
        tmp = t_1
    else if (y3 <= 410000000000.0d0) then
        tmp = (k * y2) * (y0 * -y5)
    else if (y3 <= 9d+43) then
        tmp = c * (x * (y0 * y2))
    else if (y3 <= 1.7d+81) then
        tmp = t_1
    else
        tmp = y0 * (y3 * (j * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y5 * (t * -i));
	double tmp;
	if (y3 <= -4.4e-12) {
		tmp = c * (y0 * (z * -y3));
	} else if (y3 <= -2.3e-161) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (y3 <= -1.5e-240) {
		tmp = -i * (t * (j * y5));
	} else if (y3 <= 8.2e-249) {
		tmp = c * (y4 * (t * -y2));
	} else if (y3 <= 8e-116) {
		tmp = t_1;
	} else if (y3 <= 410000000000.0) {
		tmp = (k * y2) * (y0 * -y5);
	} else if (y3 <= 9e+43) {
		tmp = c * (x * (y0 * y2));
	} else if (y3 <= 1.7e+81) {
		tmp = t_1;
	} else {
		tmp = y0 * (y3 * (j * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (y5 * (t * -i))
	tmp = 0
	if y3 <= -4.4e-12:
		tmp = c * (y0 * (z * -y3))
	elif y3 <= -2.3e-161:
		tmp = y0 * (y2 * (k * -y5))
	elif y3 <= -1.5e-240:
		tmp = -i * (t * (j * y5))
	elif y3 <= 8.2e-249:
		tmp = c * (y4 * (t * -y2))
	elif y3 <= 8e-116:
		tmp = t_1
	elif y3 <= 410000000000.0:
		tmp = (k * y2) * (y0 * -y5)
	elif y3 <= 9e+43:
		tmp = c * (x * (y0 * y2))
	elif y3 <= 1.7e+81:
		tmp = t_1
	else:
		tmp = y0 * (y3 * (j * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(y5 * Float64(t * Float64(-i))))
	tmp = 0.0
	if (y3 <= -4.4e-12)
		tmp = Float64(c * Float64(y0 * Float64(z * Float64(-y3))));
	elseif (y3 <= -2.3e-161)
		tmp = Float64(y0 * Float64(y2 * Float64(k * Float64(-y5))));
	elseif (y3 <= -1.5e-240)
		tmp = Float64(Float64(-i) * Float64(t * Float64(j * y5)));
	elseif (y3 <= 8.2e-249)
		tmp = Float64(c * Float64(y4 * Float64(t * Float64(-y2))));
	elseif (y3 <= 8e-116)
		tmp = t_1;
	elseif (y3 <= 410000000000.0)
		tmp = Float64(Float64(k * y2) * Float64(y0 * Float64(-y5)));
	elseif (y3 <= 9e+43)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (y3 <= 1.7e+81)
		tmp = t_1;
	else
		tmp = Float64(y0 * Float64(y3 * Float64(j * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * (y5 * (t * -i));
	tmp = 0.0;
	if (y3 <= -4.4e-12)
		tmp = c * (y0 * (z * -y3));
	elseif (y3 <= -2.3e-161)
		tmp = y0 * (y2 * (k * -y5));
	elseif (y3 <= -1.5e-240)
		tmp = -i * (t * (j * y5));
	elseif (y3 <= 8.2e-249)
		tmp = c * (y4 * (t * -y2));
	elseif (y3 <= 8e-116)
		tmp = t_1;
	elseif (y3 <= 410000000000.0)
		tmp = (k * y2) * (y0 * -y5);
	elseif (y3 <= 9e+43)
		tmp = c * (x * (y0 * y2));
	elseif (y3 <= 1.7e+81)
		tmp = t_1;
	else
		tmp = y0 * (y3 * (j * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(y5 * N[(t * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -4.4e-12], N[(c * N[(y0 * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -2.3e-161], N[(y0 * N[(y2 * N[(k * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1.5e-240], N[((-i) * N[(t * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 8.2e-249], N[(c * N[(y4 * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 8e-116], t$95$1, If[LessEqual[y3, 410000000000.0], N[(N[(k * y2), $MachinePrecision] * N[(y0 * (-y5)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 9e+43], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.7e+81], t$95$1, N[(y0 * N[(y3 * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y3 < -4.39999999999999983e-12

   1. Initial program 20.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 20.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 20.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 27.6%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 27.6%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. *-commutative 27.6%

         \[\leadsto -\color{blue}{z \cdot \left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \]

      3. associate--l+ 27.6%

         \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \]

      4. *-commutative 27.6%

         \[\leadsto -z \cdot \left(\color{blue}{y3 \cdot \left(c \cdot y0 - a \cdot y1\right)} + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      5. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      6. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      7. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      8. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - \color{blue}{i \cdot c}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      9. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - \color{blue}{k \cdot \left(y0 \cdot b - y1 \cdot i\right)}\right)\right) \]

      10. *-commutative 27.6%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(\color{blue}{b \cdot y0} - y1 \cdot i\right)\right)\right) \]

      11. *-commutative 27.6%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right)\right) \]

   6. Simplified 27.6%

      \[\leadsto \color{blue}{-z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in y3 around inf 48.3%

      \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3\right)} \]
   8. Step-by-step derivation

      1. *-commutative 48.3%

         \[\leadsto -z \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y3\right) \]

   9. Simplified 48.3%

      \[\leadsto -z \cdot \color{blue}{\left(\left(y0 \cdot c - a \cdot y1\right) \cdot y3\right)} \]

   10. Taylor expanded in y0 around inf 40.0%

       \[\leadsto -\color{blue}{c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]

   if -4.39999999999999983e-12 < y3 < -2.3e-161

   1. Initial program 28.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 28.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 28.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 51.8%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y0 around -inf 50.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 50.7%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right)} \]

      2. neg-mul-1 50.7%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right) \]

      3. *-commutative 50.7%

         \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(y2 \cdot \left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right)\right)} \]

      4. mul-1-neg 50.7%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 + \color{blue}{\left(-c \cdot x\right)}\right)\right) \]

      5. unsub-neg 50.7%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \]

      6. *-commutative 50.7%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 - \color{blue}{x \cdot c}\right)\right) \]

   7. Simplified 50.7%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 - x \cdot c\right)\right)} \]

   8. Taylor expanded in k around inf 38.5%

      \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y5\right)}\right) \]

   if -2.3e-161 < y3 < -1.49999999999999995e-240

   1. Initial program 29.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 29.2%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 35.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 35.1%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 35.1%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 41.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 42.2%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y5 around inf 13.8%

      \[\leadsto \color{blue}{\left(\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot y5\right)} \cdot j \]
   6. Step-by-step derivation

      1. *-commutative 13.8%

         \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)\right)} \cdot j \]

      2. mul-1-neg 13.8%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \cdot j \]

      3. unsub-neg 13.8%

         \[\leadsto \left(y5 \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \cdot j \]

      4. *-commutative 13.8%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 - \color{blue}{t \cdot i}\right)\right) \cdot j \]

   7. Simplified 13.8%

      \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)} \cdot j \]

   8. Taylor expanded in y0 around 0 30.7%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(t \cdot \left(j \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 30.7%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

      2. neg-mul-1 30.7%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(t \cdot \left(j \cdot y5\right)\right) \]

      3. *-commutative 30.7%

         \[\leadsto \left(-i\right) \cdot \left(t \cdot \color{blue}{\left(y5 \cdot j\right)}\right) \]

   10. Simplified 30.7%

       \[\leadsto \color{blue}{\left(-i\right) \cdot \left(t \cdot \left(y5 \cdot j\right)\right)} \]

   if -1.49999999999999995e-240 < y3 < 8.20000000000000007e-249

   1. Initial program 38.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 38.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 38.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 58.8%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 39.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   6. Taylor expanded in y0 around 0 43.6%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 43.6%

         \[\leadsto c \cdot \color{blue}{\left(-y4 \cdot \left(t \cdot y2\right)\right)} \]

      2. *-commutative 43.6%

         \[\leadsto c \cdot \left(-\color{blue}{\left(t \cdot y2\right) \cdot y4}\right) \]

      3. distribute-rgt-neg-in 43.6%

         \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot y2\right) \cdot \left(-y4\right)\right)} \]

   8. Simplified 43.6%

      \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot y2\right) \cdot \left(-y4\right)\right)} \]

   if 8.20000000000000007e-249 < y3 < 8e-116 or 9e43 < y3 < 1.70000000000000001e81

   1. Initial program 39.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 39.7%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 39.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 39.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 39.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 39.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 42.9%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y5 around inf 40.8%

      \[\leadsto \color{blue}{\left(\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot y5\right)} \cdot j \]
   6. Step-by-step derivation

      1. *-commutative 40.8%

         \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)\right)} \cdot j \]

      2. mul-1-neg 40.8%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \cdot j \]

      3. unsub-neg 40.8%

         \[\leadsto \left(y5 \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \cdot j \]

      4. *-commutative 40.8%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 - \color{blue}{t \cdot i}\right)\right) \cdot j \]

   7. Simplified 40.8%

      \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)} \cdot j \]

   8. Taylor expanded in y0 around 0 29.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot y5\right)\right)\right)} \cdot j \]
   9. Step-by-step derivation

      1. mul-1-neg 29.2%

         \[\leadsto \color{blue}{\left(-i \cdot \left(t \cdot y5\right)\right)} \cdot j \]

      2. associate-*r* 37.9%

         \[\leadsto \left(-\color{blue}{\left(i \cdot t\right) \cdot y5}\right) \cdot j \]

      3. distribute-rgt-neg-in 37.9%

         \[\leadsto \color{blue}{\left(\left(i \cdot t\right) \cdot \left(-y5\right)\right)} \cdot j \]

   10. Simplified 37.9%

       \[\leadsto \color{blue}{\left(\left(i \cdot t\right) \cdot \left(-y5\right)\right)} \cdot j \]

   if 8e-116 < y3 < 4.1e11

   1. Initial program 19.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 19.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 19.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 29.9%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in k around inf 28.6%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 28.6%

         \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)} \]

      2. *-commutative 28.6%

         \[\leadsto \left(k \cdot y2\right) \cdot \left(\color{blue}{y1 \cdot y4} - y0 \cdot y5\right) \]

   7. Simplified 28.6%

      \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]

   8. Taylor expanded in y1 around 0 28.6%

      \[\leadsto \left(k \cdot y2\right) \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 28.6%

         \[\leadsto \left(k \cdot y2\right) \cdot \color{blue}{\left(-y0 \cdot y5\right)} \]

      2. distribute-lft-neg-out 28.6%

         \[\leadsto \left(k \cdot y2\right) \cdot \color{blue}{\left(\left(-y0\right) \cdot y5\right)} \]

      3. *-commutative 28.6%

         \[\leadsto \left(k \cdot y2\right) \cdot \color{blue}{\left(y5 \cdot \left(-y0\right)\right)} \]

   10. Simplified 28.6%

       \[\leadsto \left(k \cdot y2\right) \cdot \color{blue}{\left(y5 \cdot \left(-y0\right)\right)} \]

   if 4.1e11 < y3 < 9e43

   1. Initial program 24.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 24.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 38.0%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 50.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   6. Taylor expanded in y0 around inf 38.6%

      \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot x\right)} \cdot y2\right) \]

   7. Taylor expanded in c around 0 38.6%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 38.6%

         \[\leadsto c \cdot \left(y0 \cdot \color{blue}{\left(y2 \cdot x\right)}\right) \]

      2. associate-*r* 50.8%

         \[\leadsto c \cdot \color{blue}{\left(\left(y0 \cdot y2\right) \cdot x\right)} \]

   9. Simplified 50.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot y2\right) \cdot x\right)} \]

   if 1.70000000000000001e81 < y3

   1. Initial program 16.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 16.5%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 22.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 22.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 22.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 23.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 38.7%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y5 around inf 32.1%

      \[\leadsto \color{blue}{\left(\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot y5\right)} \cdot j \]
   6. Step-by-step derivation

      1. *-commutative 32.1%

         \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)\right)} \cdot j \]

      2. mul-1-neg 32.1%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \cdot j \]

      3. unsub-neg 32.1%

         \[\leadsto \left(y5 \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \cdot j \]

      4. *-commutative 32.1%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 - \color{blue}{t \cdot i}\right)\right) \cdot j \]

   7. Simplified 32.1%

      \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)} \cdot j \]

   8. Taylor expanded in y0 around inf 42.6%

      \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 42.6%

         \[\leadsto y0 \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot j\right)}\right) \]

   10. Simplified 42.6%

       \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(y5 \cdot j\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -4.4 \cdot 10^{-12}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y3 \leq -2.3 \cdot 10^{-161}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y3 \leq -1.5 \cdot 10^{-240}:\\ \;\;\;\;\left(-i\right) \cdot \left(t \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq 8.2 \cdot 10^{-249}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 8 \cdot 10^{-116}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(t \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 410000000000:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y0 \cdot \left(-y5\right)\right)\\ \mathbf{elif}\;y3 \leq 9 \cdot 10^{+43}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 1.7 \cdot 10^{+81}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(t \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \end{array} \]

Alternative 25: 29.9% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{if}\;c \leq -1.7 \cdot 10^{+178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -3.25 \cdot 10^{+66}:\\ \;\;\;\;\left(x \cdot b\right) \cdot \left(y \cdot a - j \cdot y0\right)\\ \mathbf{elif}\;c \leq -2.05 \cdot 10^{-73}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{-262}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;c \leq 17000000000000:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* z (* y3 (- (* a y1) (* c y0))))))
   (if (<= c -1.7e+178)
     t_1
     (if (<= c -3.25e+66)
       (* (* x b) (- (* y a) (* j y0)))
       (if (<= c -2.05e-73)
         (* k (* y5 (- (* y i) (* y0 y2))))
         (if (<= c 2.1e-262)
           (* y1 (* y2 (- (* k y4) (* x a))))
           (if (<= c 17000000000000.0)
             (* b (* y (- (* x a) (* k y4))))
             t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = z * (y3 * ((a * y1) - (c * y0)));
	double tmp;
	if (c <= -1.7e+178) {
		tmp = t_1;
	} else if (c <= -3.25e+66) {
		tmp = (x * b) * ((y * a) - (j * y0));
	} else if (c <= -2.05e-73) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (c <= 2.1e-262) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (c <= 17000000000000.0) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (y3 * ((a * y1) - (c * y0)))
    if (c <= (-1.7d+178)) then
        tmp = t_1
    else if (c <= (-3.25d+66)) then
        tmp = (x * b) * ((y * a) - (j * y0))
    else if (c <= (-2.05d-73)) then
        tmp = k * (y5 * ((y * i) - (y0 * y2)))
    else if (c <= 2.1d-262) then
        tmp = y1 * (y2 * ((k * y4) - (x * a)))
    else if (c <= 17000000000000.0d0) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = z * (y3 * ((a * y1) - (c * y0)));
	double tmp;
	if (c <= -1.7e+178) {
		tmp = t_1;
	} else if (c <= -3.25e+66) {
		tmp = (x * b) * ((y * a) - (j * y0));
	} else if (c <= -2.05e-73) {
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	} else if (c <= 2.1e-262) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (c <= 17000000000000.0) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = z * (y3 * ((a * y1) - (c * y0)))
	tmp = 0
	if c <= -1.7e+178:
		tmp = t_1
	elif c <= -3.25e+66:
		tmp = (x * b) * ((y * a) - (j * y0))
	elif c <= -2.05e-73:
		tmp = k * (y5 * ((y * i) - (y0 * y2)))
	elif c <= 2.1e-262:
		tmp = y1 * (y2 * ((k * y4) - (x * a)))
	elif c <= 17000000000000.0:
		tmp = b * (y * ((x * a) - (k * y4)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(z * Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))))
	tmp = 0.0
	if (c <= -1.7e+178)
		tmp = t_1;
	elseif (c <= -3.25e+66)
		tmp = Float64(Float64(x * b) * Float64(Float64(y * a) - Float64(j * y0)));
	elseif (c <= -2.05e-73)
		tmp = Float64(k * Float64(y5 * Float64(Float64(y * i) - Float64(y0 * y2))));
	elseif (c <= 2.1e-262)
		tmp = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (c <= 17000000000000.0)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = z * (y3 * ((a * y1) - (c * y0)));
	tmp = 0.0;
	if (c <= -1.7e+178)
		tmp = t_1;
	elseif (c <= -3.25e+66)
		tmp = (x * b) * ((y * a) - (j * y0));
	elseif (c <= -2.05e-73)
		tmp = k * (y5 * ((y * i) - (y0 * y2)));
	elseif (c <= 2.1e-262)
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	elseif (c <= 17000000000000.0)
		tmp = b * (y * ((x * a) - (k * y4)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(z * N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.7e+178], t$95$1, If[LessEqual[c, -3.25e+66], N[(N[(x * b), $MachinePrecision] * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.05e-73], N[(k * N[(y5 * N[(N[(y * i), $MachinePrecision] - N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.1e-262], N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 17000000000000.0], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.7000000000000001e178 or 1.7e13 < c

   1. Initial program 22.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 22.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 22.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 36.2%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 36.2%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. *-commutative 36.2%

         \[\leadsto -\color{blue}{z \cdot \left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \]

      3. associate--l+ 36.2%

         \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \]

      4. *-commutative 36.2%

         \[\leadsto -z \cdot \left(\color{blue}{y3 \cdot \left(c \cdot y0 - a \cdot y1\right)} + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      5. *-commutative 36.2%

         \[\leadsto -z \cdot \left(y3 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      6. *-commutative 36.2%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      7. *-commutative 36.2%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      8. *-commutative 36.2%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - \color{blue}{i \cdot c}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      9. *-commutative 36.2%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - \color{blue}{k \cdot \left(y0 \cdot b - y1 \cdot i\right)}\right)\right) \]

      10. *-commutative 36.2%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(\color{blue}{b \cdot y0} - y1 \cdot i\right)\right)\right) \]

      11. *-commutative 36.2%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right)\right) \]

   6. Simplified 36.2%

      \[\leadsto \color{blue}{-z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in y3 around inf 45.0%

      \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3\right)} \]
   8. Step-by-step derivation

      1. *-commutative 45.0%

         \[\leadsto -z \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y3\right) \]

   9. Simplified 45.0%

      \[\leadsto -z \cdot \color{blue}{\left(\left(y0 \cdot c - a \cdot y1\right) \cdot y3\right)} \]

   if -1.7000000000000001e178 < c < -3.2500000000000001e66

   1. Initial program 25.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 25.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 41.1%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot b} \]

   5. Taylor expanded in x around inf 49.2%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]

   if -3.2500000000000001e66 < c < -2.05000000000000008e-73

   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. Step-by-step derivation

      1. associate-+l- 34.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 34.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y5 around -inf 42.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot i + y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.3%

         \[\leadsto \color{blue}{-y5 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot i + y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. associate--l+ 42.3%

         \[\leadsto -y5 \cdot \color{blue}{\left(\left(t \cdot j - k \cdot y\right) \cdot i + \left(y0 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      3. *-commutative 42.3%

         \[\leadsto -y5 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot i + \left(y0 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 42.3%

      \[\leadsto \color{blue}{-y5 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot i + \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in k around inf 46.0%

      \[\leadsto -\color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)} \]
   8. Step-by-step derivation

      1. *-commutative 46.0%

         \[\leadsto -k \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right)\right)} \]

      2. +-commutative 46.0%

         \[\leadsto -k \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(y \cdot i\right)\right)}\right) \]

      3. mul-1-neg 46.0%

         \[\leadsto -k \cdot \left(y5 \cdot \left(y0 \cdot y2 + \color{blue}{\left(-y \cdot i\right)}\right)\right) \]

      4. unsub-neg 46.0%

         \[\leadsto -k \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 - y \cdot i\right)}\right) \]

      5. *-commutative 46.0%

         \[\leadsto -k \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot y0} - y \cdot i\right)\right) \]

   9. Simplified 46.0%

      \[\leadsto -\color{blue}{k \cdot \left(y5 \cdot \left(y2 \cdot y0 - y \cdot i\right)\right)} \]

   if -2.05000000000000008e-73 < c < 2.1e-262

   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. Step-by-step derivation

      1. associate-+l- 27.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 27.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 46.8%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y1 around inf 43.5%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right) \cdot y2\right)} \]
   6. Step-by-step derivation

      1. *-commutative 43.5%

         \[\leadsto y1 \cdot \color{blue}{\left(y2 \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]

      2. +-commutative 43.5%

         \[\leadsto y1 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y4 + -1 \cdot \left(a \cdot x\right)\right)}\right) \]

      3. mul-1-neg 43.5%

         \[\leadsto y1 \cdot \left(y2 \cdot \left(k \cdot y4 + \color{blue}{\left(-a \cdot x\right)}\right)\right) \]

      4. unsub-neg 43.5%

         \[\leadsto y1 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y4 - a \cdot x\right)}\right) \]

   7. Simplified 43.5%

      \[\leadsto \color{blue}{y1 \cdot \left(y2 \cdot \left(k \cdot y4 - a \cdot x\right)\right)} \]

   if 2.1e-262 < c < 1.7e13

   1. Initial program 23.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 23.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 23.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 38.2%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot b} \]

   5. Taylor expanded in y around inf 40.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot \left(y \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 45.4%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot y\right) \cdot b} \]

      2. *-commutative 45.4%

         \[\leadsto \color{blue}{b \cdot \left(\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot y\right)} \]

      3. *-commutative 45.4%

         \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]

      4. +-commutative 45.4%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      5. mul-1-neg 45.4%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      6. unsub-neg 45.4%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   7. Simplified 45.4%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.7 \cdot 10^{+178}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq -3.25 \cdot 10^{+66}:\\ \;\;\;\;\left(x \cdot b\right) \cdot \left(y \cdot a - j \cdot y0\right)\\ \mathbf{elif}\;c \leq -2.05 \cdot 10^{-73}:\\ \;\;\;\;k \cdot \left(y5 \cdot \left(y \cdot i - y0 \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{-262}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;c \leq 17000000000000:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \end{array} \]

Alternative 26: 21.4% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-i\right) \cdot \left(t \cdot \left(j \cdot y5\right)\right)\\ \mathbf{if}\;y3 \leq -1.55 \cdot 10^{-12}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y3 \leq -6.5 \cdot 10^{-161}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y3 \leq -2.3 \cdot 10^{-242}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq 2.5 \cdot 10^{-243}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 5.2 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq 2.9 \cdot 10^{-15}:\\ \;\;\;\;k \cdot \left(\left(y0 \cdot y5\right) \cdot \left(-y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (- i) (* t (* j y5)))))
   (if (<= y3 -1.55e-12)
     (* c (* y0 (* z (- y3))))
     (if (<= y3 -6.5e-161)
       (* y0 (* y2 (* k (- y5))))
       (if (<= y3 -2.3e-242)
         t_1
         (if (<= y3 2.5e-243)
           (* c (* y4 (* t (- y2))))
           (if (<= y3 5.2e-113)
             t_1
             (if (<= y3 2.9e-15)
               (* k (* (* y0 y5) (- y2)))
               (* y0 (* y3 (* j y5)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = -i * (t * (j * y5));
	double tmp;
	if (y3 <= -1.55e-12) {
		tmp = c * (y0 * (z * -y3));
	} else if (y3 <= -6.5e-161) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (y3 <= -2.3e-242) {
		tmp = t_1;
	} else if (y3 <= 2.5e-243) {
		tmp = c * (y4 * (t * -y2));
	} else if (y3 <= 5.2e-113) {
		tmp = t_1;
	} else if (y3 <= 2.9e-15) {
		tmp = k * ((y0 * y5) * -y2);
	} else {
		tmp = y0 * (y3 * (j * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -i * (t * (j * y5))
    if (y3 <= (-1.55d-12)) then
        tmp = c * (y0 * (z * -y3))
    else if (y3 <= (-6.5d-161)) then
        tmp = y0 * (y2 * (k * -y5))
    else if (y3 <= (-2.3d-242)) then
        tmp = t_1
    else if (y3 <= 2.5d-243) then
        tmp = c * (y4 * (t * -y2))
    else if (y3 <= 5.2d-113) then
        tmp = t_1
    else if (y3 <= 2.9d-15) then
        tmp = k * ((y0 * y5) * -y2)
    else
        tmp = y0 * (y3 * (j * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = -i * (t * (j * y5));
	double tmp;
	if (y3 <= -1.55e-12) {
		tmp = c * (y0 * (z * -y3));
	} else if (y3 <= -6.5e-161) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (y3 <= -2.3e-242) {
		tmp = t_1;
	} else if (y3 <= 2.5e-243) {
		tmp = c * (y4 * (t * -y2));
	} else if (y3 <= 5.2e-113) {
		tmp = t_1;
	} else if (y3 <= 2.9e-15) {
		tmp = k * ((y0 * y5) * -y2);
	} else {
		tmp = y0 * (y3 * (j * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = -i * (t * (j * y5))
	tmp = 0
	if y3 <= -1.55e-12:
		tmp = c * (y0 * (z * -y3))
	elif y3 <= -6.5e-161:
		tmp = y0 * (y2 * (k * -y5))
	elif y3 <= -2.3e-242:
		tmp = t_1
	elif y3 <= 2.5e-243:
		tmp = c * (y4 * (t * -y2))
	elif y3 <= 5.2e-113:
		tmp = t_1
	elif y3 <= 2.9e-15:
		tmp = k * ((y0 * y5) * -y2)
	else:
		tmp = y0 * (y3 * (j * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(-i) * Float64(t * Float64(j * y5)))
	tmp = 0.0
	if (y3 <= -1.55e-12)
		tmp = Float64(c * Float64(y0 * Float64(z * Float64(-y3))));
	elseif (y3 <= -6.5e-161)
		tmp = Float64(y0 * Float64(y2 * Float64(k * Float64(-y5))));
	elseif (y3 <= -2.3e-242)
		tmp = t_1;
	elseif (y3 <= 2.5e-243)
		tmp = Float64(c * Float64(y4 * Float64(t * Float64(-y2))));
	elseif (y3 <= 5.2e-113)
		tmp = t_1;
	elseif (y3 <= 2.9e-15)
		tmp = Float64(k * Float64(Float64(y0 * y5) * Float64(-y2)));
	else
		tmp = Float64(y0 * Float64(y3 * Float64(j * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = -i * (t * (j * y5));
	tmp = 0.0;
	if (y3 <= -1.55e-12)
		tmp = c * (y0 * (z * -y3));
	elseif (y3 <= -6.5e-161)
		tmp = y0 * (y2 * (k * -y5));
	elseif (y3 <= -2.3e-242)
		tmp = t_1;
	elseif (y3 <= 2.5e-243)
		tmp = c * (y4 * (t * -y2));
	elseif (y3 <= 5.2e-113)
		tmp = t_1;
	elseif (y3 <= 2.9e-15)
		tmp = k * ((y0 * y5) * -y2);
	else
		tmp = y0 * (y3 * (j * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[((-i) * N[(t * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -1.55e-12], N[(c * N[(y0 * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -6.5e-161], N[(y0 * N[(y2 * N[(k * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -2.3e-242], t$95$1, If[LessEqual[y3, 2.5e-243], N[(c * N[(y4 * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 5.2e-113], t$95$1, If[LessEqual[y3, 2.9e-15], N[(k * N[(N[(y0 * y5), $MachinePrecision] * (-y2)), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(y3 * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y3 < -1.5500000000000001e-12

   1. Initial program 20.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 20.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 20.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 27.6%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 27.6%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. *-commutative 27.6%

         \[\leadsto -\color{blue}{z \cdot \left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \]

      3. associate--l+ 27.6%

         \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \]

      4. *-commutative 27.6%

         \[\leadsto -z \cdot \left(\color{blue}{y3 \cdot \left(c \cdot y0 - a \cdot y1\right)} + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      5. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      6. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      7. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      8. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - \color{blue}{i \cdot c}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      9. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - \color{blue}{k \cdot \left(y0 \cdot b - y1 \cdot i\right)}\right)\right) \]

      10. *-commutative 27.6%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(\color{blue}{b \cdot y0} - y1 \cdot i\right)\right)\right) \]

      11. *-commutative 27.6%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right)\right) \]

   6. Simplified 27.6%

      \[\leadsto \color{blue}{-z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in y3 around inf 48.3%

      \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3\right)} \]
   8. Step-by-step derivation

      1. *-commutative 48.3%

         \[\leadsto -z \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y3\right) \]

   9. Simplified 48.3%

      \[\leadsto -z \cdot \color{blue}{\left(\left(y0 \cdot c - a \cdot y1\right) \cdot y3\right)} \]

   10. Taylor expanded in y0 around inf 40.0%

       \[\leadsto -\color{blue}{c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]

   if -1.5500000000000001e-12 < y3 < -6.50000000000000008e-161

   1. Initial program 28.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 28.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 28.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 51.8%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y0 around -inf 50.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 50.7%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right)} \]

      2. neg-mul-1 50.7%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right) \]

      3. *-commutative 50.7%

         \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(y2 \cdot \left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right)\right)} \]

      4. mul-1-neg 50.7%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 + \color{blue}{\left(-c \cdot x\right)}\right)\right) \]

      5. unsub-neg 50.7%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \]

      6. *-commutative 50.7%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 - \color{blue}{x \cdot c}\right)\right) \]

   7. Simplified 50.7%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 - x \cdot c\right)\right)} \]

   8. Taylor expanded in k around inf 38.5%

      \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y5\right)}\right) \]

   if -6.50000000000000008e-161 < y3 < -2.29999999999999985e-242 or 2.5e-243 < y3 < 5.1999999999999998e-113

   1. Initial program 36.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 36.3%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 38.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 38.5%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 38.5%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 42.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 45.4%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y5 around inf 29.4%

      \[\leadsto \color{blue}{\left(\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot y5\right)} \cdot j \]
   6. Step-by-step derivation

      1. *-commutative 29.4%

         \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)\right)} \cdot j \]

      2. mul-1-neg 29.4%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \cdot j \]

      3. unsub-neg 29.4%

         \[\leadsto \left(y5 \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \cdot j \]

      4. *-commutative 29.4%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 - \color{blue}{t \cdot i}\right)\right) \cdot j \]

   7. Simplified 29.4%

      \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)} \cdot j \]

   8. Taylor expanded in y0 around 0 31.3%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(t \cdot \left(j \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 31.3%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

      2. neg-mul-1 31.3%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(t \cdot \left(j \cdot y5\right)\right) \]

      3. *-commutative 31.3%

         \[\leadsto \left(-i\right) \cdot \left(t \cdot \color{blue}{\left(y5 \cdot j\right)}\right) \]

   10. Simplified 31.3%

       \[\leadsto \color{blue}{\left(-i\right) \cdot \left(t \cdot \left(y5 \cdot j\right)\right)} \]

   if -2.29999999999999985e-242 < y3 < 2.5e-243

   1. Initial program 38.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 38.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 38.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 58.8%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 39.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   6. Taylor expanded in y0 around 0 43.6%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 43.6%

         \[\leadsto c \cdot \color{blue}{\left(-y4 \cdot \left(t \cdot y2\right)\right)} \]

      2. *-commutative 43.6%

         \[\leadsto c \cdot \left(-\color{blue}{\left(t \cdot y2\right) \cdot y4}\right) \]

      3. distribute-rgt-neg-in 43.6%

         \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot y2\right) \cdot \left(-y4\right)\right)} \]

   8. Simplified 43.6%

      \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot y2\right) \cdot \left(-y4\right)\right)} \]

   if 5.1999999999999998e-113 < y3 < 2.90000000000000019e-15

   1. Initial program 25.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 25.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 28.8%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in k around inf 32.0%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 31.9%

         \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)} \]

      2. *-commutative 31.9%

         \[\leadsto \left(k \cdot y2\right) \cdot \left(\color{blue}{y1 \cdot y4} - y0 \cdot y5\right) \]

   7. Simplified 31.9%

      \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]

   8. Taylor expanded in y1 around 0 27.0%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(y5 \cdot y2\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 27.0%

         \[\leadsto \color{blue}{-k \cdot \left(y0 \cdot \left(y5 \cdot y2\right)\right)} \]

      2. associate-*r* 31.8%

         \[\leadsto -k \cdot \color{blue}{\left(\left(y0 \cdot y5\right) \cdot y2\right)} \]

      3. *-commutative 31.8%

         \[\leadsto -k \cdot \left(\color{blue}{\left(y5 \cdot y0\right)} \cdot y2\right) \]

   10. Simplified 31.8%

       \[\leadsto \color{blue}{-k \cdot \left(\left(y5 \cdot y0\right) \cdot y2\right)} \]

   if 2.90000000000000019e-15 < y3

   1. Initial program 16.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 16.8%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 22.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 22.3%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 22.3%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 23.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 39.4%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y5 around inf 34.6%

      \[\leadsto \color{blue}{\left(\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot y5\right)} \cdot j \]
   6. Step-by-step derivation

      1. *-commutative 34.6%

         \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)\right)} \cdot j \]

      2. mul-1-neg 34.6%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \cdot j \]

      3. unsub-neg 34.6%

         \[\leadsto \left(y5 \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \cdot j \]

      4. *-commutative 34.6%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 - \color{blue}{t \cdot i}\right)\right) \cdot j \]

   7. Simplified 34.6%

      \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)} \cdot j \]

   8. Taylor expanded in y0 around inf 37.1%

      \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 37.1%

         \[\leadsto y0 \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot j\right)}\right) \]

   10. Simplified 37.1%

       \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(y5 \cdot j\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.55 \cdot 10^{-12}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y3 \leq -6.5 \cdot 10^{-161}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y3 \leq -2.3 \cdot 10^{-242}:\\ \;\;\;\;\left(-i\right) \cdot \left(t \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq 2.5 \cdot 10^{-243}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 5.2 \cdot 10^{-113}:\\ \;\;\;\;\left(-i\right) \cdot \left(t \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq 2.9 \cdot 10^{-15}:\\ \;\;\;\;k \cdot \left(\left(y0 \cdot y5\right) \cdot \left(-y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \end{array} \]

Alternative 27: 21.3% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-i\right) \cdot \left(t \cdot \left(j \cdot y5\right)\right)\\ \mathbf{if}\;y3 \leq -1.4 \cdot 10^{-11}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y3 \leq -2 \cdot 10^{-159}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y3 \leq -1.42 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq 9.8 \cdot 10^{-244}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 5.9 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq 4.5 \cdot 10^{-15}:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y0 \cdot \left(-y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (- i) (* t (* j y5)))))
   (if (<= y3 -1.4e-11)
     (* c (* y0 (* z (- y3))))
     (if (<= y3 -2e-159)
       (* y0 (* y2 (* k (- y5))))
       (if (<= y3 -1.42e-243)
         t_1
         (if (<= y3 9.8e-244)
           (* c (* y4 (* t (- y2))))
           (if (<= y3 5.9e-111)
             t_1
             (if (<= y3 4.5e-15)
               (* (* k y2) (* y0 (- y5)))
               (* y0 (* y3 (* j y5)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = -i * (t * (j * y5));
	double tmp;
	if (y3 <= -1.4e-11) {
		tmp = c * (y0 * (z * -y3));
	} else if (y3 <= -2e-159) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (y3 <= -1.42e-243) {
		tmp = t_1;
	} else if (y3 <= 9.8e-244) {
		tmp = c * (y4 * (t * -y2));
	} else if (y3 <= 5.9e-111) {
		tmp = t_1;
	} else if (y3 <= 4.5e-15) {
		tmp = (k * y2) * (y0 * -y5);
	} else {
		tmp = y0 * (y3 * (j * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -i * (t * (j * y5))
    if (y3 <= (-1.4d-11)) then
        tmp = c * (y0 * (z * -y3))
    else if (y3 <= (-2d-159)) then
        tmp = y0 * (y2 * (k * -y5))
    else if (y3 <= (-1.42d-243)) then
        tmp = t_1
    else if (y3 <= 9.8d-244) then
        tmp = c * (y4 * (t * -y2))
    else if (y3 <= 5.9d-111) then
        tmp = t_1
    else if (y3 <= 4.5d-15) then
        tmp = (k * y2) * (y0 * -y5)
    else
        tmp = y0 * (y3 * (j * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = -i * (t * (j * y5));
	double tmp;
	if (y3 <= -1.4e-11) {
		tmp = c * (y0 * (z * -y3));
	} else if (y3 <= -2e-159) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (y3 <= -1.42e-243) {
		tmp = t_1;
	} else if (y3 <= 9.8e-244) {
		tmp = c * (y4 * (t * -y2));
	} else if (y3 <= 5.9e-111) {
		tmp = t_1;
	} else if (y3 <= 4.5e-15) {
		tmp = (k * y2) * (y0 * -y5);
	} else {
		tmp = y0 * (y3 * (j * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = -i * (t * (j * y5))
	tmp = 0
	if y3 <= -1.4e-11:
		tmp = c * (y0 * (z * -y3))
	elif y3 <= -2e-159:
		tmp = y0 * (y2 * (k * -y5))
	elif y3 <= -1.42e-243:
		tmp = t_1
	elif y3 <= 9.8e-244:
		tmp = c * (y4 * (t * -y2))
	elif y3 <= 5.9e-111:
		tmp = t_1
	elif y3 <= 4.5e-15:
		tmp = (k * y2) * (y0 * -y5)
	else:
		tmp = y0 * (y3 * (j * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(-i) * Float64(t * Float64(j * y5)))
	tmp = 0.0
	if (y3 <= -1.4e-11)
		tmp = Float64(c * Float64(y0 * Float64(z * Float64(-y3))));
	elseif (y3 <= -2e-159)
		tmp = Float64(y0 * Float64(y2 * Float64(k * Float64(-y5))));
	elseif (y3 <= -1.42e-243)
		tmp = t_1;
	elseif (y3 <= 9.8e-244)
		tmp = Float64(c * Float64(y4 * Float64(t * Float64(-y2))));
	elseif (y3 <= 5.9e-111)
		tmp = t_1;
	elseif (y3 <= 4.5e-15)
		tmp = Float64(Float64(k * y2) * Float64(y0 * Float64(-y5)));
	else
		tmp = Float64(y0 * Float64(y3 * Float64(j * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = -i * (t * (j * y5));
	tmp = 0.0;
	if (y3 <= -1.4e-11)
		tmp = c * (y0 * (z * -y3));
	elseif (y3 <= -2e-159)
		tmp = y0 * (y2 * (k * -y5));
	elseif (y3 <= -1.42e-243)
		tmp = t_1;
	elseif (y3 <= 9.8e-244)
		tmp = c * (y4 * (t * -y2));
	elseif (y3 <= 5.9e-111)
		tmp = t_1;
	elseif (y3 <= 4.5e-15)
		tmp = (k * y2) * (y0 * -y5);
	else
		tmp = y0 * (y3 * (j * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[((-i) * N[(t * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -1.4e-11], N[(c * N[(y0 * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -2e-159], N[(y0 * N[(y2 * N[(k * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1.42e-243], t$95$1, If[LessEqual[y3, 9.8e-244], N[(c * N[(y4 * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 5.9e-111], t$95$1, If[LessEqual[y3, 4.5e-15], N[(N[(k * y2), $MachinePrecision] * N[(y0 * (-y5)), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(y3 * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y3 < -1.4e-11

   1. Initial program 20.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 20.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 20.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 27.6%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 27.6%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. *-commutative 27.6%

         \[\leadsto -\color{blue}{z \cdot \left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \]

      3. associate--l+ 27.6%

         \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \]

      4. *-commutative 27.6%

         \[\leadsto -z \cdot \left(\color{blue}{y3 \cdot \left(c \cdot y0 - a \cdot y1\right)} + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      5. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      6. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      7. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      8. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - \color{blue}{i \cdot c}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      9. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - \color{blue}{k \cdot \left(y0 \cdot b - y1 \cdot i\right)}\right)\right) \]

      10. *-commutative 27.6%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(\color{blue}{b \cdot y0} - y1 \cdot i\right)\right)\right) \]

      11. *-commutative 27.6%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right)\right) \]

   6. Simplified 27.6%

      \[\leadsto \color{blue}{-z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in y3 around inf 48.3%

      \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3\right)} \]
   8. Step-by-step derivation

      1. *-commutative 48.3%

         \[\leadsto -z \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y3\right) \]

   9. Simplified 48.3%

      \[\leadsto -z \cdot \color{blue}{\left(\left(y0 \cdot c - a \cdot y1\right) \cdot y3\right)} \]

   10. Taylor expanded in y0 around inf 40.0%

       \[\leadsto -\color{blue}{c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]

   if -1.4e-11 < y3 < -1.99999999999999998e-159

   1. Initial program 28.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 28.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 28.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 51.8%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y0 around -inf 50.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 50.7%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right)} \]

      2. neg-mul-1 50.7%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right) \]

      3. *-commutative 50.7%

         \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(y2 \cdot \left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right)\right)} \]

      4. mul-1-neg 50.7%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 + \color{blue}{\left(-c \cdot x\right)}\right)\right) \]

      5. unsub-neg 50.7%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \]

      6. *-commutative 50.7%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 - \color{blue}{x \cdot c}\right)\right) \]

   7. Simplified 50.7%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 - x \cdot c\right)\right)} \]

   8. Taylor expanded in k around inf 38.5%

      \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y5\right)}\right) \]

   if -1.99999999999999998e-159 < y3 < -1.41999999999999993e-243 or 9.80000000000000029e-244 < y3 < 5.9000000000000001e-111

   1. Initial program 36.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 36.3%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 38.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 38.5%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 38.5%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 42.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 45.4%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y5 around inf 29.4%

      \[\leadsto \color{blue}{\left(\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot y5\right)} \cdot j \]
   6. Step-by-step derivation

      1. *-commutative 29.4%

         \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)\right)} \cdot j \]

      2. mul-1-neg 29.4%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \cdot j \]

      3. unsub-neg 29.4%

         \[\leadsto \left(y5 \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \cdot j \]

      4. *-commutative 29.4%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 - \color{blue}{t \cdot i}\right)\right) \cdot j \]

   7. Simplified 29.4%

      \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)} \cdot j \]

   8. Taylor expanded in y0 around 0 31.3%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(t \cdot \left(j \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 31.3%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

      2. neg-mul-1 31.3%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(t \cdot \left(j \cdot y5\right)\right) \]

      3. *-commutative 31.3%

         \[\leadsto \left(-i\right) \cdot \left(t \cdot \color{blue}{\left(y5 \cdot j\right)}\right) \]

   10. Simplified 31.3%

       \[\leadsto \color{blue}{\left(-i\right) \cdot \left(t \cdot \left(y5 \cdot j\right)\right)} \]

   if -1.41999999999999993e-243 < y3 < 9.80000000000000029e-244

   1. Initial program 38.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 38.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 38.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 58.8%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 39.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   6. Taylor expanded in y0 around 0 43.6%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 43.6%

         \[\leadsto c \cdot \color{blue}{\left(-y4 \cdot \left(t \cdot y2\right)\right)} \]

      2. *-commutative 43.6%

         \[\leadsto c \cdot \left(-\color{blue}{\left(t \cdot y2\right) \cdot y4}\right) \]

      3. distribute-rgt-neg-in 43.6%

         \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot y2\right) \cdot \left(-y4\right)\right)} \]

   8. Simplified 43.6%

      \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot y2\right) \cdot \left(-y4\right)\right)} \]

   if 5.9000000000000001e-111 < y3 < 4.4999999999999998e-15

   1. Initial program 25.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 25.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 28.8%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in k around inf 32.0%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 31.9%

         \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)} \]

      2. *-commutative 31.9%

         \[\leadsto \left(k \cdot y2\right) \cdot \left(\color{blue}{y1 \cdot y4} - y0 \cdot y5\right) \]

   7. Simplified 31.9%

      \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]

   8. Taylor expanded in y1 around 0 31.8%

      \[\leadsto \left(k \cdot y2\right) \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 31.8%

         \[\leadsto \left(k \cdot y2\right) \cdot \color{blue}{\left(-y0 \cdot y5\right)} \]

      2. distribute-lft-neg-out 31.8%

         \[\leadsto \left(k \cdot y2\right) \cdot \color{blue}{\left(\left(-y0\right) \cdot y5\right)} \]

      3. *-commutative 31.8%

         \[\leadsto \left(k \cdot y2\right) \cdot \color{blue}{\left(y5 \cdot \left(-y0\right)\right)} \]

   10. Simplified 31.8%

       \[\leadsto \left(k \cdot y2\right) \cdot \color{blue}{\left(y5 \cdot \left(-y0\right)\right)} \]

   if 4.4999999999999998e-15 < y3

   1. Initial program 16.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 16.8%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 22.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 22.3%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 22.3%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 23.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 39.4%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y5 around inf 34.6%

      \[\leadsto \color{blue}{\left(\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot y5\right)} \cdot j \]
   6. Step-by-step derivation

      1. *-commutative 34.6%

         \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)\right)} \cdot j \]

      2. mul-1-neg 34.6%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \cdot j \]

      3. unsub-neg 34.6%

         \[\leadsto \left(y5 \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \cdot j \]

      4. *-commutative 34.6%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 - \color{blue}{t \cdot i}\right)\right) \cdot j \]

   7. Simplified 34.6%

      \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)} \cdot j \]

   8. Taylor expanded in y0 around inf 37.1%

      \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 37.1%

         \[\leadsto y0 \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot j\right)}\right) \]

   10. Simplified 37.1%

       \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(y5 \cdot j\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.4 \cdot 10^{-11}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y3 \leq -2 \cdot 10^{-159}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y3 \leq -1.42 \cdot 10^{-243}:\\ \;\;\;\;\left(-i\right) \cdot \left(t \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq 9.8 \cdot 10^{-244}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 5.9 \cdot 10^{-111}:\\ \;\;\;\;\left(-i\right) \cdot \left(t \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq 4.5 \cdot 10^{-15}:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y0 \cdot \left(-y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \end{array} \]

Alternative 28: 21.8% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-i\right) \cdot \left(t \cdot \left(j \cdot y5\right)\right)\\ \mathbf{if}\;j \leq -6.6 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.35 \cdot 10^{-181}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{-292}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 3.9 \cdot 10^{-107}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 68000000000000:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.26 \cdot 10^{+72}:\\ \;\;\;\;z \cdot \left(\left(c \cdot y0\right) \cdot \left(-y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (- i) (* t (* j y5)))))
   (if (<= j -6.6e-76)
     t_1
     (if (<= j -2.35e-181)
       (* k (* y2 (* y1 y4)))
       (if (<= j 1.35e-292)
         (* y0 (* y2 (* x c)))
         (if (<= j 3.9e-107)
           (* y0 (* y2 (* k (- y5))))
           (if (<= j 68000000000000.0)
             (* c (* y4 (* t (- y2))))
             (if (<= j 1.26e+72) (* z (* (* c y0) (- y3))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = -i * (t * (j * y5));
	double tmp;
	if (j <= -6.6e-76) {
		tmp = t_1;
	} else if (j <= -2.35e-181) {
		tmp = k * (y2 * (y1 * y4));
	} else if (j <= 1.35e-292) {
		tmp = y0 * (y2 * (x * c));
	} else if (j <= 3.9e-107) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (j <= 68000000000000.0) {
		tmp = c * (y4 * (t * -y2));
	} else if (j <= 1.26e+72) {
		tmp = z * ((c * y0) * -y3);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -i * (t * (j * y5))
    if (j <= (-6.6d-76)) then
        tmp = t_1
    else if (j <= (-2.35d-181)) then
        tmp = k * (y2 * (y1 * y4))
    else if (j <= 1.35d-292) then
        tmp = y0 * (y2 * (x * c))
    else if (j <= 3.9d-107) then
        tmp = y0 * (y2 * (k * -y5))
    else if (j <= 68000000000000.0d0) then
        tmp = c * (y4 * (t * -y2))
    else if (j <= 1.26d+72) then
        tmp = z * ((c * y0) * -y3)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = -i * (t * (j * y5));
	double tmp;
	if (j <= -6.6e-76) {
		tmp = t_1;
	} else if (j <= -2.35e-181) {
		tmp = k * (y2 * (y1 * y4));
	} else if (j <= 1.35e-292) {
		tmp = y0 * (y2 * (x * c));
	} else if (j <= 3.9e-107) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (j <= 68000000000000.0) {
		tmp = c * (y4 * (t * -y2));
	} else if (j <= 1.26e+72) {
		tmp = z * ((c * y0) * -y3);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = -i * (t * (j * y5))
	tmp = 0
	if j <= -6.6e-76:
		tmp = t_1
	elif j <= -2.35e-181:
		tmp = k * (y2 * (y1 * y4))
	elif j <= 1.35e-292:
		tmp = y0 * (y2 * (x * c))
	elif j <= 3.9e-107:
		tmp = y0 * (y2 * (k * -y5))
	elif j <= 68000000000000.0:
		tmp = c * (y4 * (t * -y2))
	elif j <= 1.26e+72:
		tmp = z * ((c * y0) * -y3)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(-i) * Float64(t * Float64(j * y5)))
	tmp = 0.0
	if (j <= -6.6e-76)
		tmp = t_1;
	elseif (j <= -2.35e-181)
		tmp = Float64(k * Float64(y2 * Float64(y1 * y4)));
	elseif (j <= 1.35e-292)
		tmp = Float64(y0 * Float64(y2 * Float64(x * c)));
	elseif (j <= 3.9e-107)
		tmp = Float64(y0 * Float64(y2 * Float64(k * Float64(-y5))));
	elseif (j <= 68000000000000.0)
		tmp = Float64(c * Float64(y4 * Float64(t * Float64(-y2))));
	elseif (j <= 1.26e+72)
		tmp = Float64(z * Float64(Float64(c * y0) * Float64(-y3)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = -i * (t * (j * y5));
	tmp = 0.0;
	if (j <= -6.6e-76)
		tmp = t_1;
	elseif (j <= -2.35e-181)
		tmp = k * (y2 * (y1 * y4));
	elseif (j <= 1.35e-292)
		tmp = y0 * (y2 * (x * c));
	elseif (j <= 3.9e-107)
		tmp = y0 * (y2 * (k * -y5));
	elseif (j <= 68000000000000.0)
		tmp = c * (y4 * (t * -y2));
	elseif (j <= 1.26e+72)
		tmp = z * ((c * y0) * -y3);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[((-i) * N[(t * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6.6e-76], t$95$1, If[LessEqual[j, -2.35e-181], N[(k * N[(y2 * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.35e-292], N[(y0 * N[(y2 * N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.9e-107], N[(y0 * N[(y2 * N[(k * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 68000000000000.0], N[(c * N[(y4 * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.26e+72], N[(z * N[(N[(c * y0), $MachinePrecision] * (-y3)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -6.59999999999999967e-76 or 1.26e72 < j

   1. Initial program 25.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 25.5%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 28.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 28.6%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 28.6%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 32.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 50.9%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y5 around inf 37.7%

      \[\leadsto \color{blue}{\left(\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot y5\right)} \cdot j \]
   6. Step-by-step derivation

      1. *-commutative 37.7%

         \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)\right)} \cdot j \]

      2. mul-1-neg 37.7%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \cdot j \]

      3. unsub-neg 37.7%

         \[\leadsto \left(y5 \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \cdot j \]

      4. *-commutative 37.7%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 - \color{blue}{t \cdot i}\right)\right) \cdot j \]

   7. Simplified 37.7%

      \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)} \cdot j \]

   8. Taylor expanded in y0 around 0 35.9%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(t \cdot \left(j \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 35.9%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

      2. neg-mul-1 35.9%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(t \cdot \left(j \cdot y5\right)\right) \]

      3. *-commutative 35.9%

         \[\leadsto \left(-i\right) \cdot \left(t \cdot \color{blue}{\left(y5 \cdot j\right)}\right) \]

   10. Simplified 35.9%

       \[\leadsto \color{blue}{\left(-i\right) \cdot \left(t \cdot \left(y5 \cdot j\right)\right)} \]

   if -6.59999999999999967e-76 < j < -2.3499999999999999e-181

   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. Step-by-step derivation

      1. associate-+l- 31.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 31.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 43.8%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in k around inf 37.6%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 33.1%

         \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)} \]

      2. *-commutative 33.1%

         \[\leadsto \left(k \cdot y2\right) \cdot \left(\color{blue}{y1 \cdot y4} - y0 \cdot y5\right) \]

   7. Simplified 33.1%

      \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]

   8. Taylor expanded in y1 around inf 46.5%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 46.5%

         \[\leadsto k \cdot \color{blue}{\left(\left(y4 \cdot y1\right) \cdot y2\right)} \]

      2. *-commutative 46.5%

         \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y4 \cdot y1\right)\right)} \]

   10. Simplified 46.5%

       \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y4 \cdot y1\right)\right)} \]

   if -2.3499999999999999e-181 < j < 1.35e-292

   1. Initial program 8.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 8.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 8.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 46.9%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y0 around -inf 39.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 39.2%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right)} \]

      2. neg-mul-1 39.2%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right) \]

      3. *-commutative 39.2%

         \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(y2 \cdot \left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right)\right)} \]

      4. mul-1-neg 39.2%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 + \color{blue}{\left(-c \cdot x\right)}\right)\right) \]

      5. unsub-neg 39.2%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \]

      6. *-commutative 39.2%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 - \color{blue}{x \cdot c}\right)\right) \]

   7. Simplified 39.2%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 - x \cdot c\right)\right)} \]

   8. Taylor expanded in k around 0 39.3%

      \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot x\right)\right)}\right) \]
   9. Step-by-step derivation

      1. neg-mul-1 39.3%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \color{blue}{\left(-c \cdot x\right)}\right) \]

      2. distribute-rgt-neg-in 39.3%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \color{blue}{\left(c \cdot \left(-x\right)\right)}\right) \]

   10. Simplified 39.3%

       \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \color{blue}{\left(c \cdot \left(-x\right)\right)}\right) \]

   if 1.35e-292 < j < 3.9000000000000001e-107

   1. Initial program 22.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 22.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 22.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 45.1%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y0 around -inf 29.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 29.9%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right)} \]

      2. neg-mul-1 29.9%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right) \]

      3. *-commutative 29.9%

         \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(y2 \cdot \left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right)\right)} \]

      4. mul-1-neg 29.9%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 + \color{blue}{\left(-c \cdot x\right)}\right)\right) \]

      5. unsub-neg 29.9%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \]

      6. *-commutative 29.9%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 - \color{blue}{x \cdot c}\right)\right) \]

   7. Simplified 29.9%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 - x \cdot c\right)\right)} \]

   8. Taylor expanded in k around inf 30.3%

      \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y5\right)}\right) \]

   if 3.9000000000000001e-107 < j < 6.8e13

   1. Initial program 42.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 42.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 42.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 50.1%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 41.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   6. Taylor expanded in y0 around 0 41.0%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 41.0%

         \[\leadsto c \cdot \color{blue}{\left(-y4 \cdot \left(t \cdot y2\right)\right)} \]

      2. *-commutative 41.0%

         \[\leadsto c \cdot \left(-\color{blue}{\left(t \cdot y2\right) \cdot y4}\right) \]

      3. distribute-rgt-neg-in 41.0%

         \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot y2\right) \cdot \left(-y4\right)\right)} \]

   8. Simplified 41.0%

      \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot y2\right) \cdot \left(-y4\right)\right)} \]

   if 6.8e13 < j < 1.26e72

   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. Step-by-step derivation

      1. associate-+l- 29.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 29.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 53.2%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 53.2%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. *-commutative 53.2%

         \[\leadsto -\color{blue}{z \cdot \left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \]

      3. associate--l+ 53.2%

         \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \]

      4. *-commutative 53.2%

         \[\leadsto -z \cdot \left(\color{blue}{y3 \cdot \left(c \cdot y0 - a \cdot y1\right)} + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      5. *-commutative 53.2%

         \[\leadsto -z \cdot \left(y3 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      6. *-commutative 53.2%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      7. *-commutative 53.2%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      8. *-commutative 53.2%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - \color{blue}{i \cdot c}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      9. *-commutative 53.2%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - \color{blue}{k \cdot \left(y0 \cdot b - y1 \cdot i\right)}\right)\right) \]

      10. *-commutative 53.2%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(\color{blue}{b \cdot y0} - y1 \cdot i\right)\right)\right) \]

      11. *-commutative 53.2%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right)\right) \]

   6. Simplified 53.2%

      \[\leadsto \color{blue}{-z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in y3 around inf 59.5%

      \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3\right)} \]
   8. Step-by-step derivation

      1. *-commutative 59.5%

         \[\leadsto -z \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y3\right) \]

   9. Simplified 59.5%

      \[\leadsto -z \cdot \color{blue}{\left(\left(y0 \cdot c - a \cdot y1\right) \cdot y3\right)} \]

   10. Taylor expanded in y0 around inf 48.1%

       \[\leadsto -z \cdot \left(\color{blue}{\left(c \cdot y0\right)} \cdot y3\right) \]
   11. Step-by-step derivation

       1. *-commutative 48.1%

          \[\leadsto -z \cdot \left(\color{blue}{\left(y0 \cdot c\right)} \cdot y3\right) \]

   12. Simplified 48.1%

       \[\leadsto -z \cdot \left(\color{blue}{\left(y0 \cdot c\right)} \cdot y3\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.6 \cdot 10^{-76}:\\ \;\;\;\;\left(-i\right) \cdot \left(t \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -2.35 \cdot 10^{-181}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{-292}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 3.9 \cdot 10^{-107}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 68000000000000:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.26 \cdot 10^{+72}:\\ \;\;\;\;z \cdot \left(\left(c \cdot y0\right) \cdot \left(-y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-i\right) \cdot \left(t \cdot \left(j \cdot y5\right)\right)\\ \end{array} \]

Alternative 29: 21.1% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2\right)\right)\\ t_2 := \left(-i\right) \cdot \left(t \cdot \left(j \cdot y5\right)\right)\\ \mathbf{if}\;j \leq -2.5 \cdot 10^{-65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -4.1 \cdot 10^{-202}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-254}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 90000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 4 \cdot 10^{+72}:\\ \;\;\;\;z \cdot \left(\left(c \cdot y0\right) \cdot \left(-y3\right)\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{+130}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (- y0) (* y5 (* k y2)))) (t_2 (* (- i) (* t (* j y5)))))
   (if (<= j -2.5e-65)
     t_2
     (if (<= j -4.1e-202)
       (* c (* y4 (* t (- y2))))
       (if (<= j 3.8e-254)
         (* y1 (* a (* z y3)))
         (if (<= j 90000000000000.0)
           t_1
           (if (<= j 4e+72)
             (* z (* (* c y0) (- y3)))
             (if (<= j 5e+130) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = -y0 * (y5 * (k * y2));
	double t_2 = -i * (t * (j * y5));
	double tmp;
	if (j <= -2.5e-65) {
		tmp = t_2;
	} else if (j <= -4.1e-202) {
		tmp = c * (y4 * (t * -y2));
	} else if (j <= 3.8e-254) {
		tmp = y1 * (a * (z * y3));
	} else if (j <= 90000000000000.0) {
		tmp = t_1;
	} else if (j <= 4e+72) {
		tmp = z * ((c * y0) * -y3);
	} else if (j <= 5e+130) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -y0 * (y5 * (k * y2))
    t_2 = -i * (t * (j * y5))
    if (j <= (-2.5d-65)) then
        tmp = t_2
    else if (j <= (-4.1d-202)) then
        tmp = c * (y4 * (t * -y2))
    else if (j <= 3.8d-254) then
        tmp = y1 * (a * (z * y3))
    else if (j <= 90000000000000.0d0) then
        tmp = t_1
    else if (j <= 4d+72) then
        tmp = z * ((c * y0) * -y3)
    else if (j <= 5d+130) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = -y0 * (y5 * (k * y2));
	double t_2 = -i * (t * (j * y5));
	double tmp;
	if (j <= -2.5e-65) {
		tmp = t_2;
	} else if (j <= -4.1e-202) {
		tmp = c * (y4 * (t * -y2));
	} else if (j <= 3.8e-254) {
		tmp = y1 * (a * (z * y3));
	} else if (j <= 90000000000000.0) {
		tmp = t_1;
	} else if (j <= 4e+72) {
		tmp = z * ((c * y0) * -y3);
	} else if (j <= 5e+130) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = -y0 * (y5 * (k * y2))
	t_2 = -i * (t * (j * y5))
	tmp = 0
	if j <= -2.5e-65:
		tmp = t_2
	elif j <= -4.1e-202:
		tmp = c * (y4 * (t * -y2))
	elif j <= 3.8e-254:
		tmp = y1 * (a * (z * y3))
	elif j <= 90000000000000.0:
		tmp = t_1
	elif j <= 4e+72:
		tmp = z * ((c * y0) * -y3)
	elif j <= 5e+130:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(-y0) * Float64(y5 * Float64(k * y2)))
	t_2 = Float64(Float64(-i) * Float64(t * Float64(j * y5)))
	tmp = 0.0
	if (j <= -2.5e-65)
		tmp = t_2;
	elseif (j <= -4.1e-202)
		tmp = Float64(c * Float64(y4 * Float64(t * Float64(-y2))));
	elseif (j <= 3.8e-254)
		tmp = Float64(y1 * Float64(a * Float64(z * y3)));
	elseif (j <= 90000000000000.0)
		tmp = t_1;
	elseif (j <= 4e+72)
		tmp = Float64(z * Float64(Float64(c * y0) * Float64(-y3)));
	elseif (j <= 5e+130)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = -y0 * (y5 * (k * y2));
	t_2 = -i * (t * (j * y5));
	tmp = 0.0;
	if (j <= -2.5e-65)
		tmp = t_2;
	elseif (j <= -4.1e-202)
		tmp = c * (y4 * (t * -y2));
	elseif (j <= 3.8e-254)
		tmp = y1 * (a * (z * y3));
	elseif (j <= 90000000000000.0)
		tmp = t_1;
	elseif (j <= 4e+72)
		tmp = z * ((c * y0) * -y3);
	elseif (j <= 5e+130)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[((-y0) * N[(y5 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-i) * N[(t * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.5e-65], t$95$2, If[LessEqual[j, -4.1e-202], N[(c * N[(y4 * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.8e-254], N[(y1 * N[(a * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 90000000000000.0], t$95$1, If[LessEqual[j, 4e+72], N[(z * N[(N[(c * y0), $MachinePrecision] * (-y3)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5e+130], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -2.49999999999999991e-65 or 4.9999999999999996e130 < j

   1. Initial program 25.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 25.3%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 27.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 27.8%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 27.8%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 32.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 51.4%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y5 around inf 36.8%

      \[\leadsto \color{blue}{\left(\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot y5\right)} \cdot j \]
   6. Step-by-step derivation

      1. *-commutative 36.8%

         \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)\right)} \cdot j \]

      2. mul-1-neg 36.8%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \cdot j \]

      3. unsub-neg 36.8%

         \[\leadsto \left(y5 \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \cdot j \]

      4. *-commutative 36.8%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 - \color{blue}{t \cdot i}\right)\right) \cdot j \]

   7. Simplified 36.8%

      \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)} \cdot j \]

   8. Taylor expanded in y0 around 0 36.5%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(t \cdot \left(j \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 36.5%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

      2. neg-mul-1 36.5%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(t \cdot \left(j \cdot y5\right)\right) \]

      3. *-commutative 36.5%

         \[\leadsto \left(-i\right) \cdot \left(t \cdot \color{blue}{\left(y5 \cdot j\right)}\right) \]

   10. Simplified 36.5%

       \[\leadsto \color{blue}{\left(-i\right) \cdot \left(t \cdot \left(y5 \cdot j\right)\right)} \]

   if -2.49999999999999991e-65 < j < -4.1000000000000004e-202

   1. Initial program 22.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 22.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 22.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 41.1%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 38.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   6. Taylor expanded in y0 around 0 42.7%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 42.7%

         \[\leadsto c \cdot \color{blue}{\left(-y4 \cdot \left(t \cdot y2\right)\right)} \]

      2. *-commutative 42.7%

         \[\leadsto c \cdot \left(-\color{blue}{\left(t \cdot y2\right) \cdot y4}\right) \]

      3. distribute-rgt-neg-in 42.7%

         \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot y2\right) \cdot \left(-y4\right)\right)} \]

   8. Simplified 42.7%

      \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot y2\right) \cdot \left(-y4\right)\right)} \]

   if -4.1000000000000004e-202 < j < 3.8000000000000001e-254

   1. Initial program 21.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 21.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 21.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 28.8%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 28.8%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. *-commutative 28.8%

         \[\leadsto -\color{blue}{z \cdot \left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \]

      3. associate--l+ 28.8%

         \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \]

      4. *-commutative 28.8%

         \[\leadsto -z \cdot \left(\color{blue}{y3 \cdot \left(c \cdot y0 - a \cdot y1\right)} + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      5. *-commutative 28.8%

         \[\leadsto -z \cdot \left(y3 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      6. *-commutative 28.8%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      7. *-commutative 28.8%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      8. *-commutative 28.8%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - \color{blue}{i \cdot c}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      9. *-commutative 28.8%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - \color{blue}{k \cdot \left(y0 \cdot b - y1 \cdot i\right)}\right)\right) \]

      10. *-commutative 28.8%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(\color{blue}{b \cdot y0} - y1 \cdot i\right)\right)\right) \]

      11. *-commutative 28.8%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right)\right) \]

   6. Simplified 28.8%

      \[\leadsto \color{blue}{-z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in y3 around inf 38.7%

      \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3\right)} \]
   8. Step-by-step derivation

      1. *-commutative 38.7%

         \[\leadsto -z \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y3\right) \]

   9. Simplified 38.7%

      \[\leadsto -z \cdot \color{blue}{\left(\left(y0 \cdot c - a \cdot y1\right) \cdot y3\right)} \]

   10. Taylor expanded in y0 around 0 29.7%

       \[\leadsto -\color{blue}{-1 \cdot \left(y1 \cdot \left(a \cdot \left(y3 \cdot z\right)\right)\right)} \]

   if 3.8000000000000001e-254 < j < 9e13 or 3.99999999999999978e72 < j < 4.9999999999999996e130

   1. Initial program 28.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 28.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 28.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 47.8%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y0 around -inf 39.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 39.3%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right)} \]

      2. neg-mul-1 39.3%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right) \]

      3. *-commutative 39.3%

         \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(y2 \cdot \left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right)\right)} \]

      4. mul-1-neg 39.3%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 + \color{blue}{\left(-c \cdot x\right)}\right)\right) \]

      5. unsub-neg 39.3%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \]

      6. *-commutative 39.3%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 - \color{blue}{x \cdot c}\right)\right) \]

   7. Simplified 39.3%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 - x \cdot c\right)\right)} \]

   8. Taylor expanded in k around inf 36.2%

      \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(k \cdot \left(y5 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 36.2%

         \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(\left(y5 \cdot y2\right) \cdot k\right)} \]

      2. associate-*l* 38.0%

         \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(y5 \cdot \left(y2 \cdot k\right)\right)} \]

   10. Simplified 38.0%

       \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(y5 \cdot \left(y2 \cdot k\right)\right)} \]

   if 9e13 < j < 3.99999999999999978e72

   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. Step-by-step derivation

      1. associate-+l- 29.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 29.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 53.2%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 53.2%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. *-commutative 53.2%

         \[\leadsto -\color{blue}{z \cdot \left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \]

      3. associate--l+ 53.2%

         \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \]

      4. *-commutative 53.2%

         \[\leadsto -z \cdot \left(\color{blue}{y3 \cdot \left(c \cdot y0 - a \cdot y1\right)} + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      5. *-commutative 53.2%

         \[\leadsto -z \cdot \left(y3 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      6. *-commutative 53.2%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      7. *-commutative 53.2%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      8. *-commutative 53.2%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - \color{blue}{i \cdot c}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      9. *-commutative 53.2%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - \color{blue}{k \cdot \left(y0 \cdot b - y1 \cdot i\right)}\right)\right) \]

      10. *-commutative 53.2%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(\color{blue}{b \cdot y0} - y1 \cdot i\right)\right)\right) \]

      11. *-commutative 53.2%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right)\right) \]

   6. Simplified 53.2%

      \[\leadsto \color{blue}{-z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in y3 around inf 59.5%

      \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3\right)} \]
   8. Step-by-step derivation

      1. *-commutative 59.5%

         \[\leadsto -z \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y3\right) \]

   9. Simplified 59.5%

      \[\leadsto -z \cdot \color{blue}{\left(\left(y0 \cdot c - a \cdot y1\right) \cdot y3\right)} \]

   10. Taylor expanded in y0 around inf 48.1%

       \[\leadsto -z \cdot \left(\color{blue}{\left(c \cdot y0\right)} \cdot y3\right) \]
   11. Step-by-step derivation

       1. *-commutative 48.1%

          \[\leadsto -z \cdot \left(\color{blue}{\left(y0 \cdot c\right)} \cdot y3\right) \]

   12. Simplified 48.1%

       \[\leadsto -z \cdot \left(\color{blue}{\left(y0 \cdot c\right)} \cdot y3\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.5 \cdot 10^{-65}:\\ \;\;\;\;\left(-i\right) \cdot \left(t \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -4.1 \cdot 10^{-202}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-254}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 90000000000000:\\ \;\;\;\;\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{+72}:\\ \;\;\;\;z \cdot \left(\left(c \cdot y0\right) \cdot \left(-y3\right)\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{+130}:\\ \;\;\;\;\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-i\right) \cdot \left(t \cdot \left(j \cdot y5\right)\right)\\ \end{array} \]

Alternative 30: 25.7% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(\left(c \cdot y0\right) \cdot \left(-y3\right)\right)\\ t_2 := b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{if}\;c \leq -4 \cdot 10^{+209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{-38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.9 \cdot 10^{-264}:\\ \;\;\;\;\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{+15}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* z (* (* c y0) (- y3)))) (t_2 (* b (* y (- (* x a) (* k y4))))))
   (if (<= c -4e+209)
     t_1
     (if (<= c -3.6e-38)
       t_2
       (if (<= c -1.9e-264)
         (* (- y0) (* y5 (* k y2)))
         (if (<= c 1.7e+15) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = z * ((c * y0) * -y3);
	double t_2 = b * (y * ((x * a) - (k * y4)));
	double tmp;
	if (c <= -4e+209) {
		tmp = t_1;
	} else if (c <= -3.6e-38) {
		tmp = t_2;
	} else if (c <= -1.9e-264) {
		tmp = -y0 * (y5 * (k * y2));
	} else if (c <= 1.7e+15) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * ((c * y0) * -y3)
    t_2 = b * (y * ((x * a) - (k * y4)))
    if (c <= (-4d+209)) then
        tmp = t_1
    else if (c <= (-3.6d-38)) then
        tmp = t_2
    else if (c <= (-1.9d-264)) then
        tmp = -y0 * (y5 * (k * y2))
    else if (c <= 1.7d+15) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = z * ((c * y0) * -y3);
	double t_2 = b * (y * ((x * a) - (k * y4)));
	double tmp;
	if (c <= -4e+209) {
		tmp = t_1;
	} else if (c <= -3.6e-38) {
		tmp = t_2;
	} else if (c <= -1.9e-264) {
		tmp = -y0 * (y5 * (k * y2));
	} else if (c <= 1.7e+15) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = z * ((c * y0) * -y3)
	t_2 = b * (y * ((x * a) - (k * y4)))
	tmp = 0
	if c <= -4e+209:
		tmp = t_1
	elif c <= -3.6e-38:
		tmp = t_2
	elif c <= -1.9e-264:
		tmp = -y0 * (y5 * (k * y2))
	elif c <= 1.7e+15:
		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(z * Float64(Float64(c * y0) * Float64(-y3)))
	t_2 = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))))
	tmp = 0.0
	if (c <= -4e+209)
		tmp = t_1;
	elseif (c <= -3.6e-38)
		tmp = t_2;
	elseif (c <= -1.9e-264)
		tmp = Float64(Float64(-y0) * Float64(y5 * Float64(k * y2)));
	elseif (c <= 1.7e+15)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = z * ((c * y0) * -y3);
	t_2 = b * (y * ((x * a) - (k * y4)));
	tmp = 0.0;
	if (c <= -4e+209)
		tmp = t_1;
	elseif (c <= -3.6e-38)
		tmp = t_2;
	elseif (c <= -1.9e-264)
		tmp = -y0 * (y5 * (k * y2));
	elseif (c <= 1.7e+15)
		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[(z * N[(N[(c * y0), $MachinePrecision] * (-y3)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4e+209], t$95$1, If[LessEqual[c, -3.6e-38], t$95$2, If[LessEqual[c, -1.9e-264], N[((-y0) * N[(y5 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.7e+15], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.0000000000000003e209 or 1.7e15 < c

   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. Step-by-step derivation

      1. associate-+l- 23.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 23.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 36.7%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 36.7%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. *-commutative 36.7%

         \[\leadsto -\color{blue}{z \cdot \left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \]

      3. associate--l+ 36.7%

         \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \]

      4. *-commutative 36.7%

         \[\leadsto -z \cdot \left(\color{blue}{y3 \cdot \left(c \cdot y0 - a \cdot y1\right)} + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      5. *-commutative 36.7%

         \[\leadsto -z \cdot \left(y3 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      6. *-commutative 36.7%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      7. *-commutative 36.7%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      8. *-commutative 36.7%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - \color{blue}{i \cdot c}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      9. *-commutative 36.7%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - \color{blue}{k \cdot \left(y0 \cdot b - y1 \cdot i\right)}\right)\right) \]

      10. *-commutative 36.7%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(\color{blue}{b \cdot y0} - y1 \cdot i\right)\right)\right) \]

      11. *-commutative 36.7%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right)\right) \]

   6. Simplified 36.7%

      \[\leadsto \color{blue}{-z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in y3 around inf 45.9%

      \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3\right)} \]
   8. Step-by-step derivation

      1. *-commutative 45.9%

         \[\leadsto -z \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y3\right) \]

   9. Simplified 45.9%

      \[\leadsto -z \cdot \color{blue}{\left(\left(y0 \cdot c - a \cdot y1\right) \cdot y3\right)} \]

   10. Taylor expanded in y0 around inf 38.7%

       \[\leadsto -z \cdot \left(\color{blue}{\left(c \cdot y0\right)} \cdot y3\right) \]
   11. Step-by-step derivation

       1. *-commutative 38.7%

          \[\leadsto -z \cdot \left(\color{blue}{\left(y0 \cdot c\right)} \cdot y3\right) \]

   12. Simplified 38.7%

       \[\leadsto -z \cdot \left(\color{blue}{\left(y0 \cdot c\right)} \cdot y3\right) \]

   if -4.0000000000000003e209 < c < -3.6000000000000001e-38 or -1.90000000000000007e-264 < c < 1.7e15

   1. Initial program 28.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 28.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 28.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 35.9%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot b} \]

   5. Taylor expanded in y around inf 35.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot \left(y \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 39.6%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot y\right) \cdot b} \]

      2. *-commutative 39.6%

         \[\leadsto \color{blue}{b \cdot \left(\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot y\right)} \]

      3. *-commutative 39.6%

         \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]

      4. +-commutative 39.6%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      5. mul-1-neg 39.6%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      6. unsub-neg 39.6%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   7. Simplified 39.6%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   if -3.6000000000000001e-38 < c < -1.90000000000000007e-264

   1. Initial program 21.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 21.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 21.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 48.0%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in y0 around -inf 31.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 31.7%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right)} \]

      2. neg-mul-1 31.7%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(\left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right) \cdot y2\right) \]

      3. *-commutative 31.7%

         \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(y2 \cdot \left(k \cdot y5 + -1 \cdot \left(c \cdot x\right)\right)\right)} \]

      4. mul-1-neg 31.7%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 + \color{blue}{\left(-c \cdot x\right)}\right)\right) \]

      5. unsub-neg 31.7%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \color{blue}{\left(k \cdot y5 - c \cdot x\right)}\right) \]

      6. *-commutative 31.7%

         \[\leadsto \left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 - \color{blue}{x \cdot c}\right)\right) \]

   7. Simplified 31.7%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(y2 \cdot \left(k \cdot y5 - x \cdot c\right)\right)} \]

   8. Taylor expanded in k around inf 29.5%

      \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(k \cdot \left(y5 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 29.5%

         \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(\left(y5 \cdot y2\right) \cdot k\right)} \]

      2. associate-*l* 34.0%

         \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(y5 \cdot \left(y2 \cdot k\right)\right)} \]

   10. Simplified 34.0%

       \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(y5 \cdot \left(y2 \cdot k\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4 \cdot 10^{+209}:\\ \;\;\;\;z \cdot \left(\left(c \cdot y0\right) \cdot \left(-y3\right)\right)\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{-38}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq -1.9 \cdot 10^{-264}:\\ \;\;\;\;\left(-y0\right) \cdot \left(y5 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{+15}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(c \cdot y0\right) \cdot \left(-y3\right)\right)\\ \end{array} \]

Alternative 31: 28.1% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -1.1 \cdot 10^{+37}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -3.95 \cdot 10^{-85}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 2.6 \cdot 10^{-57}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 9.2 \cdot 10^{+216}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 7.8 \cdot 10^{+288}:\\ \;\;\;\;k \cdot \left(\left(y0 \cdot y5\right) \cdot \left(-y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(y0 \cdot \left(-y3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -1.1e+37)
   (* j (* y5 (* y0 y3)))
   (if (<= y0 -3.95e-85)
     (* z (* y3 (* a y1)))
     (if (<= y0 2.6e-57)
       (* b (* y (- (* x a) (* k y4))))
       (if (<= y0 9.2e+216)
         (* c (* y2 (- (* x y0) (* t y4))))
         (if (<= y0 7.8e+288)
           (* k (* (* y0 y5) (- y2)))
           (* z (* c (* y0 (- y3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -1.1e+37) {
		tmp = j * (y5 * (y0 * y3));
	} else if (y0 <= -3.95e-85) {
		tmp = z * (y3 * (a * y1));
	} else if (y0 <= 2.6e-57) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y0 <= 9.2e+216) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y0 <= 7.8e+288) {
		tmp = k * ((y0 * y5) * -y2);
	} else {
		tmp = z * (c * (y0 * -y3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y0 <= (-1.1d+37)) then
        tmp = j * (y5 * (y0 * y3))
    else if (y0 <= (-3.95d-85)) then
        tmp = z * (y3 * (a * y1))
    else if (y0 <= 2.6d-57) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (y0 <= 9.2d+216) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (y0 <= 7.8d+288) then
        tmp = k * ((y0 * y5) * -y2)
    else
        tmp = z * (c * (y0 * -y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -1.1e+37) {
		tmp = j * (y5 * (y0 * y3));
	} else if (y0 <= -3.95e-85) {
		tmp = z * (y3 * (a * y1));
	} else if (y0 <= 2.6e-57) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y0 <= 9.2e+216) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y0 <= 7.8e+288) {
		tmp = k * ((y0 * y5) * -y2);
	} else {
		tmp = z * (c * (y0 * -y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y0 <= -1.1e+37:
		tmp = j * (y5 * (y0 * y3))
	elif y0 <= -3.95e-85:
		tmp = z * (y3 * (a * y1))
	elif y0 <= 2.6e-57:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif y0 <= 9.2e+216:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif y0 <= 7.8e+288:
		tmp = k * ((y0 * y5) * -y2)
	else:
		tmp = z * (c * (y0 * -y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -1.1e+37)
		tmp = Float64(j * Float64(y5 * Float64(y0 * y3)));
	elseif (y0 <= -3.95e-85)
		tmp = Float64(z * Float64(y3 * Float64(a * y1)));
	elseif (y0 <= 2.6e-57)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (y0 <= 9.2e+216)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (y0 <= 7.8e+288)
		tmp = Float64(k * Float64(Float64(y0 * y5) * Float64(-y2)));
	else
		tmp = Float64(z * Float64(c * Float64(y0 * 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)
	tmp = 0.0;
	if (y0 <= -1.1e+37)
		tmp = j * (y5 * (y0 * y3));
	elseif (y0 <= -3.95e-85)
		tmp = z * (y3 * (a * y1));
	elseif (y0 <= 2.6e-57)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (y0 <= 9.2e+216)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (y0 <= 7.8e+288)
		tmp = k * ((y0 * y5) * -y2);
	else
		tmp = z * (c * (y0 * -y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -1.1e+37], N[(j * N[(y5 * N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -3.95e-85], N[(z * N[(y3 * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.6e-57], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 9.2e+216], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 7.8e+288], N[(k * N[(N[(y0 * y5), $MachinePrecision] * (-y2)), $MachinePrecision]), $MachinePrecision], N[(z * N[(c * N[(y0 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y0 < -1.1e37

   1. Initial program 18.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 18.4%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 22.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 22.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 22.0%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 23.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 33.3%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y5 around inf 44.7%

      \[\leadsto \color{blue}{\left(\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot y5\right)} \cdot j \]
   6. Step-by-step derivation

      1. *-commutative 44.7%

         \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)\right)} \cdot j \]

      2. mul-1-neg 44.7%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \cdot j \]

      3. unsub-neg 44.7%

         \[\leadsto \left(y5 \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \cdot j \]

      4. *-commutative 44.7%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 - \color{blue}{t \cdot i}\right)\right) \cdot j \]

   7. Simplified 44.7%

      \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)} \cdot j \]

   8. Taylor expanded in y0 around inf 44.6%

      \[\leadsto \left(y5 \cdot \color{blue}{\left(y0 \cdot y3\right)}\right) \cdot j \]

   if -1.1e37 < y0 < -3.9500000000000002e-85

   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. Step-by-step derivation

      1. associate-+l- 27.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 27.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 37.6%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 37.6%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. *-commutative 37.6%

         \[\leadsto -\color{blue}{z \cdot \left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \]

      3. associate--l+ 37.6%

         \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \]

      4. *-commutative 37.6%

         \[\leadsto -z \cdot \left(\color{blue}{y3 \cdot \left(c \cdot y0 - a \cdot y1\right)} + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      5. *-commutative 37.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      6. *-commutative 37.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      7. *-commutative 37.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      8. *-commutative 37.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - \color{blue}{i \cdot c}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      9. *-commutative 37.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - \color{blue}{k \cdot \left(y0 \cdot b - y1 \cdot i\right)}\right)\right) \]

      10. *-commutative 37.6%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(\color{blue}{b \cdot y0} - y1 \cdot i\right)\right)\right) \]

      11. *-commutative 37.6%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right)\right) \]

   6. Simplified 37.6%

      \[\leadsto \color{blue}{-z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in y3 around inf 38.1%

      \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3\right)} \]
   8. Step-by-step derivation

      1. *-commutative 38.1%

         \[\leadsto -z \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y3\right) \]

   9. Simplified 38.1%

      \[\leadsto -z \cdot \color{blue}{\left(\left(y0 \cdot c - a \cdot y1\right) \cdot y3\right)} \]

   10. Taylor expanded in y0 around 0 34.7%

       \[\leadsto -z \cdot \left(\color{blue}{\left(-1 \cdot \left(y1 \cdot a\right)\right)} \cdot y3\right) \]
   11. Step-by-step derivation

       1. mul-1-neg 34.7%

          \[\leadsto -z \cdot \left(\color{blue}{\left(-y1 \cdot a\right)} \cdot y3\right) \]

       2. *-commutative 34.7%

          \[\leadsto -z \cdot \left(\left(-\color{blue}{a \cdot y1}\right) \cdot y3\right) \]

       3. distribute-rgt-neg-in 34.7%

          \[\leadsto -z \cdot \left(\color{blue}{\left(a \cdot \left(-y1\right)\right)} \cdot y3\right) \]

   12. Simplified 34.7%

       \[\leadsto -z \cdot \left(\color{blue}{\left(a \cdot \left(-y1\right)\right)} \cdot y3\right) \]

   if -3.9500000000000002e-85 < y0 < 2.59999999999999985e-57

   1. Initial program 33.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 33.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 33.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 37.2%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot b} \]

   5. Taylor expanded in y around inf 36.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot \left(y \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 37.2%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot y\right) \cdot b} \]

      2. *-commutative 37.2%

         \[\leadsto \color{blue}{b \cdot \left(\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot y\right)} \]

      3. *-commutative 37.2%

         \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]

      4. +-commutative 37.2%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      5. mul-1-neg 37.2%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      6. unsub-neg 37.2%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   7. Simplified 37.2%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   if 2.59999999999999985e-57 < y0 < 9.19999999999999983e216

   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. Step-by-step derivation

      1. associate-+l- 26.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 26.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 39.4%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 42.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   if 9.19999999999999983e216 < y0 < 7.79999999999999957e288

   1. Initial program 6.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 6.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 6.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 38.6%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in k around inf 51.0%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 51.0%

         \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)} \]

      2. *-commutative 51.0%

         \[\leadsto \left(k \cdot y2\right) \cdot \left(\color{blue}{y1 \cdot y4} - y0 \cdot y5\right) \]

   7. Simplified 51.0%

      \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]

   8. Taylor expanded in y1 around 0 44.9%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(y5 \cdot y2\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 44.9%

         \[\leadsto \color{blue}{-k \cdot \left(y0 \cdot \left(y5 \cdot y2\right)\right)} \]

      2. associate-*r* 50.9%

         \[\leadsto -k \cdot \color{blue}{\left(\left(y0 \cdot y5\right) \cdot y2\right)} \]

      3. *-commutative 50.9%

         \[\leadsto -k \cdot \left(\color{blue}{\left(y5 \cdot y0\right)} \cdot y2\right) \]

   10. Simplified 50.9%

       \[\leadsto \color{blue}{-k \cdot \left(\left(y5 \cdot y0\right) \cdot y2\right)} \]

   if 7.79999999999999957e288 < 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. Step-by-step derivation

      1. associate-+l- 0.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 28.6%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 28.6%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. *-commutative 28.6%

         \[\leadsto -\color{blue}{z \cdot \left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \]

      3. associate--l+ 28.6%

         \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \]

      4. *-commutative 28.6%

         \[\leadsto -z \cdot \left(\color{blue}{y3 \cdot \left(c \cdot y0 - a \cdot y1\right)} + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      5. *-commutative 28.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      6. *-commutative 28.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      7. *-commutative 28.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      8. *-commutative 28.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - \color{blue}{i \cdot c}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      9. *-commutative 28.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - \color{blue}{k \cdot \left(y0 \cdot b - y1 \cdot i\right)}\right)\right) \]

      10. *-commutative 28.6%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(\color{blue}{b \cdot y0} - y1 \cdot i\right)\right)\right) \]

      11. *-commutative 28.6%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right)\right) \]

   6. Simplified 28.6%

      \[\leadsto \color{blue}{-z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in y3 around inf 43.0%

      \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3\right)} \]
   8. Step-by-step derivation

      1. *-commutative 43.0%

         \[\leadsto -z \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y3\right) \]

   9. Simplified 43.0%

      \[\leadsto -z \cdot \color{blue}{\left(\left(y0 \cdot c - a \cdot y1\right) \cdot y3\right)} \]

   10. Taylor expanded in y0 around inf 57.7%

       \[\leadsto -z \cdot \color{blue}{\left(c \cdot \left(y0 \cdot y3\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 57.7%

          \[\leadsto -z \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot c\right)} \]

       2. *-commutative 57.7%

          \[\leadsto -z \cdot \left(\color{blue}{\left(y3 \cdot y0\right)} \cdot c\right) \]

   12. Simplified 57.7%

       \[\leadsto -z \cdot \color{blue}{\left(\left(y3 \cdot y0\right) \cdot c\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.1 \cdot 10^{+37}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -3.95 \cdot 10^{-85}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 2.6 \cdot 10^{-57}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 9.2 \cdot 10^{+216}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 7.8 \cdot 10^{+288}:\\ \;\;\;\;k \cdot \left(\left(y0 \cdot y5\right) \cdot \left(-y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(y0 \cdot \left(-y3\right)\right)\right)\\ \end{array} \]

Alternative 32: 29.8% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{if}\;y0 \leq -4 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -7.8 \cdot 10^{-85}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 1.38 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.65 \cdot 10^{+259}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* j (- (* y3 y5) (* x b))))))
   (if (<= y0 -4e+36)
     t_1
     (if (<= y0 -7.8e-85)
       (* z (* y3 (* a y1)))
       (if (<= y0 1.38e-55)
         (* b (* y (- (* x a) (* k y4))))
         (if (<= y0 1.65e+259) (* c (* y2 (- (* x y0) (* t y4)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (j * ((y3 * y5) - (x * b)));
	double tmp;
	if (y0 <= -4e+36) {
		tmp = t_1;
	} else if (y0 <= -7.8e-85) {
		tmp = z * (y3 * (a * y1));
	} else if (y0 <= 1.38e-55) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y0 <= 1.65e+259) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y0 * (j * ((y3 * y5) - (x * b)))
    if (y0 <= (-4d+36)) then
        tmp = t_1
    else if (y0 <= (-7.8d-85)) then
        tmp = z * (y3 * (a * y1))
    else if (y0 <= 1.38d-55) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (y0 <= 1.65d+259) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (j * ((y3 * y5) - (x * b)));
	double tmp;
	if (y0 <= -4e+36) {
		tmp = t_1;
	} else if (y0 <= -7.8e-85) {
		tmp = z * (y3 * (a * y1));
	} else if (y0 <= 1.38e-55) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y0 <= 1.65e+259) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * (j * ((y3 * y5) - (x * b)))
	tmp = 0
	if y0 <= -4e+36:
		tmp = t_1
	elif y0 <= -7.8e-85:
		tmp = z * (y3 * (a * y1))
	elif y0 <= 1.38e-55:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif y0 <= 1.65e+259:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(x * b))))
	tmp = 0.0
	if (y0 <= -4e+36)
		tmp = t_1;
	elseif (y0 <= -7.8e-85)
		tmp = Float64(z * Float64(y3 * Float64(a * y1)));
	elseif (y0 <= 1.38e-55)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (y0 <= 1.65e+259)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y0 * (j * ((y3 * y5) - (x * b)));
	tmp = 0.0;
	if (y0 <= -4e+36)
		tmp = t_1;
	elseif (y0 <= -7.8e-85)
		tmp = z * (y3 * (a * y1));
	elseif (y0 <= 1.38e-55)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (y0 <= 1.65e+259)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -4e+36], t$95$1, If[LessEqual[y0, -7.8e-85], N[(z * N[(y3 * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.38e-55], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.65e+259], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y0 < -4.00000000000000017e36 or 1.65e259 < y0

   1. Initial program 14.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 14.6%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 17.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 17.5%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 17.5%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 19.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 26.6%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y0 around inf 50.6%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(y3 \cdot y5 - b \cdot x\right) \cdot j\right)} \]

   if -4.00000000000000017e36 < y0 < -7.79999999999999977e-85

   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. Step-by-step derivation

      1. associate-+l- 27.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 27.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 37.6%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 37.6%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. *-commutative 37.6%

         \[\leadsto -\color{blue}{z \cdot \left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \]

      3. associate--l+ 37.6%

         \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \]

      4. *-commutative 37.6%

         \[\leadsto -z \cdot \left(\color{blue}{y3 \cdot \left(c \cdot y0 - a \cdot y1\right)} + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      5. *-commutative 37.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      6. *-commutative 37.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      7. *-commutative 37.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      8. *-commutative 37.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - \color{blue}{i \cdot c}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      9. *-commutative 37.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - \color{blue}{k \cdot \left(y0 \cdot b - y1 \cdot i\right)}\right)\right) \]

      10. *-commutative 37.6%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(\color{blue}{b \cdot y0} - y1 \cdot i\right)\right)\right) \]

      11. *-commutative 37.6%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right)\right) \]

   6. Simplified 37.6%

      \[\leadsto \color{blue}{-z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in y3 around inf 38.1%

      \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3\right)} \]
   8. Step-by-step derivation

      1. *-commutative 38.1%

         \[\leadsto -z \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y3\right) \]

   9. Simplified 38.1%

      \[\leadsto -z \cdot \color{blue}{\left(\left(y0 \cdot c - a \cdot y1\right) \cdot y3\right)} \]

   10. Taylor expanded in y0 around 0 34.7%

       \[\leadsto -z \cdot \left(\color{blue}{\left(-1 \cdot \left(y1 \cdot a\right)\right)} \cdot y3\right) \]
   11. Step-by-step derivation

       1. mul-1-neg 34.7%

          \[\leadsto -z \cdot \left(\color{blue}{\left(-y1 \cdot a\right)} \cdot y3\right) \]

       2. *-commutative 34.7%

          \[\leadsto -z \cdot \left(\left(-\color{blue}{a \cdot y1}\right) \cdot y3\right) \]

       3. distribute-rgt-neg-in 34.7%

          \[\leadsto -z \cdot \left(\color{blue}{\left(a \cdot \left(-y1\right)\right)} \cdot y3\right) \]

   12. Simplified 34.7%

       \[\leadsto -z \cdot \left(\color{blue}{\left(a \cdot \left(-y1\right)\right)} \cdot y3\right) \]

   if -7.79999999999999977e-85 < y0 < 1.3799999999999999e-55

   1. Initial program 33.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 33.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 33.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 37.2%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot b} \]

   5. Taylor expanded in y around inf 36.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot \left(y \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 37.2%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot y\right) \cdot b} \]

      2. *-commutative 37.2%

         \[\leadsto \color{blue}{b \cdot \left(\left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right) \cdot y\right)} \]

      3. *-commutative 37.2%

         \[\leadsto b \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]

      4. +-commutative 37.2%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      5. mul-1-neg 37.2%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      6. unsub-neg 37.2%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

   7. Simplified 37.2%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   if 1.3799999999999999e-55 < y0 < 1.65e259

   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. Step-by-step derivation

      1. associate-+l- 23.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 23.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 42.3%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 42.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -4 \cdot 10^{+36}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq -7.8 \cdot 10^{-85}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 1.38 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.65 \cdot 10^{+259}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \end{array} \]

Alternative 33: 21.9% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-i\right) \cdot \left(t \cdot \left(j \cdot y5\right)\right)\\ \mathbf{if}\;y3 \leq -4.8 \cdot 10^{-11}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y3 \leq -5.8 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y3 \leq 4.5 \cdot 10^{-247}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 4.5 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (- i) (* t (* j y5)))))
   (if (<= y3 -4.8e-11)
     (* c (* y0 (* z (- y3))))
     (if (<= y3 -5.8e-240)
       t_1
       (if (<= y3 4.5e-247)
         (* c (* y4 (* t (- y2))))
         (if (<= y3 4.5e+86) t_1 (* y0 (* y3 (* j y5)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = -i * (t * (j * y5));
	double tmp;
	if (y3 <= -4.8e-11) {
		tmp = c * (y0 * (z * -y3));
	} else if (y3 <= -5.8e-240) {
		tmp = t_1;
	} else if (y3 <= 4.5e-247) {
		tmp = c * (y4 * (t * -y2));
	} else if (y3 <= 4.5e+86) {
		tmp = t_1;
	} else {
		tmp = y0 * (y3 * (j * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -i * (t * (j * y5))
    if (y3 <= (-4.8d-11)) then
        tmp = c * (y0 * (z * -y3))
    else if (y3 <= (-5.8d-240)) then
        tmp = t_1
    else if (y3 <= 4.5d-247) then
        tmp = c * (y4 * (t * -y2))
    else if (y3 <= 4.5d+86) then
        tmp = t_1
    else
        tmp = y0 * (y3 * (j * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = -i * (t * (j * y5));
	double tmp;
	if (y3 <= -4.8e-11) {
		tmp = c * (y0 * (z * -y3));
	} else if (y3 <= -5.8e-240) {
		tmp = t_1;
	} else if (y3 <= 4.5e-247) {
		tmp = c * (y4 * (t * -y2));
	} else if (y3 <= 4.5e+86) {
		tmp = t_1;
	} else {
		tmp = y0 * (y3 * (j * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = -i * (t * (j * y5))
	tmp = 0
	if y3 <= -4.8e-11:
		tmp = c * (y0 * (z * -y3))
	elif y3 <= -5.8e-240:
		tmp = t_1
	elif y3 <= 4.5e-247:
		tmp = c * (y4 * (t * -y2))
	elif y3 <= 4.5e+86:
		tmp = t_1
	else:
		tmp = y0 * (y3 * (j * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(-i) * Float64(t * Float64(j * y5)))
	tmp = 0.0
	if (y3 <= -4.8e-11)
		tmp = Float64(c * Float64(y0 * Float64(z * Float64(-y3))));
	elseif (y3 <= -5.8e-240)
		tmp = t_1;
	elseif (y3 <= 4.5e-247)
		tmp = Float64(c * Float64(y4 * Float64(t * Float64(-y2))));
	elseif (y3 <= 4.5e+86)
		tmp = t_1;
	else
		tmp = Float64(y0 * Float64(y3 * Float64(j * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = -i * (t * (j * y5));
	tmp = 0.0;
	if (y3 <= -4.8e-11)
		tmp = c * (y0 * (z * -y3));
	elseif (y3 <= -5.8e-240)
		tmp = t_1;
	elseif (y3 <= 4.5e-247)
		tmp = c * (y4 * (t * -y2));
	elseif (y3 <= 4.5e+86)
		tmp = t_1;
	else
		tmp = y0 * (y3 * (j * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[((-i) * N[(t * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -4.8e-11], N[(c * N[(y0 * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -5.8e-240], t$95$1, If[LessEqual[y3, 4.5e-247], N[(c * N[(y4 * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 4.5e+86], t$95$1, N[(y0 * N[(y3 * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y3 < -4.8000000000000002e-11

   1. Initial program 20.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 20.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 20.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 27.6%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 27.6%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. *-commutative 27.6%

         \[\leadsto -\color{blue}{z \cdot \left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \]

      3. associate--l+ 27.6%

         \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \]

      4. *-commutative 27.6%

         \[\leadsto -z \cdot \left(\color{blue}{y3 \cdot \left(c \cdot y0 - a \cdot y1\right)} + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      5. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      6. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      7. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      8. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - \color{blue}{i \cdot c}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      9. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - \color{blue}{k \cdot \left(y0 \cdot b - y1 \cdot i\right)}\right)\right) \]

      10. *-commutative 27.6%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(\color{blue}{b \cdot y0} - y1 \cdot i\right)\right)\right) \]

      11. *-commutative 27.6%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right)\right) \]

   6. Simplified 27.6%

      \[\leadsto \color{blue}{-z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in y3 around inf 48.3%

      \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3\right)} \]
   8. Step-by-step derivation

      1. *-commutative 48.3%

         \[\leadsto -z \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y3\right) \]

   9. Simplified 48.3%

      \[\leadsto -z \cdot \color{blue}{\left(\left(y0 \cdot c - a \cdot y1\right) \cdot y3\right)} \]

   10. Taylor expanded in y0 around inf 40.0%

       \[\leadsto -\color{blue}{c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]

   if -4.8000000000000002e-11 < y3 < -5.8000000000000004e-240 or 4.5000000000000002e-247 < y3 < 4.49999999999999993e86

   1. Initial program 28.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 28.5%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 30.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 30.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 30.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 32.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 41.5%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y5 around inf 29.9%

      \[\leadsto \color{blue}{\left(\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot y5\right)} \cdot j \]
   6. Step-by-step derivation

      1. *-commutative 29.9%

         \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)\right)} \cdot j \]

      2. mul-1-neg 29.9%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \cdot j \]

      3. unsub-neg 29.9%

         \[\leadsto \left(y5 \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \cdot j \]

      4. *-commutative 29.9%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 - \color{blue}{t \cdot i}\right)\right) \cdot j \]

   7. Simplified 29.9%

      \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)} \cdot j \]

   8. Taylor expanded in y0 around 0 24.9%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(t \cdot \left(j \cdot y5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 24.9%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

      2. neg-mul-1 24.9%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(t \cdot \left(j \cdot y5\right)\right) \]

      3. *-commutative 24.9%

         \[\leadsto \left(-i\right) \cdot \left(t \cdot \color{blue}{\left(y5 \cdot j\right)}\right) \]

   10. Simplified 24.9%

       \[\leadsto \color{blue}{\left(-i\right) \cdot \left(t \cdot \left(y5 \cdot j\right)\right)} \]

   if -5.8000000000000004e-240 < y3 < 4.5000000000000002e-247

   1. Initial program 38.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 38.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 38.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 58.8%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 39.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   6. Taylor expanded in y0 around 0 43.6%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 43.6%

         \[\leadsto c \cdot \color{blue}{\left(-y4 \cdot \left(t \cdot y2\right)\right)} \]

      2. *-commutative 43.6%

         \[\leadsto c \cdot \left(-\color{blue}{\left(t \cdot y2\right) \cdot y4}\right) \]

      3. distribute-rgt-neg-in 43.6%

         \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot y2\right) \cdot \left(-y4\right)\right)} \]

   8. Simplified 43.6%

      \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot y2\right) \cdot \left(-y4\right)\right)} \]

   if 4.49999999999999993e86 < y3

   1. Initial program 17.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 17.8%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 23.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 23.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 23.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 25.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 35.9%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y5 around inf 32.6%

      \[\leadsto \color{blue}{\left(\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot y5\right)} \cdot j \]
   6. Step-by-step derivation

      1. *-commutative 32.6%

         \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)\right)} \cdot j \]

      2. mul-1-neg 32.6%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \cdot j \]

      3. unsub-neg 32.6%

         \[\leadsto \left(y5 \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \cdot j \]

      4. *-commutative 32.6%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 - \color{blue}{t \cdot i}\right)\right) \cdot j \]

   7. Simplified 32.6%

      \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)} \cdot j \]

   8. Taylor expanded in y0 around inf 43.9%

      \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 43.9%

         \[\leadsto y0 \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot j\right)}\right) \]

   10. Simplified 43.9%

       \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(y5 \cdot j\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -4.8 \cdot 10^{-11}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y3 \leq -5.8 \cdot 10^{-240}:\\ \;\;\;\;\left(-i\right) \cdot \left(t \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq 4.5 \cdot 10^{-247}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 4.5 \cdot 10^{+86}:\\ \;\;\;\;\left(-i\right) \cdot \left(t \cdot \left(j \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \end{array} \]

Alternative 34: 23.2% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{if}\;j \leq -135000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.8 \cdot 10^{-178}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{-14}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* y3 (* j y5)))))
   (if (<= j -135000000.0)
     t_1
     (if (<= j -2.8e-178)
       (* k (* y4 (* y1 y2)))
       (if (<= j 4.5e-14) (* c (* x (* y0 y2))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (y3 * (j * y5));
	double tmp;
	if (j <= -135000000.0) {
		tmp = t_1;
	} else if (j <= -2.8e-178) {
		tmp = k * (y4 * (y1 * y2));
	} else if (j <= 4.5e-14) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y0 * (y3 * (j * y5))
    if (j <= (-135000000.0d0)) then
        tmp = t_1
    else if (j <= (-2.8d-178)) then
        tmp = k * (y4 * (y1 * y2))
    else if (j <= 4.5d-14) then
        tmp = c * (x * (y0 * y2))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (y3 * (j * y5));
	double tmp;
	if (j <= -135000000.0) {
		tmp = t_1;
	} else if (j <= -2.8e-178) {
		tmp = k * (y4 * (y1 * y2));
	} else if (j <= 4.5e-14) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * (y3 * (j * y5))
	tmp = 0
	if j <= -135000000.0:
		tmp = t_1
	elif j <= -2.8e-178:
		tmp = k * (y4 * (y1 * y2))
	elif j <= 4.5e-14:
		tmp = c * (x * (y0 * y2))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(y3 * Float64(j * y5)))
	tmp = 0.0
	if (j <= -135000000.0)
		tmp = t_1;
	elseif (j <= -2.8e-178)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	elseif (j <= 4.5e-14)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y0 * (y3 * (j * y5));
	tmp = 0.0;
	if (j <= -135000000.0)
		tmp = t_1;
	elseif (j <= -2.8e-178)
		tmp = k * (y4 * (y1 * y2));
	elseif (j <= 4.5e-14)
		tmp = c * (x * (y0 * y2));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y0 * N[(y3 * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -135000000.0], t$95$1, If[LessEqual[j, -2.8e-178], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.5e-14], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.35e8 or 4.4999999999999998e-14 < j

   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. Step-by-step derivation

      1. +-commutative 27.7%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 31.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 31.5%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 31.5%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 34.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 46.9%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y5 around inf 36.4%

      \[\leadsto \color{blue}{\left(\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot y5\right)} \cdot j \]
   6. Step-by-step derivation

      1. *-commutative 36.4%

         \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)\right)} \cdot j \]

      2. mul-1-neg 36.4%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \cdot j \]

      3. unsub-neg 36.4%

         \[\leadsto \left(y5 \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \cdot j \]

      4. *-commutative 36.4%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 - \color{blue}{t \cdot i}\right)\right) \cdot j \]

   7. Simplified 36.4%

      \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)} \cdot j \]

   8. Taylor expanded in y0 around inf 32.3%

      \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 32.3%

         \[\leadsto y0 \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot j\right)}\right) \]

   10. Simplified 32.3%

       \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(y5 \cdot j\right)\right)} \]

   if -1.35e8 < j < -2.80000000000000019e-178

   1. Initial program 27.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 27.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 27.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 41.9%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in k around inf 31.6%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 26.7%

         \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)} \]

      2. *-commutative 26.7%

         \[\leadsto \left(k \cdot y2\right) \cdot \left(\color{blue}{y1 \cdot y4} - y0 \cdot y5\right) \]

   7. Simplified 26.7%

      \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]

   8. Taylor expanded in y1 around inf 33.8%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 33.8%

         \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \]

   10. Simplified 33.8%

       \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y2 \cdot y1\right)\right)} \]

   if -2.80000000000000019e-178 < j < 4.4999999999999998e-14

   1. Initial program 20.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 20.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 20.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 47.1%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 25.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   6. Taylor expanded in y0 around inf 20.0%

      \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot x\right)} \cdot y2\right) \]

   7. Taylor expanded in c around 0 21.2%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 21.2%

         \[\leadsto c \cdot \left(y0 \cdot \color{blue}{\left(y2 \cdot x\right)}\right) \]

      2. associate-*r* 21.2%

         \[\leadsto c \cdot \color{blue}{\left(\left(y0 \cdot y2\right) \cdot x\right)} \]

   9. Simplified 21.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot y2\right) \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 29.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -135000000:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -2.8 \cdot 10^{-178}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{-14}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \end{array} \]

Alternative 35: 21.7% accurate, 7.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -5.8 \cdot 10^{-12}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 1.3 \cdot 10^{-15}:\\ \;\;\;\;k \cdot \left(\left(y0 \cdot y5\right) \cdot \left(-y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 -5.8e-12)
   (* c (* y0 (* z (- y3))))
   (if (<= y3 1.3e-15) (* k (* (* y0 y5) (- y2))) (* y0 (* y3 (* j 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 <= -5.8e-12) {
		tmp = c * (y0 * (z * -y3));
	} else if (y3 <= 1.3e-15) {
		tmp = k * ((y0 * y5) * -y2);
	} else {
		tmp = y0 * (y3 * (j * 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 <= (-5.8d-12)) then
        tmp = c * (y0 * (z * -y3))
    else if (y3 <= 1.3d-15) then
        tmp = k * ((y0 * y5) * -y2)
    else
        tmp = y0 * (y3 * (j * 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 <= -5.8e-12) {
		tmp = c * (y0 * (z * -y3));
	} else if (y3 <= 1.3e-15) {
		tmp = k * ((y0 * y5) * -y2);
	} else {
		tmp = y0 * (y3 * (j * 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 <= -5.8e-12:
		tmp = c * (y0 * (z * -y3))
	elif y3 <= 1.3e-15:
		tmp = k * ((y0 * y5) * -y2)
	else:
		tmp = y0 * (y3 * (j * 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 <= -5.8e-12)
		tmp = Float64(c * Float64(y0 * Float64(z * Float64(-y3))));
	elseif (y3 <= 1.3e-15)
		tmp = Float64(k * Float64(Float64(y0 * y5) * Float64(-y2)));
	else
		tmp = Float64(y0 * Float64(y3 * Float64(j * 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 <= -5.8e-12)
		tmp = c * (y0 * (z * -y3));
	elseif (y3 <= 1.3e-15)
		tmp = k * ((y0 * y5) * -y2);
	else
		tmp = y0 * (y3 * (j * 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, -5.8e-12], N[(c * N[(y0 * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.3e-15], N[(k * N[(N[(y0 * y5), $MachinePrecision] * (-y2)), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(y3 * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y3 < -5.8000000000000003e-12

   1. Initial program 20.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 20.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 20.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 27.6%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 27.6%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. *-commutative 27.6%

         \[\leadsto -\color{blue}{z \cdot \left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \]

      3. associate--l+ 27.6%

         \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \]

      4. *-commutative 27.6%

         \[\leadsto -z \cdot \left(\color{blue}{y3 \cdot \left(c \cdot y0 - a \cdot y1\right)} + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      5. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      6. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      7. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      8. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - \color{blue}{i \cdot c}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      9. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - \color{blue}{k \cdot \left(y0 \cdot b - y1 \cdot i\right)}\right)\right) \]

      10. *-commutative 27.6%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(\color{blue}{b \cdot y0} - y1 \cdot i\right)\right)\right) \]

      11. *-commutative 27.6%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right)\right) \]

   6. Simplified 27.6%

      \[\leadsto \color{blue}{-z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in y3 around inf 48.3%

      \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3\right)} \]
   8. Step-by-step derivation

      1. *-commutative 48.3%

         \[\leadsto -z \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y3\right) \]

   9. Simplified 48.3%

      \[\leadsto -z \cdot \color{blue}{\left(\left(y0 \cdot c - a \cdot y1\right) \cdot y3\right)} \]

   10. Taylor expanded in y0 around inf 40.0%

       \[\leadsto -\color{blue}{c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]

   if -5.8000000000000003e-12 < y3 < 1.30000000000000002e-15

   1. Initial program 33.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 33.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 33.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 44.6%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in k around inf 27.8%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 25.5%

         \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)} \]

      2. *-commutative 25.5%

         \[\leadsto \left(k \cdot y2\right) \cdot \left(\color{blue}{y1 \cdot y4} - y0 \cdot y5\right) \]

   7. Simplified 25.5%

      \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]

   8. Taylor expanded in y1 around 0 25.4%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(y5 \cdot y2\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 25.4%

         \[\leadsto \color{blue}{-k \cdot \left(y0 \cdot \left(y5 \cdot y2\right)\right)} \]

      2. associate-*r* 24.6%

         \[\leadsto -k \cdot \color{blue}{\left(\left(y0 \cdot y5\right) \cdot y2\right)} \]

      3. *-commutative 24.6%

         \[\leadsto -k \cdot \left(\color{blue}{\left(y5 \cdot y0\right)} \cdot y2\right) \]

   10. Simplified 24.6%

       \[\leadsto \color{blue}{-k \cdot \left(\left(y5 \cdot y0\right) \cdot y2\right)} \]

   if 1.30000000000000002e-15 < y3

   1. Initial program 16.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 16.8%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 22.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 22.3%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 22.3%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 23.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 39.4%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y5 around inf 34.6%

      \[\leadsto \color{blue}{\left(\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot y5\right)} \cdot j \]
   6. Step-by-step derivation

      1. *-commutative 34.6%

         \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)\right)} \cdot j \]

      2. mul-1-neg 34.6%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \cdot j \]

      3. unsub-neg 34.6%

         \[\leadsto \left(y5 \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \cdot j \]

      4. *-commutative 34.6%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 - \color{blue}{t \cdot i}\right)\right) \cdot j \]

   7. Simplified 34.6%

      \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)} \cdot j \]

   8. Taylor expanded in y0 around inf 37.1%

      \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 37.1%

         \[\leadsto y0 \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot j\right)}\right) \]

   10. Simplified 37.1%

       \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(y5 \cdot j\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -5.8 \cdot 10^{-12}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 1.3 \cdot 10^{-15}:\\ \;\;\;\;k \cdot \left(\left(y0 \cdot y5\right) \cdot \left(-y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \end{array} \]

Alternative 36: 21.3% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -2.3 \cdot 10^{+118} \lor \neg \left(y1 \leq 2.6 \cdot 10^{-114}\right):\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y1 -2.3e+118) (not (<= y1 2.6e-114)))
   (* k (* y2 (* y1 y4)))
   (* c (* y2 (* x y0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y1 <= -2.3e+118) || !(y1 <= 2.6e-114)) {
		tmp = k * (y2 * (y1 * y4));
	} else {
		tmp = c * (y2 * (x * y0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y1 <= (-2.3d+118)) .or. (.not. (y1 <= 2.6d-114))) then
        tmp = k * (y2 * (y1 * y4))
    else
        tmp = c * (y2 * (x * y0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y1 <= -2.3e+118) || !(y1 <= 2.6e-114)) {
		tmp = k * (y2 * (y1 * y4));
	} else {
		tmp = c * (y2 * (x * y0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y1 <= -2.3e+118) or not (y1 <= 2.6e-114):
		tmp = k * (y2 * (y1 * y4))
	else:
		tmp = c * (y2 * (x * y0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y1 <= -2.3e+118) || !(y1 <= 2.6e-114))
		tmp = Float64(k * Float64(y2 * Float64(y1 * y4)));
	else
		tmp = Float64(c * Float64(y2 * Float64(x * y0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y1 <= -2.3e+118) || ~((y1 <= 2.6e-114)))
		tmp = k * (y2 * (y1 * y4));
	else
		tmp = c * (y2 * (x * y0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y1, -2.3e+118], N[Not[LessEqual[y1, 2.6e-114]], $MachinePrecision]], N[(k * N[(y2 * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y2 * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y1 < -2.30000000000000016e118 or 2.60000000000000013e-114 < y1

   1. Initial program 23.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 23.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 23.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 37.5%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in k around inf 32.8%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 27.5%

         \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)} \]

      2. *-commutative 27.5%

         \[\leadsto \left(k \cdot y2\right) \cdot \left(\color{blue}{y1 \cdot y4} - y0 \cdot y5\right) \]

   7. Simplified 27.5%

      \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]

   8. Taylor expanded in y1 around inf 23.5%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 24.2%

         \[\leadsto k \cdot \color{blue}{\left(\left(y4 \cdot y1\right) \cdot y2\right)} \]

      2. *-commutative 24.2%

         \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y4 \cdot y1\right)\right)} \]

   10. Simplified 24.2%

       \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y4 \cdot y1\right)\right)} \]

   if -2.30000000000000016e118 < y1 < 2.60000000000000013e-114

   1. Initial program 28.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 28.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 28.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 42.6%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 28.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   6. Taylor expanded in y0 around inf 21.4%

      \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot x\right)} \cdot y2\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 22.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -2.3 \cdot 10^{+118} \lor \neg \left(y1 \leq 2.6 \cdot 10^{-114}\right):\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right)\\ \end{array} \]

Alternative 37: 21.4% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -1.55 \cdot 10^{+118}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 2.4 \cdot 10^{-114}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -1.55e+118)
   (* k (* y4 (* y1 y2)))
   (if (<= y1 2.4e-114) (* c (* y2 (* x y0))) (* k (* y2 (* y1 y4))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -1.55e+118) {
		tmp = k * (y4 * (y1 * y2));
	} else if (y1 <= 2.4e-114) {
		tmp = c * (y2 * (x * y0));
	} else {
		tmp = k * (y2 * (y1 * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y1 <= (-1.55d+118)) then
        tmp = k * (y4 * (y1 * y2))
    else if (y1 <= 2.4d-114) then
        tmp = c * (y2 * (x * y0))
    else
        tmp = k * (y2 * (y1 * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -1.55e+118) {
		tmp = k * (y4 * (y1 * y2));
	} else if (y1 <= 2.4e-114) {
		tmp = c * (y2 * (x * y0));
	} else {
		tmp = k * (y2 * (y1 * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -1.55e+118:
		tmp = k * (y4 * (y1 * y2))
	elif y1 <= 2.4e-114:
		tmp = c * (y2 * (x * y0))
	else:
		tmp = k * (y2 * (y1 * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -1.55e+118)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	elseif (y1 <= 2.4e-114)
		tmp = Float64(c * Float64(y2 * Float64(x * y0)));
	else
		tmp = Float64(k * Float64(y2 * Float64(y1 * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y1 <= -1.55e+118)
		tmp = k * (y4 * (y1 * y2));
	elseif (y1 <= 2.4e-114)
		tmp = c * (y2 * (x * y0));
	else
		tmp = k * (y2 * (y1 * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y1, -1.55e+118], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.4e-114], N[(c * N[(y2 * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y2 * N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y1 < -1.54999999999999993e118

   1. Initial program 20.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 20.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 20.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 41.6%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in k around inf 30.4%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 22.1%

         \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)} \]

      2. *-commutative 22.1%

         \[\leadsto \left(k \cdot y2\right) \cdot \left(\color{blue}{y1 \cdot y4} - y0 \cdot y5\right) \]

   7. Simplified 22.1%

      \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]

   8. Taylor expanded in y1 around inf 30.3%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 30.3%

         \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \]

   10. Simplified 30.3%

       \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y2 \cdot y1\right)\right)} \]

   if -1.54999999999999993e118 < y1 < 2.4000000000000001e-114

   1. Initial program 28.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 28.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 28.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 42.6%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 28.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   6. Taylor expanded in y0 around inf 21.4%

      \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot x\right)} \cdot y2\right) \]

   if 2.4000000000000001e-114 < y1

   1. Initial program 23.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 23.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 23.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 36.0%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in k around inf 33.6%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 29.4%

         \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)} \]

      2. *-commutative 29.4%

         \[\leadsto \left(k \cdot y2\right) \cdot \left(\color{blue}{y1 \cdot y4} - y0 \cdot y5\right) \]

   7. Simplified 29.4%

      \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]

   8. Taylor expanded in y1 around inf 21.0%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 23.0%

         \[\leadsto k \cdot \color{blue}{\left(\left(y4 \cdot y1\right) \cdot y2\right)} \]

      2. *-commutative 23.0%

         \[\leadsto k \cdot \color{blue}{\left(y2 \cdot \left(y4 \cdot y1\right)\right)} \]

   10. Simplified 23.0%

       \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y4 \cdot y1\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 23.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.55 \cdot 10^{+118}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 2.4 \cdot 10^{-114}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4\right)\right)\\ \end{array} \]

Alternative 38: 21.6% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -3 \cdot 10^{-12}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 2.4 \cdot 10^{+87}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 -3e-12)
   (* c (* y0 (* z (- y3))))
   (if (<= y3 2.4e+87) (* c (* x (* y0 y2))) (* y0 (* y3 (* j 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 <= -3e-12) {
		tmp = c * (y0 * (z * -y3));
	} else if (y3 <= 2.4e+87) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = y0 * (y3 * (j * 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 <= (-3d-12)) then
        tmp = c * (y0 * (z * -y3))
    else if (y3 <= 2.4d+87) then
        tmp = c * (x * (y0 * y2))
    else
        tmp = y0 * (y3 * (j * 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 <= -3e-12) {
		tmp = c * (y0 * (z * -y3));
	} else if (y3 <= 2.4e+87) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = y0 * (y3 * (j * 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 <= -3e-12:
		tmp = c * (y0 * (z * -y3))
	elif y3 <= 2.4e+87:
		tmp = c * (x * (y0 * y2))
	else:
		tmp = y0 * (y3 * (j * 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 <= -3e-12)
		tmp = Float64(c * Float64(y0 * Float64(z * Float64(-y3))));
	elseif (y3 <= 2.4e+87)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	else
		tmp = Float64(y0 * Float64(y3 * Float64(j * 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 <= -3e-12)
		tmp = c * (y0 * (z * -y3));
	elseif (y3 <= 2.4e+87)
		tmp = c * (x * (y0 * y2));
	else
		tmp = y0 * (y3 * (j * 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, -3e-12], N[(c * N[(y0 * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.4e+87], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(y3 * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y3 < -3.0000000000000001e-12

   1. Initial program 20.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 20.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 20.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 27.6%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 27.6%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. *-commutative 27.6%

         \[\leadsto -\color{blue}{z \cdot \left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \]

      3. associate--l+ 27.6%

         \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \]

      4. *-commutative 27.6%

         \[\leadsto -z \cdot \left(\color{blue}{y3 \cdot \left(c \cdot y0 - a \cdot y1\right)} + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      5. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(\color{blue}{y0 \cdot c} - a \cdot y1\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      6. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      7. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      8. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - \color{blue}{i \cdot c}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \]

      9. *-commutative 27.6%

         \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - \color{blue}{k \cdot \left(y0 \cdot b - y1 \cdot i\right)}\right)\right) \]

      10. *-commutative 27.6%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(\color{blue}{b \cdot y0} - y1 \cdot i\right)\right)\right) \]

      11. *-commutative 27.6%

          \[\leadsto -z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - \color{blue}{i \cdot y1}\right)\right)\right) \]

   6. Simplified 27.6%

      \[\leadsto \color{blue}{-z \cdot \left(y3 \cdot \left(y0 \cdot c - y1 \cdot a\right) + \left(t \cdot \left(b \cdot a - i \cdot c\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   7. Taylor expanded in y3 around inf 48.3%

      \[\leadsto -z \cdot \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3\right)} \]
   8. Step-by-step derivation

      1. *-commutative 48.3%

         \[\leadsto -z \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y3\right) \]

   9. Simplified 48.3%

      \[\leadsto -z \cdot \color{blue}{\left(\left(y0 \cdot c - a \cdot y1\right) \cdot y3\right)} \]

   10. Taylor expanded in y0 around inf 40.0%

       \[\leadsto -\color{blue}{c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]

   if -3.0000000000000001e-12 < y3 < 2.39999999999999981e87

   1. Initial program 30.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 30.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 30.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 43.4%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 25.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   6. Taylor expanded in y0 around inf 18.1%

      \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot x\right)} \cdot y2\right) \]

   7. Taylor expanded in c around 0 17.4%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 17.4%

         \[\leadsto c \cdot \left(y0 \cdot \color{blue}{\left(y2 \cdot x\right)}\right) \]

      2. associate-*r* 18.1%

         \[\leadsto c \cdot \color{blue}{\left(\left(y0 \cdot y2\right) \cdot x\right)} \]

   9. Simplified 18.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot y2\right) \cdot x\right)} \]

   if 2.39999999999999981e87 < y3

   1. Initial program 18.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 18.2%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 24.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 24.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 24.2%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 26.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 36.6%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in y5 around inf 33.3%

      \[\leadsto \color{blue}{\left(\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot y5\right)} \cdot j \]
   6. Step-by-step derivation

      1. *-commutative 33.3%

         \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)\right)} \cdot j \]

      2. mul-1-neg 33.3%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \cdot j \]

      3. unsub-neg 33.3%

         \[\leadsto \left(y5 \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \cdot j \]

      4. *-commutative 33.3%

         \[\leadsto \left(y5 \cdot \left(y0 \cdot y3 - \color{blue}{t \cdot i}\right)\right) \cdot j \]

   7. Simplified 33.3%

      \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)} \cdot j \]

   8. Taylor expanded in y0 around inf 44.8%

      \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 44.8%

         \[\leadsto y0 \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot j\right)}\right) \]

   10. Simplified 44.8%

       \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(y5 \cdot j\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 28.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -3 \cdot 10^{-12}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 2.4 \cdot 10^{+87}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)\\ \end{array} \]

Alternative 39: 16.6% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* c (* y2 (* x y0))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return c * (y2 * (x * 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 = c * (y2 * (x * 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 c * (y2 * (x * y0));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return c * (y2 * (x * y0))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(c * Float64(y2 * Float64(x * y0)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = c * (y2 * (x * y0));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(c * N[(y2 * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 25.6%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Step-by-step derivation

   1. associate-+l- 25.6%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

3. Simplified 25.6%

   \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

4. Taylor expanded in y2 around inf 40.1%

   \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

5. Taylor expanded in c around inf 24.4%

   \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

6. Taylor expanded in y0 around inf 16.1%

   \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot x\right)} \cdot y2\right) \]

7. Final simplification 16.1%

   \[\leadsto c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right) \]

Alternative 40: 16.9% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* c (* x (* y0 y2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return c * (x * (y0 * y2));
}

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 = c * (x * (y0 * y2))
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 c * (x * (y0 * y2));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return c * (x * (y0 * y2))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(c * Float64(x * Float64(y0 * y2)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = c * (x * (y0 * y2));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 25.6%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Step-by-step derivation

   1. associate-+l- 25.6%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

3. Simplified 25.6%

   \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

4. Taylor expanded in y2 around inf 40.1%

   \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

5. Taylor expanded in c around inf 24.4%

   \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

6. Taylor expanded in y0 around inf 16.1%

   \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot x\right)} \cdot y2\right) \]

7. Taylor expanded in c around 0 16.1%

   \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)} \]
8. Step-by-step derivation

   1. *-commutative 16.1%

      \[\leadsto c \cdot \left(y0 \cdot \color{blue}{\left(y2 \cdot x\right)}\right) \]

   2. associate-*r* 16.5%

      \[\leadsto c \cdot \color{blue}{\left(\left(y0 \cdot y2\right) \cdot x\right)} \]

9. Simplified 16.5%

   \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot y2\right) \cdot x\right)} \]

10. Final simplification 16.5%

    \[\leadsto c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right) \]

Developer target: 28.4% 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 2023181 
(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)))))