Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.5% → 37.7%

Time: 1.1min

Alternatives: 40

Speedup: 2.6×

• 88.6% 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: 30.5% 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: 37.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot y4 - y0 \cdot y5\\ t_2 := b \cdot y4 - i \cdot y5\\ t_3 := t \cdot j - y \cdot k\\ t_4 := b \cdot y0 - i \cdot y1\\ t_5 := y4 \cdot \left(\left(b \cdot t\_3 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_6 := c \cdot y4 - a \cdot y5\\ t_7 := y3 \cdot \left(y \cdot t\_6 + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{if}\;y2 \leq -6.8 \cdot 10^{+158}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y2 \leq -8.5 \cdot 10^{+38}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - i \cdot t\_3\right)\right)\\ \mathbf{elif}\;y2 \leq -1.75 \cdot 10^{-102}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y2 \leq -1.85 \cdot 10^{-148}:\\ \;\;\;\;y \cdot \left(\left(y3 \cdot t\_6 - c \cdot \left(x \cdot i\right)\right) - k \cdot t\_2\right)\\ \mathbf{elif}\;y2 \leq -5.4 \cdot 10^{-163}:\\ \;\;\;\;k \cdot \left(z \cdot t\_4 + \left(y2 \cdot t\_1 - y \cdot t\_2\right)\right)\\ \mathbf{elif}\;y2 \leq -9.8 \cdot 10^{-179}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;y2 \leq 1.78 \cdot 10^{-270}:\\ \;\;\;\;z \cdot \left(\left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right) + k \cdot t\_4\right)\\ \mathbf{elif}\;y2 \leq 1.15 \cdot 10^{-81}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;y2 \leq 7 \cdot 10^{-19}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 1.05 \cdot 10^{+123}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y2 \leq 1.8 \cdot 10^{+189}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(k \cdot t\_1 + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y1 y4) (* y0 y5)))
        (t_2 (- (* b y4) (* i y5)))
        (t_3 (- (* t j) (* y k)))
        (t_4 (- (* b y0) (* i y1)))
        (t_5
         (*
          y4
          (+
           (+ (* b t_3) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2))))))
        (t_6 (- (* c y4) (* a y5)))
        (t_7 (* y3 (+ (* y t_6) (* j (- (* y0 y5) (* y1 y4)))))))
   (if (<= y2 -6.8e+158)
     (* y2 (* y4 (- (* k y1) (* t c))))
     (if (<= y2 -8.5e+38)
       (*
        y5
        (+
         (* a (- (* t y2) (* y y3)))
         (- (* y0 (- (* j y3) (* k y2))) (* i t_3))))
       (if (<= y2 -1.75e-102)
         t_5
         (if (<= y2 -1.85e-148)
           (* y (- (- (* y3 t_6) (* c (* x i))) (* k t_2)))
           (if (<= y2 -5.4e-163)
             (* k (+ (* z t_4) (- (* y2 t_1) (* y t_2))))
             (if (<= y2 -9.8e-179)
               t_7
               (if (<= y2 1.78e-270)
                 (*
                  z
                  (+
                   (+ (* t (- (* c i) (* a b))) (* y3 (- (* a y1) (* c y0))))
                   (* k t_4)))
                 (if (<= y2 1.15e-81)
                   t_7
                   (if (<= y2 7e-19)
                     (* b (* x (- (* y a) (* j y0))))
                     (if (<= y2 1.05e+123)
                       t_5
                       (if (<= y2 1.8e+189)
                         (*
                          x
                          (+
                           (+
                            (* y (- (* a b) (* c i)))
                            (* y2 (- (* c y0) (* a y1))))
                           (* j (- (* i y1) (* b y0)))))
                         (*
                          y2
                          (+
                           (* k t_1)
                           (* t (- (* a y5) (* c y4))))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double t_2 = (b * y4) - (i * y5);
	double t_3 = (t * j) - (y * k);
	double t_4 = (b * y0) - (i * y1);
	double t_5 = y4 * (((b * t_3) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_6 = (c * y4) - (a * y5);
	double t_7 = y3 * ((y * t_6) + (j * ((y0 * y5) - (y1 * y4))));
	double tmp;
	if (y2 <= -6.8e+158) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y2 <= -8.5e+38) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * ((j * y3) - (k * y2))) - (i * t_3)));
	} else if (y2 <= -1.75e-102) {
		tmp = t_5;
	} else if (y2 <= -1.85e-148) {
		tmp = y * (((y3 * t_6) - (c * (x * i))) - (k * t_2));
	} else if (y2 <= -5.4e-163) {
		tmp = k * ((z * t_4) + ((y2 * t_1) - (y * t_2)));
	} else if (y2 <= -9.8e-179) {
		tmp = t_7;
	} else if (y2 <= 1.78e-270) {
		tmp = z * (((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))) + (k * t_4));
	} else if (y2 <= 1.15e-81) {
		tmp = t_7;
	} else if (y2 <= 7e-19) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y2 <= 1.05e+123) {
		tmp = t_5;
	} else if (y2 <= 1.8e+189) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else {
		tmp = y2 * ((k * t_1) + (t * ((a * y5) - (c * y4))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_1 = (y1 * y4) - (y0 * y5)
    t_2 = (b * y4) - (i * y5)
    t_3 = (t * j) - (y * k)
    t_4 = (b * y0) - (i * y1)
    t_5 = y4 * (((b * t_3) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    t_6 = (c * y4) - (a * y5)
    t_7 = y3 * ((y * t_6) + (j * ((y0 * y5) - (y1 * y4))))
    if (y2 <= (-6.8d+158)) then
        tmp = y2 * (y4 * ((k * y1) - (t * c)))
    else if (y2 <= (-8.5d+38)) then
        tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * ((j * y3) - (k * y2))) - (i * t_3)))
    else if (y2 <= (-1.75d-102)) then
        tmp = t_5
    else if (y2 <= (-1.85d-148)) then
        tmp = y * (((y3 * t_6) - (c * (x * i))) - (k * t_2))
    else if (y2 <= (-5.4d-163)) then
        tmp = k * ((z * t_4) + ((y2 * t_1) - (y * t_2)))
    else if (y2 <= (-9.8d-179)) then
        tmp = t_7
    else if (y2 <= 1.78d-270) then
        tmp = z * (((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))) + (k * t_4))
    else if (y2 <= 1.15d-81) then
        tmp = t_7
    else if (y2 <= 7d-19) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y2 <= 1.05d+123) then
        tmp = t_5
    else if (y2 <= 1.8d+189) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    else
        tmp = y2 * ((k * t_1) + (t * ((a * y5) - (c * y4))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double t_2 = (b * y4) - (i * y5);
	double t_3 = (t * j) - (y * k);
	double t_4 = (b * y0) - (i * y1);
	double t_5 = y4 * (((b * t_3) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_6 = (c * y4) - (a * y5);
	double t_7 = y3 * ((y * t_6) + (j * ((y0 * y5) - (y1 * y4))));
	double tmp;
	if (y2 <= -6.8e+158) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (y2 <= -8.5e+38) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * ((j * y3) - (k * y2))) - (i * t_3)));
	} else if (y2 <= -1.75e-102) {
		tmp = t_5;
	} else if (y2 <= -1.85e-148) {
		tmp = y * (((y3 * t_6) - (c * (x * i))) - (k * t_2));
	} else if (y2 <= -5.4e-163) {
		tmp = k * ((z * t_4) + ((y2 * t_1) - (y * t_2)));
	} else if (y2 <= -9.8e-179) {
		tmp = t_7;
	} else if (y2 <= 1.78e-270) {
		tmp = z * (((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))) + (k * t_4));
	} else if (y2 <= 1.15e-81) {
		tmp = t_7;
	} else if (y2 <= 7e-19) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y2 <= 1.05e+123) {
		tmp = t_5;
	} else if (y2 <= 1.8e+189) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else {
		tmp = y2 * ((k * t_1) + (t * ((a * y5) - (c * y4))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y1 * y4) - (y0 * y5)
	t_2 = (b * y4) - (i * y5)
	t_3 = (t * j) - (y * k)
	t_4 = (b * y0) - (i * y1)
	t_5 = y4 * (((b * t_3) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	t_6 = (c * y4) - (a * y5)
	t_7 = y3 * ((y * t_6) + (j * ((y0 * y5) - (y1 * y4))))
	tmp = 0
	if y2 <= -6.8e+158:
		tmp = y2 * (y4 * ((k * y1) - (t * c)))
	elif y2 <= -8.5e+38:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * ((j * y3) - (k * y2))) - (i * t_3)))
	elif y2 <= -1.75e-102:
		tmp = t_5
	elif y2 <= -1.85e-148:
		tmp = y * (((y3 * t_6) - (c * (x * i))) - (k * t_2))
	elif y2 <= -5.4e-163:
		tmp = k * ((z * t_4) + ((y2 * t_1) - (y * t_2)))
	elif y2 <= -9.8e-179:
		tmp = t_7
	elif y2 <= 1.78e-270:
		tmp = z * (((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))) + (k * t_4))
	elif y2 <= 1.15e-81:
		tmp = t_7
	elif y2 <= 7e-19:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y2 <= 1.05e+123:
		tmp = t_5
	elif y2 <= 1.8e+189:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	else:
		tmp = y2 * ((k * t_1) + (t * ((a * y5) - (c * y4))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_2 = Float64(Float64(b * y4) - Float64(i * y5))
	t_3 = Float64(Float64(t * j) - Float64(y * k))
	t_4 = Float64(Float64(b * y0) - Float64(i * y1))
	t_5 = Float64(y4 * Float64(Float64(Float64(b * t_3) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_6 = Float64(Float64(c * y4) - Float64(a * y5))
	t_7 = Float64(y3 * Float64(Float64(y * t_6) + Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4)))))
	tmp = 0.0
	if (y2 <= -6.8e+158)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (y2 <= -8.5e+38)
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))) - Float64(i * t_3))));
	elseif (y2 <= -1.75e-102)
		tmp = t_5;
	elseif (y2 <= -1.85e-148)
		tmp = Float64(y * Float64(Float64(Float64(y3 * t_6) - Float64(c * Float64(x * i))) - Float64(k * t_2)));
	elseif (y2 <= -5.4e-163)
		tmp = Float64(k * Float64(Float64(z * t_4) + Float64(Float64(y2 * t_1) - Float64(y * t_2))));
	elseif (y2 <= -9.8e-179)
		tmp = t_7;
	elseif (y2 <= 1.78e-270)
		tmp = Float64(z * Float64(Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) + Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0)))) + Float64(k * t_4)));
	elseif (y2 <= 1.15e-81)
		tmp = t_7;
	elseif (y2 <= 7e-19)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y2 <= 1.05e+123)
		tmp = t_5;
	elseif (y2 <= 1.8e+189)
		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)))));
	else
		tmp = Float64(y2 * Float64(Float64(k * t_1) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y1 * y4) - (y0 * y5);
	t_2 = (b * y4) - (i * y5);
	t_3 = (t * j) - (y * k);
	t_4 = (b * y0) - (i * y1);
	t_5 = y4 * (((b * t_3) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	t_6 = (c * y4) - (a * y5);
	t_7 = y3 * ((y * t_6) + (j * ((y0 * y5) - (y1 * y4))));
	tmp = 0.0;
	if (y2 <= -6.8e+158)
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	elseif (y2 <= -8.5e+38)
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * ((j * y3) - (k * y2))) - (i * t_3)));
	elseif (y2 <= -1.75e-102)
		tmp = t_5;
	elseif (y2 <= -1.85e-148)
		tmp = y * (((y3 * t_6) - (c * (x * i))) - (k * t_2));
	elseif (y2 <= -5.4e-163)
		tmp = k * ((z * t_4) + ((y2 * t_1) - (y * t_2)));
	elseif (y2 <= -9.8e-179)
		tmp = t_7;
	elseif (y2 <= 1.78e-270)
		tmp = z * (((t * ((c * i) - (a * b))) + (y3 * ((a * y1) - (c * y0)))) + (k * t_4));
	elseif (y2 <= 1.15e-81)
		tmp = t_7;
	elseif (y2 <= 7e-19)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y2 <= 1.05e+123)
		tmp = t_5;
	elseif (y2 <= 1.8e+189)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	else
		tmp = y2 * ((k * t_1) + (t * ((a * y5) - (c * y4))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y4 * N[(N[(N[(b * t$95$3), $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$6 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(y3 * N[(N[(y * t$95$6), $MachinePrecision] + N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -6.8e+158], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -8.5e+38], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.75e-102], t$95$5, If[LessEqual[y2, -1.85e-148], N[(y * N[(N[(N[(y3 * t$95$6), $MachinePrecision] - N[(c * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -5.4e-163], N[(k * N[(N[(z * t$95$4), $MachinePrecision] + N[(N[(y2 * t$95$1), $MachinePrecision] - N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -9.8e-179], t$95$7, If[LessEqual[y2, 1.78e-270], N[(z * N[(N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.15e-81], t$95$7, If[LessEqual[y2, 7e-19], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.05e+123], t$95$5, If[LessEqual[y2, 1.8e+189], 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], N[(y2 * N[(N[(k * t$95$1), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y2 < -6.7999999999999998e158

   1. Initial program 17.2%

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

   3. Simplified 17.2%

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

   5. Taylor expanded in y4 around inf 34.7%

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

   6. Taylor expanded in y2 around inf 65.9%

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

   if -6.7999999999999998e158 < y2 < -8.4999999999999997e38

   1. Initial program 31.8%

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

   3. Simplified 31.8%

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

   5. Taylor expanded in y5 around -inf 55.3%

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

   if -8.4999999999999997e38 < y2 < -1.74999999999999993e-102 or 7.00000000000000031e-19 < y2 < 1.04999999999999997e123

   1. Initial program 34.0%

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

   3. Simplified 34.0%

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

   5. Taylor expanded in y4 around inf 65.3%

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

   if -1.74999999999999993e-102 < y2 < -1.85000000000000017e-148

   1. Initial program 37.5%

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

   3. Simplified 37.5%

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

   5. Taylor expanded in i around -inf 50.0%

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

      1. mul-1-neg 50.0%

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

      2. *-commutative 50.0%

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

      3. *-commutative 50.0%

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

   7. Simplified 50.0%

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

   8. Taylor expanded in y around inf 75.1%

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

      1. associate-*r* 75.1%

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

      2. neg-mul-1 75.1%

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

      3. mul-1-neg 75.1%

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

   10. Simplified 75.1%

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

   if -1.85000000000000017e-148 < y2 < -5.40000000000000029e-163

   1. Initial program 33.9%

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

   3. Simplified 33.9%

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

   5. Taylor expanded in k around inf 83.7%

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

      1. +-commutative 83.7%

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

      2. mul-1-neg 83.7%

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

      3. unsub-neg 83.7%

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

      4. *-commutative 83.7%

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

      5. mul-1-neg 83.7%

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

   7. Simplified 83.7%

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

   if -5.40000000000000029e-163 < y2 < -9.7999999999999999e-179 or 1.7799999999999999e-270 < y2 < 1.14999999999999996e-81

   1. Initial program 29.4%

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

   3. Simplified 29.4%

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

   5. Taylor expanded in i around -inf 40.0%

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

      1. mul-1-neg 40.0%

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

      2. *-commutative 40.0%

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

      3. *-commutative 40.0%

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

   7. Simplified 40.0%

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

   8. Taylor expanded in y3 around -inf 57.0%

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

   if -9.7999999999999999e-179 < y2 < 1.7799999999999999e-270

   1. Initial program 33.6%

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

   3. Simplified 33.6%

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

   5. Taylor expanded in z around inf 67.0%

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

      1. mul-1-neg 67.0%

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

      2. unsub-neg 67.0%

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

      3. mul-1-neg 67.0%

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

      4. mul-1-neg 67.0%

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

   7. Simplified 67.0%

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

   if 1.14999999999999996e-81 < y2 < 7.00000000000000031e-19

   1. Initial program 18.7%

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

   3. Simplified 18.7%

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

   5. Taylor expanded in b around inf 56.2%

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

   6. Taylor expanded in x around inf 81.4%

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

   if 1.04999999999999997e123 < y2 < 1.80000000000000004e189

   1. Initial program 19.8%

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

   3. Simplified 19.8%

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

   5. Taylor expanded in x around inf 60.8%

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

   if 1.80000000000000004e189 < y2

   1. Initial program 7.3%

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

   3. Simplified 7.3%

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

   5. Taylor expanded in i around -inf 10.8%

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

      1. mul-1-neg 10.8%

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

      2. *-commutative 10.8%

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

      3. *-commutative 10.8%

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

   7. Simplified 10.8%

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

   8. Taylor expanded in y2 around inf 65.2%

      \[\leadsto \color{blue}{y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -6.8 \cdot 10^{+158}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;y2 \leq -8.5 \cdot 10^{+38}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - i \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -1.75 \cdot 10^{-102}:\\ \;\;\;\;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}\;y2 \leq -1.85 \cdot 10^{-148}:\\ \;\;\;\;y \cdot \left(\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right) - c \cdot \left(x \cdot i\right)\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -5.4 \cdot 10^{-163}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -9.8 \cdot 10^{-179}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 1.78 \cdot 10^{-270}:\\ \;\;\;\;z \cdot \left(\left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right) + k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 1.15 \cdot 10^{-81}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 7 \cdot 10^{-19}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 1.05 \cdot 10^{+123}:\\ \;\;\;\;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}\;y2 \leq 1.8 \cdot 10^{+189}:\\ \;\;\;\;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{else}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 54.2% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (+
          (+
           (+
            (+
             (+
              (* (- (* a b) (* c i)) (- (* x y) (* z t)))
              (* (- (* x j) (* z k)) (- (* i y1) (* b y0))))
             (* (- (* x y2) (* z y3)) (- (* 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_1 INFINITY)
     t_1
     (* y3 (+ (* y (- (* c y4) (* a y5))) (* j (- (* y0 y5) (* 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 t_1 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((x * j) - (z * k)) * ((i * y1) - (b * y0)))) + (((x * y2) - (z * y3)) * ((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_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((x * j) - (z * k)) * ((i * y1) - (b * y0)))) + (((x * y2) - (z * y3)) * ((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_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((x * j) - (z * k)) * ((i * y1) - (b * y0)))) + (((x * y2) - (z * y3)) * ((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_1 <= math.inf:
		tmp = t_1
	else:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(a * b) - Float64(c * i)) * Float64(Float64(x * y) - Float64(z * t))) + Float64(Float64(Float64(x * j) - Float64(z * k)) * Float64(Float64(i * y1) - Float64(b * y0)))) + Float64(Float64(Float64(x * y2) - Float64(z * y3)) * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(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_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(j * Float64(Float64(y0 * y5) - 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)
	t_1 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((x * j) - (z * k)) * ((i * y1) - (b * y0)))) + (((x * y2) - (z * y3)) * ((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_1 <= Inf)
		tmp = t_1;
	else
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (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_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision] * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(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$1, Infinity], t$95$1, N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

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 91.1%

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

   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%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in i around -inf 12.8%

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

      1. mul-1-neg 12.8%

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

      2. *-commutative 12.8%

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

      3. *-commutative 12.8%

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

   7. Simplified 12.8%

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

   8. Taylor expanded in y3 around -inf 39.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.1%

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

Alternative 3: 31.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot y5 - c \cdot y4\\ t_2 := t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + c \cdot \left(z \cdot i\right)\right) + y2 \cdot t\_1\right)\\ \mathbf{if}\;y5 \leq -2.7 \cdot 10^{+247}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -7.6 \cdot 10^{+134}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y5 \leq -4 \cdot 10^{+34}:\\ \;\;\;\;\left(y \cdot b\right) \cdot \left(x \cdot a - k \cdot y4\right)\\ \mathbf{elif}\;y5 \leq -1.12 \cdot 10^{-51}:\\ \;\;\;\;\left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1\right)\\ \mathbf{elif}\;y5 \leq -2.4 \cdot 10^{-101}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot t\_1\right)\\ \mathbf{elif}\;y5 \leq -1.7 \cdot 10^{-210}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;y5 \leq 9 \cdot 10^{-268}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 2.7 \cdot 10^{-207}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.32 \cdot 10^{-135}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.06 \cdot 10^{+18}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 6.5 \cdot 10^{+136}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a y5) (* c y4)))
        (t_2
         (* t (+ (+ (* j (- (* b y4) (* i y5))) (* c (* z i))) (* y2 t_1)))))
   (if (<= y5 -2.7e+247)
     (* y3 (+ (* y (- (* c y4) (* a y5))) (* j (- (* y0 y5) (* y1 y4)))))
     (if (<= y5 -7.6e+134)
       t_2
       (if (<= y5 -4e+34)
         (* (* y b) (- (* x a) (* k y4)))
         (if (<= y5 -1.12e-51)
           (* (- (* x j) (* z k)) (* i y1))
           (if (<= y5 -2.4e-101)
             (* y2 (+ (* k (- (* y1 y4) (* y0 y5))) (* t t_1)))
             (if (<= y5 -1.7e-210)
               (* y1 (* z (- (* a y3) (* i k))))
               (if (<= y5 9e-268)
                 (* b (* j (- (* t y4) (* x y0))))
                 (if (<= y5 2.7e-207)
                   (* c (* y4 (- (* y y3) (* t y2))))
                   (if (<= y5 1.32e-135)
                     (* y1 (* a (- (* z y3) (* x y2))))
                     (if (<= y5 1.06e+18)
                       (* b (* x (- (* y a) (* j y0))))
                       (if (<= y5 6.5e+136)
                         t_2
                         (* y (* y5 (- (* i k) (* a y3)))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y5) - (c * y4);
	double t_2 = t * (((j * ((b * y4) - (i * y5))) + (c * (z * i))) + (y2 * t_1));
	double tmp;
	if (y5 <= -2.7e+247) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	} else if (y5 <= -7.6e+134) {
		tmp = t_2;
	} else if (y5 <= -4e+34) {
		tmp = (y * b) * ((x * a) - (k * y4));
	} else if (y5 <= -1.12e-51) {
		tmp = ((x * j) - (z * k)) * (i * y1);
	} else if (y5 <= -2.4e-101) {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + (t * t_1));
	} else if (y5 <= -1.7e-210) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (y5 <= 9e-268) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y5 <= 2.7e-207) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y5 <= 1.32e-135) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (y5 <= 1.06e+18) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y5 <= 6.5e+136) {
		tmp = t_2;
	} else {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * y5) - (c * y4)
    t_2 = t * (((j * ((b * y4) - (i * y5))) + (c * (z * i))) + (y2 * t_1))
    if (y5 <= (-2.7d+247)) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))))
    else if (y5 <= (-7.6d+134)) then
        tmp = t_2
    else if (y5 <= (-4d+34)) then
        tmp = (y * b) * ((x * a) - (k * y4))
    else if (y5 <= (-1.12d-51)) then
        tmp = ((x * j) - (z * k)) * (i * y1)
    else if (y5 <= (-2.4d-101)) then
        tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + (t * t_1))
    else if (y5 <= (-1.7d-210)) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (y5 <= 9d-268) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y5 <= 2.7d-207) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (y5 <= 1.32d-135) then
        tmp = y1 * (a * ((z * y3) - (x * y2)))
    else if (y5 <= 1.06d+18) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y5 <= 6.5d+136) then
        tmp = t_2
    else
        tmp = y * (y5 * ((i * k) - (a * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y5) - (c * y4);
	double t_2 = t * (((j * ((b * y4) - (i * y5))) + (c * (z * i))) + (y2 * t_1));
	double tmp;
	if (y5 <= -2.7e+247) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	} else if (y5 <= -7.6e+134) {
		tmp = t_2;
	} else if (y5 <= -4e+34) {
		tmp = (y * b) * ((x * a) - (k * y4));
	} else if (y5 <= -1.12e-51) {
		tmp = ((x * j) - (z * k)) * (i * y1);
	} else if (y5 <= -2.4e-101) {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + (t * t_1));
	} else if (y5 <= -1.7e-210) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (y5 <= 9e-268) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y5 <= 2.7e-207) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y5 <= 1.32e-135) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (y5 <= 1.06e+18) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y5 <= 6.5e+136) {
		tmp = t_2;
	} else {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (a * y5) - (c * y4)
	t_2 = t * (((j * ((b * y4) - (i * y5))) + (c * (z * i))) + (y2 * t_1))
	tmp = 0
	if y5 <= -2.7e+247:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))))
	elif y5 <= -7.6e+134:
		tmp = t_2
	elif y5 <= -4e+34:
		tmp = (y * b) * ((x * a) - (k * y4))
	elif y5 <= -1.12e-51:
		tmp = ((x * j) - (z * k)) * (i * y1)
	elif y5 <= -2.4e-101:
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + (t * t_1))
	elif y5 <= -1.7e-210:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif y5 <= 9e-268:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y5 <= 2.7e-207:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif y5 <= 1.32e-135:
		tmp = y1 * (a * ((z * y3) - (x * y2)))
	elif y5 <= 1.06e+18:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y5 <= 6.5e+136:
		tmp = t_2
	else:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(a * y5) - Float64(c * y4))
	t_2 = Float64(t * Float64(Float64(Float64(j * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(c * Float64(z * i))) + Float64(y2 * t_1)))
	tmp = 0.0
	if (y5 <= -2.7e+247)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4)))));
	elseif (y5 <= -7.6e+134)
		tmp = t_2;
	elseif (y5 <= -4e+34)
		tmp = Float64(Float64(y * b) * Float64(Float64(x * a) - Float64(k * y4)));
	elseif (y5 <= -1.12e-51)
		tmp = Float64(Float64(Float64(x * j) - Float64(z * k)) * Float64(i * y1));
	elseif (y5 <= -2.4e-101)
		tmp = Float64(y2 * Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(t * t_1)));
	elseif (y5 <= -1.7e-210)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (y5 <= 9e-268)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y5 <= 2.7e-207)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (y5 <= 1.32e-135)
		tmp = Float64(y1 * Float64(a * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (y5 <= 1.06e+18)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y5 <= 6.5e+136)
		tmp = t_2;
	else
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (a * y5) - (c * y4);
	t_2 = t * (((j * ((b * y4) - (i * y5))) + (c * (z * i))) + (y2 * t_1));
	tmp = 0.0;
	if (y5 <= -2.7e+247)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	elseif (y5 <= -7.6e+134)
		tmp = t_2;
	elseif (y5 <= -4e+34)
		tmp = (y * b) * ((x * a) - (k * y4));
	elseif (y5 <= -1.12e-51)
		tmp = ((x * j) - (z * k)) * (i * y1);
	elseif (y5 <= -2.4e-101)
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + (t * t_1));
	elseif (y5 <= -1.7e-210)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (y5 <= 9e-268)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y5 <= 2.7e-207)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (y5 <= 1.32e-135)
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	elseif (y5 <= 1.06e+18)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y5 <= 6.5e+136)
		tmp = t_2;
	else
		tmp = y * (y5 * ((i * k) - (a * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -2.7e+247], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -7.6e+134], t$95$2, If[LessEqual[y5, -4e+34], N[(N[(y * b), $MachinePrecision] * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.12e-51], N[(N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision] * N[(i * y1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2.4e-101], N[(y2 * N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.7e-210], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 9e-268], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.7e-207], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.32e-135], N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.06e+18], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 6.5e+136], t$95$2, N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if y5 < -2.7e247

   1. Initial program 18.2%

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

   3. Simplified 18.2%

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

   5. Taylor expanded in i around -inf 18.2%

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

      1. mul-1-neg 18.2%

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

      2. *-commutative 18.2%

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

      3. *-commutative 18.2%

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

   7. Simplified 18.2%

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

   8. Taylor expanded in y3 around -inf 81.8%

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

   if -2.7e247 < y5 < -7.59999999999999997e134 or 1.06e18 < y5 < 6.4999999999999998e136

   1. Initial program 30.5%

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

   3. Simplified 30.5%

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

   5. Taylor expanded in i around -inf 35.1%

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

      1. mul-1-neg 35.1%

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

      2. *-commutative 35.1%

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

      3. *-commutative 35.1%

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

   7. Simplified 35.1%

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

   8. Taylor expanded in t around inf 70.1%

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

      1. associate--r+ 70.1%

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

      2. mul-1-neg 70.1%

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

   10. Simplified 70.1%

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

   if -7.59999999999999997e134 < y5 < -3.99999999999999978e34

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in b around inf 72.3%

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

   6. Taylor expanded in y around -inf 56.0%

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

      1. mul-1-neg 56.0%

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

      2. associate-*r* 56.0%

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

      3. mul-1-neg 56.0%

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

   8. Simplified 56.0%

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

   if -3.99999999999999978e34 < y5 < -1.11999999999999998e-51

   1. Initial program 44.4%

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

   3. Simplified 44.4%

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

   5. Taylor expanded in y1 around inf 77.8%

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

      1. +-commutative 77.8%

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

      2. mul-1-neg 77.8%

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

      3. unsub-neg 77.8%

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

      4. *-commutative 77.8%

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

      5. *-commutative 77.8%

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

      6. *-commutative 77.8%

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

      7. mul-1-neg 77.8%

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

      8. *-commutative 77.8%

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

   7. Simplified 77.8%

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

   8. Taylor expanded in i around inf 100.0%

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

      1. associate-*r* 88.9%

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

   10. Simplified 88.9%

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

   if -1.11999999999999998e-51 < y5 < -2.4e-101

   1. Initial program 15.4%

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

   3. Simplified 15.4%

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

   5. Taylor expanded in i around -inf 15.4%

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

      1. mul-1-neg 15.4%

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

      2. *-commutative 15.4%

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

      3. *-commutative 15.4%

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

   7. Simplified 15.4%

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

   8. Taylor expanded in y2 around inf 69.4%

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

   if -2.4e-101 < y5 < -1.69999999999999987e-210

   1. Initial program 55.3%

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

   3. Simplified 55.3%

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

   5. Taylor expanded in y1 around inf 37.9%

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

      1. +-commutative 37.9%

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

      2. mul-1-neg 37.9%

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

      3. unsub-neg 37.9%

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

      4. *-commutative 37.9%

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

      5. *-commutative 37.9%

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

      6. *-commutative 37.9%

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

      7. mul-1-neg 37.9%

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

      8. *-commutative 37.9%

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

   7. Simplified 37.9%

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

   8. Taylor expanded in z around -inf 53.1%

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

      1. mul-1-neg 53.1%

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

   10. Simplified 53.1%

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

   if -1.69999999999999987e-210 < y5 < 9.0000000000000003e-268

   1. Initial program 39.2%

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

   3. Simplified 39.2%

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

   5. Taylor expanded in b around inf 62.5%

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

   6. Taylor expanded in j around inf 58.3%

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

   if 9.0000000000000003e-268 < y5 < 2.7e-207

   1. Initial program 38.3%

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

   3. Simplified 38.3%

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

   5. Taylor expanded in y4 around inf 69.4%

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

   6. Taylor expanded in c around inf 62.2%

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

   if 2.7e-207 < y5 < 1.32000000000000007e-135

   1. Initial program 12.8%

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

   3. Simplified 12.8%

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

   5. Taylor expanded in y1 around inf 60.2%

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

      1. +-commutative 60.2%

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

      2. mul-1-neg 60.2%

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

      3. unsub-neg 60.2%

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

      4. *-commutative 60.2%

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

      5. *-commutative 60.2%

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

      6. *-commutative 60.2%

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

      7. mul-1-neg 60.2%

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

      8. *-commutative 60.2%

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

   7. Simplified 60.2%

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

   8. Taylor expanded in a around inf 60.5%

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

   if 1.32000000000000007e-135 < y5 < 1.06e18

   1. Initial program 14.2%

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

   3. Simplified 14.2%

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

   5. Taylor expanded in b around inf 35.0%

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

   6. Taylor expanded in x around inf 45.5%

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

   if 6.4999999999999998e136 < y5

   1. Initial program 9.2%

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

   3. Simplified 9.2%

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

   5. Taylor expanded in i around -inf 15.8%

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

      1. mul-1-neg 15.8%

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

      2. *-commutative 15.8%

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

      3. *-commutative 15.8%

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

   7. Simplified 15.8%

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

   8. Taylor expanded in y around inf 45.2%

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

      1. associate-*r* 45.2%

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

      2. neg-mul-1 45.2%

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

      3. mul-1-neg 45.2%

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

   10. Simplified 45.2%

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

   11. Taylor expanded in y5 around inf 58.8%

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

       1. +-commutative 58.8%

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

       2. mul-1-neg 58.8%

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

       3. unsub-neg 58.8%

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

       4. *-commutative 58.8%

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

       5. *-commutative 58.8%

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

   13. Simplified 58.8%

       \[\leadsto y \cdot \color{blue}{\left(y5 \cdot \left(k \cdot i - y3 \cdot a\right)\right)} \]
3. Recombined 11 regimes into one program.

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2.7 \cdot 10^{+247}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -7.6 \cdot 10^{+134}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + c \cdot \left(z \cdot i\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -4 \cdot 10^{+34}:\\ \;\;\;\;\left(y \cdot b\right) \cdot \left(x \cdot a - k \cdot y4\right)\\ \mathbf{elif}\;y5 \leq -1.12 \cdot 10^{-51}:\\ \;\;\;\;\left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1\right)\\ \mathbf{elif}\;y5 \leq -2.4 \cdot 10^{-101}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -1.7 \cdot 10^{-210}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;y5 \leq 9 \cdot 10^{-268}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 2.7 \cdot 10^{-207}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.32 \cdot 10^{-135}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.06 \cdot 10^{+18}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 6.5 \cdot 10^{+136}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + c \cdot \left(z \cdot i\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 35.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot y5 - y1 \cdot y4\\ t_2 := c \cdot y0 - a \cdot y1\\ t_3 := y1 \cdot y4 - y0 \cdot y5\\ t_4 := t \cdot j - y \cdot k\\ t_5 := i \cdot y1 - b \cdot y0\\ t_6 := b \cdot y4 - i \cdot y5\\ t_7 := y4 \cdot t\_4\\ \mathbf{if}\;j \leq -1.5 \cdot 10^{+259}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot t\_3 - y \cdot t\_6\right) - i \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -2.95 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t\_2\right) + j \cdot t\_5\right)\\ \mathbf{elif}\;j \leq -1.95 \cdot 10^{+93}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot t\_3 + x \cdot t\_2\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -6.2 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -2.5 \cdot 10^{-226}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t\_4 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq -7.9 \cdot 10^{-292}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot t\_1\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-252}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 1.02 \cdot 10^{-69}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + t\_7\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{+110}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{+264}:\\ \;\;\;\;j \cdot \left(\left(t \cdot t\_6 + y3 \cdot t\_1\right) + x \cdot t\_5\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\_7\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y0 y5) (* y1 y4)))
        (t_2 (- (* c y0) (* a y1)))
        (t_3 (- (* y1 y4) (* y0 y5)))
        (t_4 (- (* t j) (* y k)))
        (t_5 (- (* i y1) (* b y0)))
        (t_6 (- (* b y4) (* i y5)))
        (t_7 (* y4 t_4)))
   (if (<= j -1.5e+259)
     (* k (- (- (* y2 t_3) (* y t_6)) (* i (* z y1))))
     (if (<= j -2.95e+125)
       (* x (+ (+ (* y (- (* a b) (* c i))) (* y2 t_2)) (* j t_5)))
       (if (<= j -1.95e+93)
         (* y2 (+ (+ (* k t_3) (* x t_2)) (* t (- (* a y5) (* c y4)))))
         (if (<= j -6.2e+42)
           (* x (* y0 (- (* c y2) (* b j))))
           (if (<= j -2.5e-226)
             (*
              y4
              (+
               (+ (* b t_4) (* y1 (- (* k y2) (* j y3))))
               (* c (- (* y y3) (* t y2)))))
             (if (<= j -7.9e-292)
               (* y3 (+ (* y (- (* c y4) (* a y5))) (* j t_1)))
               (if (<= j 2.6e-252)
                 (* y2 (* y4 (- (* k y1) (* t c))))
                 (if (<= j 1.02e-69)
                   (*
                    b
                    (+
                     (+ (* a (- (* x y) (* z t))) t_7)
                     (* y0 (- (* z k) (* x j)))))
                   (if (<= j 1.7e+110)
                     (* y1 (* z (- (* a y3) (* i k))))
                     (if (<= j 1.3e+264)
                       (* j (+ (+ (* t t_6) (* y3 t_1)) (* x t_5)))
                       (* b t_7)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * y5) - (y1 * y4);
	double t_2 = (c * y0) - (a * y1);
	double t_3 = (y1 * y4) - (y0 * y5);
	double t_4 = (t * j) - (y * k);
	double t_5 = (i * y1) - (b * y0);
	double t_6 = (b * y4) - (i * y5);
	double t_7 = y4 * t_4;
	double tmp;
	if (j <= -1.5e+259) {
		tmp = k * (((y2 * t_3) - (y * t_6)) - (i * (z * y1)));
	} else if (j <= -2.95e+125) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * t_5));
	} else if (j <= -1.95e+93) {
		tmp = y2 * (((k * t_3) + (x * t_2)) + (t * ((a * y5) - (c * y4))));
	} else if (j <= -6.2e+42) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (j <= -2.5e-226) {
		tmp = y4 * (((b * t_4) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (j <= -7.9e-292) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * t_1));
	} else if (j <= 2.6e-252) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (j <= 1.02e-69) {
		tmp = b * (((a * ((x * y) - (z * t))) + t_7) + (y0 * ((z * k) - (x * j))));
	} else if (j <= 1.7e+110) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (j <= 1.3e+264) {
		tmp = j * (((t * t_6) + (y3 * t_1)) + (x * t_5));
	} else {
		tmp = b * t_7;
	}
	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 = (y0 * y5) - (y1 * y4)
    t_2 = (c * y0) - (a * y1)
    t_3 = (y1 * y4) - (y0 * y5)
    t_4 = (t * j) - (y * k)
    t_5 = (i * y1) - (b * y0)
    t_6 = (b * y4) - (i * y5)
    t_7 = y4 * t_4
    if (j <= (-1.5d+259)) then
        tmp = k * (((y2 * t_3) - (y * t_6)) - (i * (z * y1)))
    else if (j <= (-2.95d+125)) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * t_5))
    else if (j <= (-1.95d+93)) then
        tmp = y2 * (((k * t_3) + (x * t_2)) + (t * ((a * y5) - (c * y4))))
    else if (j <= (-6.2d+42)) then
        tmp = x * (y0 * ((c * y2) - (b * j)))
    else if (j <= (-2.5d-226)) then
        tmp = y4 * (((b * t_4) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else if (j <= (-7.9d-292)) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * t_1))
    else if (j <= 2.6d-252) then
        tmp = y2 * (y4 * ((k * y1) - (t * c)))
    else if (j <= 1.02d-69) then
        tmp = b * (((a * ((x * y) - (z * t))) + t_7) + (y0 * ((z * k) - (x * j))))
    else if (j <= 1.7d+110) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (j <= 1.3d+264) then
        tmp = j * (((t * t_6) + (y3 * t_1)) + (x * t_5))
    else
        tmp = b * t_7
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * y5) - (y1 * y4);
	double t_2 = (c * y0) - (a * y1);
	double t_3 = (y1 * y4) - (y0 * y5);
	double t_4 = (t * j) - (y * k);
	double t_5 = (i * y1) - (b * y0);
	double t_6 = (b * y4) - (i * y5);
	double t_7 = y4 * t_4;
	double tmp;
	if (j <= -1.5e+259) {
		tmp = k * (((y2 * t_3) - (y * t_6)) - (i * (z * y1)));
	} else if (j <= -2.95e+125) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * t_5));
	} else if (j <= -1.95e+93) {
		tmp = y2 * (((k * t_3) + (x * t_2)) + (t * ((a * y5) - (c * y4))));
	} else if (j <= -6.2e+42) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (j <= -2.5e-226) {
		tmp = y4 * (((b * t_4) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (j <= -7.9e-292) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * t_1));
	} else if (j <= 2.6e-252) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (j <= 1.02e-69) {
		tmp = b * (((a * ((x * y) - (z * t))) + t_7) + (y0 * ((z * k) - (x * j))));
	} else if (j <= 1.7e+110) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (j <= 1.3e+264) {
		tmp = j * (((t * t_6) + (y3 * t_1)) + (x * t_5));
	} else {
		tmp = b * t_7;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y0 * y5) - (y1 * y4)
	t_2 = (c * y0) - (a * y1)
	t_3 = (y1 * y4) - (y0 * y5)
	t_4 = (t * j) - (y * k)
	t_5 = (i * y1) - (b * y0)
	t_6 = (b * y4) - (i * y5)
	t_7 = y4 * t_4
	tmp = 0
	if j <= -1.5e+259:
		tmp = k * (((y2 * t_3) - (y * t_6)) - (i * (z * y1)))
	elif j <= -2.95e+125:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * t_5))
	elif j <= -1.95e+93:
		tmp = y2 * (((k * t_3) + (x * t_2)) + (t * ((a * y5) - (c * y4))))
	elif j <= -6.2e+42:
		tmp = x * (y0 * ((c * y2) - (b * j)))
	elif j <= -2.5e-226:
		tmp = y4 * (((b * t_4) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	elif j <= -7.9e-292:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * t_1))
	elif j <= 2.6e-252:
		tmp = y2 * (y4 * ((k * y1) - (t * c)))
	elif j <= 1.02e-69:
		tmp = b * (((a * ((x * y) - (z * t))) + t_7) + (y0 * ((z * k) - (x * j))))
	elif j <= 1.7e+110:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif j <= 1.3e+264:
		tmp = j * (((t * t_6) + (y3 * t_1)) + (x * t_5))
	else:
		tmp = b * t_7
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y0 * y5) - Float64(y1 * y4))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	t_3 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_4 = Float64(Float64(t * j) - Float64(y * k))
	t_5 = Float64(Float64(i * y1) - Float64(b * y0))
	t_6 = Float64(Float64(b * y4) - Float64(i * y5))
	t_7 = Float64(y4 * t_4)
	tmp = 0.0
	if (j <= -1.5e+259)
		tmp = Float64(k * Float64(Float64(Float64(y2 * t_3) - Float64(y * t_6)) - Float64(i * Float64(z * y1))));
	elseif (j <= -2.95e+125)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_2)) + Float64(j * t_5)));
	elseif (j <= -1.95e+93)
		tmp = Float64(y2 * Float64(Float64(Float64(k * t_3) + Float64(x * t_2)) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (j <= -6.2e+42)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (j <= -2.5e-226)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_4) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (j <= -7.9e-292)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(j * t_1)));
	elseif (j <= 2.6e-252)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (j <= 1.02e-69)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + t_7) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (j <= 1.7e+110)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (j <= 1.3e+264)
		tmp = Float64(j * Float64(Float64(Float64(t * t_6) + Float64(y3 * t_1)) + Float64(x * t_5)));
	else
		tmp = Float64(b * t_7);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y0 * y5) - (y1 * y4);
	t_2 = (c * y0) - (a * y1);
	t_3 = (y1 * y4) - (y0 * y5);
	t_4 = (t * j) - (y * k);
	t_5 = (i * y1) - (b * y0);
	t_6 = (b * y4) - (i * y5);
	t_7 = y4 * t_4;
	tmp = 0.0;
	if (j <= -1.5e+259)
		tmp = k * (((y2 * t_3) - (y * t_6)) - (i * (z * y1)));
	elseif (j <= -2.95e+125)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * t_5));
	elseif (j <= -1.95e+93)
		tmp = y2 * (((k * t_3) + (x * t_2)) + (t * ((a * y5) - (c * y4))));
	elseif (j <= -6.2e+42)
		tmp = x * (y0 * ((c * y2) - (b * j)));
	elseif (j <= -2.5e-226)
		tmp = y4 * (((b * t_4) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	elseif (j <= -7.9e-292)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * t_1));
	elseif (j <= 2.6e-252)
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	elseif (j <= 1.02e-69)
		tmp = b * (((a * ((x * y) - (z * t))) + t_7) + (y0 * ((z * k) - (x * j))));
	elseif (j <= 1.7e+110)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (j <= 1.3e+264)
		tmp = j * (((t * t_6) + (y3 * t_1)) + (x * t_5));
	else
		tmp = b * t_7;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(y4 * t$95$4), $MachinePrecision]}, If[LessEqual[j, -1.5e+259], N[(k * N[(N[(N[(y2 * t$95$3), $MachinePrecision] - N[(y * t$95$6), $MachinePrecision]), $MachinePrecision] - N[(i * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.95e+125], 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 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.95e+93], N[(y2 * N[(N[(N[(k * t$95$3), $MachinePrecision] + N[(x * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6.2e+42], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.5e-226], N[(y4 * N[(N[(N[(b * t$95$4), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -7.9e-292], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.6e-252], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.02e-69], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$7), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.7e+110], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.3e+264], N[(j * N[(N[(N[(t * t$95$6), $MachinePrecision] + N[(y3 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * t$95$7), $MachinePrecision]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if j < -1.50000000000000006e259

   1. Initial program 10.0%

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

   3. Simplified 10.0%

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

   5. Taylor expanded in i around -inf 10.0%

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

      1. mul-1-neg 10.0%

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

      2. *-commutative 10.0%

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

      3. *-commutative 10.0%

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

   7. Simplified 10.0%

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

   8. Taylor expanded in k around inf 80.0%

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

   if -1.50000000000000006e259 < j < -2.95e125

   1. Initial program 22.4%

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

   3. Simplified 22.4%

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

   5. Taylor expanded in x around inf 56.0%

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

   if -2.95e125 < j < -1.9500000000000001e93

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in y2 around inf 75.2%

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

   if -1.9500000000000001e93 < j < -6.2000000000000003e42

   1. Initial program 39.7%

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

   3. Simplified 39.7%

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

   5. Taylor expanded in y0 around inf 49.9%

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

      1. +-commutative 49.9%

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

      2. mul-1-neg 49.9%

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

      3. unsub-neg 49.9%

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

      4. *-commutative 49.9%

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

      5. *-commutative 49.9%

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

      6. *-commutative 49.9%

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

      7. *-commutative 49.9%

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

   7. Simplified 49.9%

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

   8. Taylor expanded in x around inf 70.1%

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

   if -6.2000000000000003e42 < j < -2.4999999999999999e-226

   1. Initial program 27.8%

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

   3. Simplified 27.8%

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

   5. Taylor expanded in y4 around inf 64.7%

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

   if -2.4999999999999999e-226 < j < -7.90000000000000018e-292

   1. Initial program 33.7%

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

   3. Simplified 33.7%

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

   5. Taylor expanded in i around -inf 28.5%

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

      1. mul-1-neg 28.5%

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

      2. *-commutative 28.5%

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

      3. *-commutative 28.5%

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

   7. Simplified 28.5%

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

   8. Taylor expanded in y3 around -inf 56.6%

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

   if -7.90000000000000018e-292 < j < 2.5999999999999999e-252

   1. Initial program 26.0%

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

   3. Simplified 26.0%

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

   5. Taylor expanded in y4 around inf 42.2%

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

   6. Taylor expanded in y2 around inf 67.5%

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

   if 2.5999999999999999e-252 < j < 1.02000000000000005e-69

   1. Initial program 39.0%

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

   3. Simplified 39.0%

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

   5. Taylor expanded in b around inf 55.5%

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

   if 1.02000000000000005e-69 < j < 1.7000000000000001e110

   1. Initial program 29.7%

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

   3. Simplified 29.7%

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

   5. Taylor expanded in y1 around inf 41.0%

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

      1. +-commutative 41.0%

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

      2. mul-1-neg 41.0%

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

      3. unsub-neg 41.0%

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

      4. *-commutative 41.0%

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

      5. *-commutative 41.0%

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

      6. *-commutative 41.0%

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

      7. mul-1-neg 41.0%

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

      8. *-commutative 41.0%

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

   7. Simplified 41.0%

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

   8. Taylor expanded in z around -inf 54.8%

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

      1. mul-1-neg 54.8%

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

   10. Simplified 54.8%

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

   if 1.7000000000000001e110 < j < 1.3e264

   1. Initial program 18.2%

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

   3. Simplified 18.2%

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

   5. Taylor expanded in j around inf 64.1%

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

      1. +-commutative 64.1%

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

      2. mul-1-neg 64.1%

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

      3. unsub-neg 64.1%

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

      4. *-commutative 64.1%

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

   7. Simplified 64.1%

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

   if 1.3e264 < j

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in y4 around inf 82.7%

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

   6. Taylor expanded in b around inf 90.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
3. Recombined 11 regimes into one program.

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.5 \cdot 10^{+259}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - i \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -2.95 \cdot 10^{+125}:\\ \;\;\;\;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}\;j \leq -1.95 \cdot 10^{+93}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -6.2 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -2.5 \cdot 10^{-226}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq -7.9 \cdot 10^{-292}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-252}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 1.02 \cdot 10^{-69}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{+110}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{+264}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 37.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot y - z \cdot t\right)\\ t_2 := b \cdot t\_1\\ t_3 := k \cdot \left(b \cdot y4 - i \cdot y5\right)\\ t_4 := y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\\ t_5 := y0 \cdot \left(z \cdot k - x \cdot j\right)\\ t_6 := y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ t_7 := y \cdot \left(\left(t\_4 - c \cdot \left(x \cdot i\right)\right) - t\_3\right)\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{+252}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{+143}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{+96}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{+52}:\\ \;\;\;\;b \cdot \left(\left(t\_1 + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + t\_5\right)\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \left(t\_4 + \left(x \cdot \left(a \cdot b - c \cdot i\right) - t\_3\right)\right)\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-24}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-84}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;a \leq -2.95 \cdot 10^{-215}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-175}:\\ \;\;\;\;b \cdot t\_5\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+84}:\\ \;\;\;\;t\_7\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (- (* x y) (* z t))))
        (t_2 (* b t_1))
        (t_3 (* k (- (* b y4) (* i y5))))
        (t_4 (* y3 (- (* c y4) (* a y5))))
        (t_5 (* y0 (- (* z k) (* x j))))
        (t_6
         (*
          y2
          (+
           (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
           (* t (- (* a y5) (* c y4))))))
        (t_7 (* y (- (- t_4 (* c (* x i))) t_3))))
   (if (<= a -5.2e+252)
     (* y1 (* a (- (* z y3) (* x y2))))
     (if (<= a -5.8e+143)
       t_2
       (if (<= a -1.3e+96)
         (* b (* x (- (* y a) (* j y0))))
         (if (<= a -3.1e+52)
           (* b (+ (+ t_1 (* y4 (- (* t j) (* y k)))) t_5))
           (if (<= a -4.5e+21)
             (* y (+ t_4 (- (* x (- (* a b) (* c i))) t_3)))
             (if (<= a -1.9e-24)
               t_6
               (if (<= a -8.5e-84)
                 t_7
                 (if (<= a -2.95e-215)
                   t_6
                   (if (<= a 1.5e-175)
                     (* b t_5)
                     (if (<= a 3e+84) t_7 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 = a * ((x * y) - (z * t));
	double t_2 = b * t_1;
	double t_3 = k * ((b * y4) - (i * y5));
	double t_4 = y3 * ((c * y4) - (a * y5));
	double t_5 = y0 * ((z * k) - (x * j));
	double t_6 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	double t_7 = y * ((t_4 - (c * (x * i))) - t_3);
	double tmp;
	if (a <= -5.2e+252) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (a <= -5.8e+143) {
		tmp = t_2;
	} else if (a <= -1.3e+96) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (a <= -3.1e+52) {
		tmp = b * ((t_1 + (y4 * ((t * j) - (y * k)))) + t_5);
	} else if (a <= -4.5e+21) {
		tmp = y * (t_4 + ((x * ((a * b) - (c * i))) - t_3));
	} else if (a <= -1.9e-24) {
		tmp = t_6;
	} else if (a <= -8.5e-84) {
		tmp = t_7;
	} else if (a <= -2.95e-215) {
		tmp = t_6;
	} else if (a <= 1.5e-175) {
		tmp = b * t_5;
	} else if (a <= 3e+84) {
		tmp = t_7;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_1 = a * ((x * y) - (z * t))
    t_2 = b * t_1
    t_3 = k * ((b * y4) - (i * y5))
    t_4 = y3 * ((c * y4) - (a * y5))
    t_5 = y0 * ((z * k) - (x * j))
    t_6 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    t_7 = y * ((t_4 - (c * (x * i))) - t_3)
    if (a <= (-5.2d+252)) then
        tmp = y1 * (a * ((z * y3) - (x * y2)))
    else if (a <= (-5.8d+143)) then
        tmp = t_2
    else if (a <= (-1.3d+96)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (a <= (-3.1d+52)) then
        tmp = b * ((t_1 + (y4 * ((t * j) - (y * k)))) + t_5)
    else if (a <= (-4.5d+21)) then
        tmp = y * (t_4 + ((x * ((a * b) - (c * i))) - t_3))
    else if (a <= (-1.9d-24)) then
        tmp = t_6
    else if (a <= (-8.5d-84)) then
        tmp = t_7
    else if (a <= (-2.95d-215)) then
        tmp = t_6
    else if (a <= 1.5d-175) then
        tmp = b * t_5
    else if (a <= 3d+84) then
        tmp = t_7
    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 = a * ((x * y) - (z * t));
	double t_2 = b * t_1;
	double t_3 = k * ((b * y4) - (i * y5));
	double t_4 = y3 * ((c * y4) - (a * y5));
	double t_5 = y0 * ((z * k) - (x * j));
	double t_6 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	double t_7 = y * ((t_4 - (c * (x * i))) - t_3);
	double tmp;
	if (a <= -5.2e+252) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (a <= -5.8e+143) {
		tmp = t_2;
	} else if (a <= -1.3e+96) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (a <= -3.1e+52) {
		tmp = b * ((t_1 + (y4 * ((t * j) - (y * k)))) + t_5);
	} else if (a <= -4.5e+21) {
		tmp = y * (t_4 + ((x * ((a * b) - (c * i))) - t_3));
	} else if (a <= -1.9e-24) {
		tmp = t_6;
	} else if (a <= -8.5e-84) {
		tmp = t_7;
	} else if (a <= -2.95e-215) {
		tmp = t_6;
	} else if (a <= 1.5e-175) {
		tmp = b * t_5;
	} else if (a <= 3e+84) {
		tmp = t_7;
	} 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 = a * ((x * y) - (z * t))
	t_2 = b * t_1
	t_3 = k * ((b * y4) - (i * y5))
	t_4 = y3 * ((c * y4) - (a * y5))
	t_5 = y0 * ((z * k) - (x * j))
	t_6 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	t_7 = y * ((t_4 - (c * (x * i))) - t_3)
	tmp = 0
	if a <= -5.2e+252:
		tmp = y1 * (a * ((z * y3) - (x * y2)))
	elif a <= -5.8e+143:
		tmp = t_2
	elif a <= -1.3e+96:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif a <= -3.1e+52:
		tmp = b * ((t_1 + (y4 * ((t * j) - (y * k)))) + t_5)
	elif a <= -4.5e+21:
		tmp = y * (t_4 + ((x * ((a * b) - (c * i))) - t_3))
	elif a <= -1.9e-24:
		tmp = t_6
	elif a <= -8.5e-84:
		tmp = t_7
	elif a <= -2.95e-215:
		tmp = t_6
	elif a <= 1.5e-175:
		tmp = b * t_5
	elif a <= 3e+84:
		tmp = t_7
	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(a * Float64(Float64(x * y) - Float64(z * t)))
	t_2 = Float64(b * t_1)
	t_3 = Float64(k * Float64(Float64(b * y4) - Float64(i * y5)))
	t_4 = Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5)))
	t_5 = Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))
	t_6 = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))))
	t_7 = Float64(y * Float64(Float64(t_4 - Float64(c * Float64(x * i))) - t_3))
	tmp = 0.0
	if (a <= -5.2e+252)
		tmp = Float64(y1 * Float64(a * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (a <= -5.8e+143)
		tmp = t_2;
	elseif (a <= -1.3e+96)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (a <= -3.1e+52)
		tmp = Float64(b * Float64(Float64(t_1 + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + t_5));
	elseif (a <= -4.5e+21)
		tmp = Float64(y * Float64(t_4 + Float64(Float64(x * Float64(Float64(a * b) - Float64(c * i))) - t_3)));
	elseif (a <= -1.9e-24)
		tmp = t_6;
	elseif (a <= -8.5e-84)
		tmp = t_7;
	elseif (a <= -2.95e-215)
		tmp = t_6;
	elseif (a <= 1.5e-175)
		tmp = Float64(b * t_5);
	elseif (a <= 3e+84)
		tmp = t_7;
	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 = a * ((x * y) - (z * t));
	t_2 = b * t_1;
	t_3 = k * ((b * y4) - (i * y5));
	t_4 = y3 * ((c * y4) - (a * y5));
	t_5 = y0 * ((z * k) - (x * j));
	t_6 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	t_7 = y * ((t_4 - (c * (x * i))) - t_3);
	tmp = 0.0;
	if (a <= -5.2e+252)
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	elseif (a <= -5.8e+143)
		tmp = t_2;
	elseif (a <= -1.3e+96)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (a <= -3.1e+52)
		tmp = b * ((t_1 + (y4 * ((t * j) - (y * k)))) + t_5);
	elseif (a <= -4.5e+21)
		tmp = y * (t_4 + ((x * ((a * b) - (c * i))) - t_3));
	elseif (a <= -1.9e-24)
		tmp = t_6;
	elseif (a <= -8.5e-84)
		tmp = t_7;
	elseif (a <= -2.95e-215)
		tmp = t_6;
	elseif (a <= 1.5e-175)
		tmp = b * t_5;
	elseif (a <= 3e+84)
		tmp = t_7;
	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[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(k * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(y * N[(N[(t$95$4 - N[(c * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.2e+252], N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.8e+143], t$95$2, If[LessEqual[a, -1.3e+96], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.1e+52], N[(b * N[(N[(t$95$1 + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.5e+21], N[(y * N[(t$95$4 + N[(N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.9e-24], t$95$6, If[LessEqual[a, -8.5e-84], t$95$7, If[LessEqual[a, -2.95e-215], t$95$6, If[LessEqual[a, 1.5e-175], N[(b * t$95$5), $MachinePrecision], If[LessEqual[a, 3e+84], t$95$7, t$95$2]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -5.20000000000000035e252

   1. Initial program 17.6%

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

   3. Simplified 17.6%

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

   5. Taylor expanded in y1 around inf 47.2%

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

      1. +-commutative 47.2%

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

      2. mul-1-neg 47.2%

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

      3. unsub-neg 47.2%

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

      4. *-commutative 47.2%

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

      5. *-commutative 47.2%

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

      6. *-commutative 47.2%

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

      7. mul-1-neg 47.2%

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

      8. *-commutative 47.2%

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

   7. Simplified 47.2%

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

   8. Taylor expanded in a around inf 70.7%

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

   if -5.20000000000000035e252 < a < -5.7999999999999996e143 or 2.99999999999999996e84 < a

   1. Initial program 24.2%

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

   3. Simplified 24.2%

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

   5. Taylor expanded in b around inf 57.2%

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

   6. Taylor expanded in a around inf 64.3%

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

   if -5.7999999999999996e143 < a < -1.3e96

   1. Initial program 19.5%

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

   3. Simplified 19.5%

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

   5. Taylor expanded in b around inf 19.0%

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

   6. Taylor expanded in x around inf 62.9%

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

   if -1.3e96 < a < -3.1e52

   1. Initial program 33.3%

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

   3. Simplified 33.3%

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

   5. Taylor expanded in b around inf 66.8%

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

   if -3.1e52 < a < -4.5e21

   1. Initial program 18.2%

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

   3. Simplified 18.2%

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

   5. Taylor expanded in y around inf 82.1%

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

      1. +-commutative 82.1%

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

      2. mul-1-neg 82.1%

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

      3. unsub-neg 82.1%

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

      4. *-commutative 82.1%

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

      5. *-commutative 82.1%

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

      6. mul-1-neg 82.1%

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

   7. Simplified 82.1%

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

   if -4.5e21 < a < -1.90000000000000013e-24 or -8.4999999999999994e-84 < a < -2.9499999999999999e-215

   1. Initial program 21.5%

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

   3. Simplified 21.5%

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

   5. Taylor expanded in y2 around inf 68.0%

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

   if -1.90000000000000013e-24 < a < -8.4999999999999994e-84 or 1.5e-175 < a < 2.99999999999999996e84

   1. Initial program 29.0%

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

   3. Simplified 29.0%

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

   5. Taylor expanded in i around -inf 35.2%

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

      1. mul-1-neg 35.2%

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

      2. *-commutative 35.2%

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

      3. *-commutative 35.2%

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

   7. Simplified 35.2%

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

   8. Taylor expanded in y around inf 58.7%

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

      1. associate-*r* 58.7%

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

      2. neg-mul-1 58.7%

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

      3. mul-1-neg 58.7%

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

   10. Simplified 58.7%

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

   if -2.9499999999999999e-215 < a < 1.5e-175

   1. Initial program 36.0%

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

   3. Simplified 36.0%

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

   5. Taylor expanded in b around inf 46.8%

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

   6. Taylor expanded in y0 around inf 52.2%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+252}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{+143}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{+96}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{+52}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-24}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \left(\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right) - c \cdot \left(x \cdot i\right)\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -2.95 \cdot 10^{-215}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-175}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \left(\left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right) - c \cdot \left(x \cdot i\right)\right) - k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 36.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot y4 - i \cdot y5\\ t_2 := c \cdot y0 - a \cdot y1\\ t_3 := y1 \cdot y4 - y0 \cdot y5\\ t_4 := t \cdot j - y \cdot k\\ t_5 := i \cdot y1 - b \cdot y0\\ t_6 := y4 \cdot t\_4\\ \mathbf{if}\;j \leq -2.3 \cdot 10^{+258}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot t\_3 - y \cdot t\_1\right) - i \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -1.4 \cdot 10^{+127}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t\_2\right) + j \cdot t\_5\right)\\ \mathbf{elif}\;j \leq -2.05 \cdot 10^{+93}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot t\_3 + x \cdot t\_2\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -3.4 \cdot 10^{-218}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t\_4 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{-259}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - i \cdot t\_4\right)\right)\\ \mathbf{elif}\;j \leq 2.25 \cdot 10^{-65}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + t\_6\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{+110}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;j \leq 1.55 \cdot 10^{+263}:\\ \;\;\;\;j \cdot \left(\left(t \cdot t\_1 + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot t\_5\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\_6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* b y4) (* i y5)))
        (t_2 (- (* c y0) (* a y1)))
        (t_3 (- (* y1 y4) (* y0 y5)))
        (t_4 (- (* t j) (* y k)))
        (t_5 (- (* i y1) (* b y0)))
        (t_6 (* y4 t_4)))
   (if (<= j -2.3e+258)
     (* k (- (- (* y2 t_3) (* y t_1)) (* i (* z y1))))
     (if (<= j -1.4e+127)
       (* x (+ (+ (* y (- (* a b) (* c i))) (* y2 t_2)) (* j t_5)))
       (if (<= j -2.05e+93)
         (* y2 (+ (+ (* k t_3) (* x t_2)) (* t (- (* a y5) (* c y4)))))
         (if (<= j -7.5e+42)
           (* x (* y0 (- (* c y2) (* b j))))
           (if (<= j -3.4e-218)
             (*
              y4
              (+
               (+ (* b t_4) (* y1 (- (* k y2) (* j y3))))
               (* c (- (* y y3) (* t y2)))))
             (if (<= j 1.25e-259)
               (*
                y5
                (+
                 (* a (- (* t y2) (* y y3)))
                 (- (* y0 (- (* j y3) (* k y2))) (* i t_4))))
               (if (<= j 2.25e-65)
                 (*
                  b
                  (+
                   (+ (* a (- (* x y) (* z t))) t_6)
                   (* y0 (- (* z k) (* x j)))))
                 (if (<= j 1.9e+110)
                   (* y1 (* z (- (* a y3) (* i k))))
                   (if (<= j 1.55e+263)
                     (*
                      j
                      (+
                       (+ (* t t_1) (* y3 (- (* y0 y5) (* y1 y4))))
                       (* x t_5)))
                     (* b t_6))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y4) - (i * y5);
	double t_2 = (c * y0) - (a * y1);
	double t_3 = (y1 * y4) - (y0 * y5);
	double t_4 = (t * j) - (y * k);
	double t_5 = (i * y1) - (b * y0);
	double t_6 = y4 * t_4;
	double tmp;
	if (j <= -2.3e+258) {
		tmp = k * (((y2 * t_3) - (y * t_1)) - (i * (z * y1)));
	} else if (j <= -1.4e+127) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * t_5));
	} else if (j <= -2.05e+93) {
		tmp = y2 * (((k * t_3) + (x * t_2)) + (t * ((a * y5) - (c * y4))));
	} else if (j <= -7.5e+42) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (j <= -3.4e-218) {
		tmp = y4 * (((b * t_4) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (j <= 1.25e-259) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * ((j * y3) - (k * y2))) - (i * t_4)));
	} else if (j <= 2.25e-65) {
		tmp = b * (((a * ((x * y) - (z * t))) + t_6) + (y0 * ((z * k) - (x * j))));
	} else if (j <= 1.9e+110) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (j <= 1.55e+263) {
		tmp = j * (((t * t_1) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_5));
	} else {
		tmp = b * t_6;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = (b * y4) - (i * y5)
    t_2 = (c * y0) - (a * y1)
    t_3 = (y1 * y4) - (y0 * y5)
    t_4 = (t * j) - (y * k)
    t_5 = (i * y1) - (b * y0)
    t_6 = y4 * t_4
    if (j <= (-2.3d+258)) then
        tmp = k * (((y2 * t_3) - (y * t_1)) - (i * (z * y1)))
    else if (j <= (-1.4d+127)) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * t_5))
    else if (j <= (-2.05d+93)) then
        tmp = y2 * (((k * t_3) + (x * t_2)) + (t * ((a * y5) - (c * y4))))
    else if (j <= (-7.5d+42)) then
        tmp = x * (y0 * ((c * y2) - (b * j)))
    else if (j <= (-3.4d-218)) then
        tmp = y4 * (((b * t_4) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else if (j <= 1.25d-259) then
        tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * ((j * y3) - (k * y2))) - (i * t_4)))
    else if (j <= 2.25d-65) then
        tmp = b * (((a * ((x * y) - (z * t))) + t_6) + (y0 * ((z * k) - (x * j))))
    else if (j <= 1.9d+110) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (j <= 1.55d+263) then
        tmp = j * (((t * t_1) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_5))
    else
        tmp = b * t_6
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y4) - (i * y5);
	double t_2 = (c * y0) - (a * y1);
	double t_3 = (y1 * y4) - (y0 * y5);
	double t_4 = (t * j) - (y * k);
	double t_5 = (i * y1) - (b * y0);
	double t_6 = y4 * t_4;
	double tmp;
	if (j <= -2.3e+258) {
		tmp = k * (((y2 * t_3) - (y * t_1)) - (i * (z * y1)));
	} else if (j <= -1.4e+127) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * t_5));
	} else if (j <= -2.05e+93) {
		tmp = y2 * (((k * t_3) + (x * t_2)) + (t * ((a * y5) - (c * y4))));
	} else if (j <= -7.5e+42) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (j <= -3.4e-218) {
		tmp = y4 * (((b * t_4) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (j <= 1.25e-259) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * ((j * y3) - (k * y2))) - (i * t_4)));
	} else if (j <= 2.25e-65) {
		tmp = b * (((a * ((x * y) - (z * t))) + t_6) + (y0 * ((z * k) - (x * j))));
	} else if (j <= 1.9e+110) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (j <= 1.55e+263) {
		tmp = j * (((t * t_1) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_5));
	} else {
		tmp = b * t_6;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (b * y4) - (i * y5)
	t_2 = (c * y0) - (a * y1)
	t_3 = (y1 * y4) - (y0 * y5)
	t_4 = (t * j) - (y * k)
	t_5 = (i * y1) - (b * y0)
	t_6 = y4 * t_4
	tmp = 0
	if j <= -2.3e+258:
		tmp = k * (((y2 * t_3) - (y * t_1)) - (i * (z * y1)))
	elif j <= -1.4e+127:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * t_5))
	elif j <= -2.05e+93:
		tmp = y2 * (((k * t_3) + (x * t_2)) + (t * ((a * y5) - (c * y4))))
	elif j <= -7.5e+42:
		tmp = x * (y0 * ((c * y2) - (b * j)))
	elif j <= -3.4e-218:
		tmp = y4 * (((b * t_4) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	elif j <= 1.25e-259:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * ((j * y3) - (k * y2))) - (i * t_4)))
	elif j <= 2.25e-65:
		tmp = b * (((a * ((x * y) - (z * t))) + t_6) + (y0 * ((z * k) - (x * j))))
	elif j <= 1.9e+110:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif j <= 1.55e+263:
		tmp = j * (((t * t_1) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_5))
	else:
		tmp = b * t_6
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(b * y4) - Float64(i * y5))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	t_3 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_4 = Float64(Float64(t * j) - Float64(y * k))
	t_5 = Float64(Float64(i * y1) - Float64(b * y0))
	t_6 = Float64(y4 * t_4)
	tmp = 0.0
	if (j <= -2.3e+258)
		tmp = Float64(k * Float64(Float64(Float64(y2 * t_3) - Float64(y * t_1)) - Float64(i * Float64(z * y1))));
	elseif (j <= -1.4e+127)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_2)) + Float64(j * t_5)));
	elseif (j <= -2.05e+93)
		tmp = Float64(y2 * Float64(Float64(Float64(k * t_3) + Float64(x * t_2)) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (j <= -7.5e+42)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (j <= -3.4e-218)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_4) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (j <= 1.25e-259)
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))) - Float64(i * t_4))));
	elseif (j <= 2.25e-65)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + t_6) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (j <= 1.9e+110)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (j <= 1.55e+263)
		tmp = Float64(j * Float64(Float64(Float64(t * t_1) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * t_5)));
	else
		tmp = Float64(b * t_6);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (b * y4) - (i * y5);
	t_2 = (c * y0) - (a * y1);
	t_3 = (y1 * y4) - (y0 * y5);
	t_4 = (t * j) - (y * k);
	t_5 = (i * y1) - (b * y0);
	t_6 = y4 * t_4;
	tmp = 0.0;
	if (j <= -2.3e+258)
		tmp = k * (((y2 * t_3) - (y * t_1)) - (i * (z * y1)));
	elseif (j <= -1.4e+127)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * t_5));
	elseif (j <= -2.05e+93)
		tmp = y2 * (((k * t_3) + (x * t_2)) + (t * ((a * y5) - (c * y4))));
	elseif (j <= -7.5e+42)
		tmp = x * (y0 * ((c * y2) - (b * j)));
	elseif (j <= -3.4e-218)
		tmp = y4 * (((b * t_4) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	elseif (j <= 1.25e-259)
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((y0 * ((j * y3) - (k * y2))) - (i * t_4)));
	elseif (j <= 2.25e-65)
		tmp = b * (((a * ((x * y) - (z * t))) + t_6) + (y0 * ((z * k) - (x * j))));
	elseif (j <= 1.9e+110)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (j <= 1.55e+263)
		tmp = j * (((t * t_1) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * t_5));
	else
		tmp = b * t_6;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(y4 * t$95$4), $MachinePrecision]}, If[LessEqual[j, -2.3e+258], N[(k * N[(N[(N[(y2 * t$95$3), $MachinePrecision] - N[(y * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(i * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.4e+127], 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 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.05e+93], N[(y2 * N[(N[(N[(k * t$95$3), $MachinePrecision] + N[(x * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -7.5e+42], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.4e-218], N[(y4 * N[(N[(N[(b * t$95$4), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.25e-259], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.25e-65], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.9e+110], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.55e+263], N[(j * N[(N[(N[(t * t$95$1), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * t$95$6), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if j < -2.3000000000000001e258

   1. Initial program 10.0%

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

   3. Simplified 10.0%

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

   5. Taylor expanded in i around -inf 10.0%

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

      1. mul-1-neg 10.0%

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

      2. *-commutative 10.0%

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

      3. *-commutative 10.0%

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

   7. Simplified 10.0%

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

   8. Taylor expanded in k around inf 80.0%

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

   if -2.3000000000000001e258 < j < -1.4000000000000001e127

   1. Initial program 22.4%

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

   3. Simplified 22.4%

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

   5. Taylor expanded in x around inf 56.0%

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

   if -1.4000000000000001e127 < j < -2.0500000000000001e93

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in y2 around inf 75.2%

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

   if -2.0500000000000001e93 < j < -7.50000000000000041e42

   1. Initial program 39.7%

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

   3. Simplified 39.7%

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

   5. Taylor expanded in y0 around inf 49.9%

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

      1. +-commutative 49.9%

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

      2. mul-1-neg 49.9%

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

      3. unsub-neg 49.9%

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

      4. *-commutative 49.9%

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

      5. *-commutative 49.9%

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

      6. *-commutative 49.9%

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

      7. *-commutative 49.9%

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

   7. Simplified 49.9%

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

   8. Taylor expanded in x around inf 70.1%

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

   if -7.50000000000000041e42 < j < -3.39999999999999986e-218

   1. Initial program 26.7%

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

   3. Simplified 26.7%

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

   5. Taylor expanded in y4 around inf 67.5%

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

   if -3.39999999999999986e-218 < j < 1.24999999999999994e-259

   1. Initial program 36.3%

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

   3. Simplified 36.3%

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

   5. Taylor expanded in y5 around -inf 54.2%

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

   if 1.24999999999999994e-259 < j < 2.2499999999999999e-65

   1. Initial program 36.0%

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

   3. Simplified 36.0%

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

   5. Taylor expanded in b around inf 53.1%

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

   if 2.2499999999999999e-65 < j < 1.89999999999999994e110

   1. Initial program 29.7%

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

   3. Simplified 29.7%

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

   5. Taylor expanded in y1 around inf 41.0%

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

      1. +-commutative 41.0%

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

      2. mul-1-neg 41.0%

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

      3. unsub-neg 41.0%

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

      4. *-commutative 41.0%

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

      5. *-commutative 41.0%

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

      6. *-commutative 41.0%

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

      7. mul-1-neg 41.0%

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

      8. *-commutative 41.0%

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

   7. Simplified 41.0%

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

   8. Taylor expanded in z around -inf 54.8%

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

      1. mul-1-neg 54.8%

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

   10. Simplified 54.8%

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

   if 1.89999999999999994e110 < j < 1.5500000000000001e263

   1. Initial program 18.2%

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

   3. Simplified 18.2%

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

   5. Taylor expanded in j around inf 64.1%

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

      1. +-commutative 64.1%

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

      2. mul-1-neg 64.1%

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

      3. unsub-neg 64.1%

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

      4. *-commutative 64.1%

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

   7. Simplified 64.1%

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

   if 1.5500000000000001e263 < j

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in y4 around inf 82.7%

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

   6. Taylor expanded in b around inf 90.9%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.3 \cdot 10^{+258}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - i \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -1.4 \cdot 10^{+127}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -2.05 \cdot 10^{+93}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -3.4 \cdot 10^{-218}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{-259}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right) - i \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.25 \cdot 10^{-65}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{+110}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;j \leq 1.55 \cdot 10^{+263}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 35.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot y5 - c \cdot y4\\ t_2 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_3 := b \cdot y4 - i \cdot y5\\ t_4 := t \cdot \left(\left(j \cdot t\_3 + c \cdot \left(z \cdot i\right)\right) + y2 \cdot t\_1\right)\\ t_5 := y1 \cdot y4 - y0 \cdot y5\\ \mathbf{if}\;y5 \leq -2.9 \cdot 10^{+249}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -5 \cdot 10^{+141}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y5 \leq -6.8 \cdot 10^{+53}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y5 \leq -2 \cdot 10^{-52}:\\ \;\;\;\;\left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1\right)\\ \mathbf{elif}\;y5 \leq -1.32 \cdot 10^{-101}:\\ \;\;\;\;y2 \cdot \left(k \cdot t\_5 + t \cdot t\_1\right)\\ \mathbf{elif}\;y5 \leq -4.5 \cdot 10^{-190}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;y5 \leq 1.9 \cdot 10^{-229}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y5 \leq 5.5 \cdot 10^{-33}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot t\_5 - y \cdot t\_3\right) - i \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y5 \leq 3 \cdot 10^{+137}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a y5) (* c y4)))
        (t_2
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j))))))
        (t_3 (- (* b y4) (* i y5)))
        (t_4 (* t (+ (+ (* j t_3) (* c (* z i))) (* y2 t_1))))
        (t_5 (- (* y1 y4) (* y0 y5))))
   (if (<= y5 -2.9e+249)
     (* y3 (+ (* y (- (* c y4) (* a y5))) (* j (- (* y0 y5) (* y1 y4)))))
     (if (<= y5 -5e+141)
       t_4
       (if (<= y5 -6.8e+53)
         t_2
         (if (<= y5 -2e-52)
           (* (- (* x j) (* z k)) (* i y1))
           (if (<= y5 -1.32e-101)
             (* y2 (+ (* k t_5) (* t t_1)))
             (if (<= y5 -4.5e-190)
               (* y1 (* z (- (* a y3) (* i k))))
               (if (<= y5 1.9e-229)
                 t_2
                 (if (<= y5 5.5e-33)
                   (* k (- (- (* y2 t_5) (* y t_3)) (* i (* z y1))))
                   (if (<= y5 3e+137)
                     t_4
                     (* y (* y5 (- (* i k) (* a y3)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y5) - (c * y4);
	double t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_3 = (b * y4) - (i * y5);
	double t_4 = t * (((j * t_3) + (c * (z * i))) + (y2 * t_1));
	double t_5 = (y1 * y4) - (y0 * y5);
	double tmp;
	if (y5 <= -2.9e+249) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	} else if (y5 <= -5e+141) {
		tmp = t_4;
	} else if (y5 <= -6.8e+53) {
		tmp = t_2;
	} else if (y5 <= -2e-52) {
		tmp = ((x * j) - (z * k)) * (i * y1);
	} else if (y5 <= -1.32e-101) {
		tmp = y2 * ((k * t_5) + (t * t_1));
	} else if (y5 <= -4.5e-190) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (y5 <= 1.9e-229) {
		tmp = t_2;
	} else if (y5 <= 5.5e-33) {
		tmp = k * (((y2 * t_5) - (y * t_3)) - (i * (z * y1)));
	} else if (y5 <= 3e+137) {
		tmp = t_4;
	} else {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (a * y5) - (c * y4)
    t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    t_3 = (b * y4) - (i * y5)
    t_4 = t * (((j * t_3) + (c * (z * i))) + (y2 * t_1))
    t_5 = (y1 * y4) - (y0 * y5)
    if (y5 <= (-2.9d+249)) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))))
    else if (y5 <= (-5d+141)) then
        tmp = t_4
    else if (y5 <= (-6.8d+53)) then
        tmp = t_2
    else if (y5 <= (-2d-52)) then
        tmp = ((x * j) - (z * k)) * (i * y1)
    else if (y5 <= (-1.32d-101)) then
        tmp = y2 * ((k * t_5) + (t * t_1))
    else if (y5 <= (-4.5d-190)) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (y5 <= 1.9d-229) then
        tmp = t_2
    else if (y5 <= 5.5d-33) then
        tmp = k * (((y2 * t_5) - (y * t_3)) - (i * (z * y1)))
    else if (y5 <= 3d+137) then
        tmp = t_4
    else
        tmp = y * (y5 * ((i * k) - (a * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y5) - (c * y4);
	double t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_3 = (b * y4) - (i * y5);
	double t_4 = t * (((j * t_3) + (c * (z * i))) + (y2 * t_1));
	double t_5 = (y1 * y4) - (y0 * y5);
	double tmp;
	if (y5 <= -2.9e+249) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	} else if (y5 <= -5e+141) {
		tmp = t_4;
	} else if (y5 <= -6.8e+53) {
		tmp = t_2;
	} else if (y5 <= -2e-52) {
		tmp = ((x * j) - (z * k)) * (i * y1);
	} else if (y5 <= -1.32e-101) {
		tmp = y2 * ((k * t_5) + (t * t_1));
	} else if (y5 <= -4.5e-190) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (y5 <= 1.9e-229) {
		tmp = t_2;
	} else if (y5 <= 5.5e-33) {
		tmp = k * (((y2 * t_5) - (y * t_3)) - (i * (z * y1)));
	} else if (y5 <= 3e+137) {
		tmp = t_4;
	} else {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (a * y5) - (c * y4)
	t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	t_3 = (b * y4) - (i * y5)
	t_4 = t * (((j * t_3) + (c * (z * i))) + (y2 * t_1))
	t_5 = (y1 * y4) - (y0 * y5)
	tmp = 0
	if y5 <= -2.9e+249:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))))
	elif y5 <= -5e+141:
		tmp = t_4
	elif y5 <= -6.8e+53:
		tmp = t_2
	elif y5 <= -2e-52:
		tmp = ((x * j) - (z * k)) * (i * y1)
	elif y5 <= -1.32e-101:
		tmp = y2 * ((k * t_5) + (t * t_1))
	elif y5 <= -4.5e-190:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif y5 <= 1.9e-229:
		tmp = t_2
	elif y5 <= 5.5e-33:
		tmp = k * (((y2 * t_5) - (y * t_3)) - (i * (z * y1)))
	elif y5 <= 3e+137:
		tmp = t_4
	else:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(a * y5) - Float64(c * y4))
	t_2 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	t_3 = Float64(Float64(b * y4) - Float64(i * y5))
	t_4 = Float64(t * Float64(Float64(Float64(j * t_3) + Float64(c * Float64(z * i))) + Float64(y2 * t_1)))
	t_5 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	tmp = 0.0
	if (y5 <= -2.9e+249)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4)))));
	elseif (y5 <= -5e+141)
		tmp = t_4;
	elseif (y5 <= -6.8e+53)
		tmp = t_2;
	elseif (y5 <= -2e-52)
		tmp = Float64(Float64(Float64(x * j) - Float64(z * k)) * Float64(i * y1));
	elseif (y5 <= -1.32e-101)
		tmp = Float64(y2 * Float64(Float64(k * t_5) + Float64(t * t_1)));
	elseif (y5 <= -4.5e-190)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (y5 <= 1.9e-229)
		tmp = t_2;
	elseif (y5 <= 5.5e-33)
		tmp = Float64(k * Float64(Float64(Float64(y2 * t_5) - Float64(y * t_3)) - Float64(i * Float64(z * y1))));
	elseif (y5 <= 3e+137)
		tmp = t_4;
	else
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (a * y5) - (c * y4);
	t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	t_3 = (b * y4) - (i * y5);
	t_4 = t * (((j * t_3) + (c * (z * i))) + (y2 * t_1));
	t_5 = (y1 * y4) - (y0 * y5);
	tmp = 0.0;
	if (y5 <= -2.9e+249)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	elseif (y5 <= -5e+141)
		tmp = t_4;
	elseif (y5 <= -6.8e+53)
		tmp = t_2;
	elseif (y5 <= -2e-52)
		tmp = ((x * j) - (z * k)) * (i * y1);
	elseif (y5 <= -1.32e-101)
		tmp = y2 * ((k * t_5) + (t * t_1));
	elseif (y5 <= -4.5e-190)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (y5 <= 1.9e-229)
		tmp = t_2;
	elseif (y5 <= 5.5e-33)
		tmp = k * (((y2 * t_5) - (y * t_3)) - (i * (z * y1)));
	elseif (y5 <= 3e+137)
		tmp = t_4;
	else
		tmp = y * (y5 * ((i * k) - (a * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t * N[(N[(N[(j * t$95$3), $MachinePrecision] + N[(c * N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -2.9e+249], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -5e+141], t$95$4, If[LessEqual[y5, -6.8e+53], t$95$2, If[LessEqual[y5, -2e-52], N[(N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision] * N[(i * y1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.32e-101], N[(y2 * N[(N[(k * t$95$5), $MachinePrecision] + N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -4.5e-190], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.9e-229], t$95$2, If[LessEqual[y5, 5.5e-33], N[(k * N[(N[(N[(y2 * t$95$5), $MachinePrecision] - N[(y * t$95$3), $MachinePrecision]), $MachinePrecision] - N[(i * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3e+137], t$95$4, N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y5 < -2.90000000000000017e249

   1. Initial program 18.2%

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

   3. Simplified 18.2%

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

   5. Taylor expanded in i around -inf 18.2%

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

      1. mul-1-neg 18.2%

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

      2. *-commutative 18.2%

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

      3. *-commutative 18.2%

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

   7. Simplified 18.2%

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

   8. Taylor expanded in y3 around -inf 81.8%

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

   if -2.90000000000000017e249 < y5 < -5.00000000000000025e141 or 5.5e-33 < y5 < 3.0000000000000001e137

   1. Initial program 27.0%

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

   3. Simplified 27.0%

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

   5. Taylor expanded in i around -inf 36.8%

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

      1. mul-1-neg 36.8%

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

      2. *-commutative 36.8%

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

      3. *-commutative 36.8%

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

   7. Simplified 36.8%

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

   8. Taylor expanded in t around inf 65.9%

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

      1. associate--r+ 65.9%

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

      2. mul-1-neg 65.9%

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

   10. Simplified 65.9%

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

   if -5.00000000000000025e141 < y5 < -6.79999999999999995e53 or -4.50000000000000021e-190 < y5 < 1.9000000000000001e-229

   1. Initial program 42.2%

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

   3. Simplified 42.2%

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

   5. Taylor expanded in b around inf 68.4%

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

   if -6.79999999999999995e53 < y5 < -2e-52

   1. Initial program 30.8%

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

   3. Simplified 30.8%

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

   5. Taylor expanded in y1 around inf 61.8%

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

      1. +-commutative 61.8%

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

      2. mul-1-neg 61.8%

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

      3. unsub-neg 61.8%

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

      4. *-commutative 61.8%

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

      5. *-commutative 61.8%

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

      6. *-commutative 61.8%

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

      7. mul-1-neg 61.8%

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

      8. *-commutative 61.8%

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

   7. Simplified 61.8%

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

   8. Taylor expanded in i around inf 77.2%

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

      1. associate-*r* 69.5%

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

   10. Simplified 69.5%

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

   if -2e-52 < y5 < -1.32e-101

   1. Initial program 15.4%

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

   3. Simplified 15.4%

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

   5. Taylor expanded in i around -inf 15.4%

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

      1. mul-1-neg 15.4%

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

      2. *-commutative 15.4%

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

      3. *-commutative 15.4%

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

   7. Simplified 15.4%

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

   8. Taylor expanded in y2 around inf 69.4%

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

   if -1.32e-101 < y5 < -4.50000000000000021e-190

   1. Initial program 47.6%

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

   3. Simplified 47.6%

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

   5. Taylor expanded in y1 around inf 39.7%

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

      1. +-commutative 39.7%

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

      2. mul-1-neg 39.7%

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

      3. unsub-neg 39.7%

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

      4. *-commutative 39.7%

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

      5. *-commutative 39.7%

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

      6. *-commutative 39.7%

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

      7. mul-1-neg 39.7%

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

      8. *-commutative 39.7%

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

   7. Simplified 39.7%

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

   8. Taylor expanded in z around -inf 53.4%

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

      1. mul-1-neg 53.4%

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

   10. Simplified 53.4%

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

   if 1.9000000000000001e-229 < y5 < 5.5e-33

   1. Initial program 17.6%

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

   3. Simplified 17.6%

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

   5. Taylor expanded in i around -inf 17.9%

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

      1. mul-1-neg 17.9%

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

      2. *-commutative 17.9%

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

      3. *-commutative 17.9%

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

   7. Simplified 17.9%

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

   8. Taylor expanded in k around inf 47.5%

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

   if 3.0000000000000001e137 < y5

   1. Initial program 9.2%

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

   3. Simplified 9.2%

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

   5. Taylor expanded in i around -inf 15.8%

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

      1. mul-1-neg 15.8%

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

      2. *-commutative 15.8%

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

      3. *-commutative 15.8%

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

   7. Simplified 15.8%

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

   8. Taylor expanded in y around inf 45.2%

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

      1. associate-*r* 45.2%

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

      2. neg-mul-1 45.2%

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

      3. mul-1-neg 45.2%

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

   10. Simplified 45.2%

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

   11. Taylor expanded in y5 around inf 58.8%

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

       1. +-commutative 58.8%

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

       2. mul-1-neg 58.8%

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

       3. unsub-neg 58.8%

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

       4. *-commutative 58.8%

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

       5. *-commutative 58.8%

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

   13. Simplified 58.8%

       \[\leadsto y \cdot \color{blue}{\left(y5 \cdot \left(k \cdot i - y3 \cdot a\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2.9 \cdot 10^{+249}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -5 \cdot 10^{+141}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + c \cdot \left(z \cdot i\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -6.8 \cdot 10^{+53}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -2 \cdot 10^{-52}:\\ \;\;\;\;\left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1\right)\\ \mathbf{elif}\;y5 \leq -1.32 \cdot 10^{-101}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -4.5 \cdot 10^{-190}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;y5 \leq 1.9 \cdot 10^{-229}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 5.5 \cdot 10^{-33}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - i \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y5 \leq 3 \cdot 10^{+137}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + c \cdot \left(z \cdot i\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 37.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot y5 - y1 \cdot y4\\ t_2 := a \cdot y5 - c \cdot y4\\ t_3 := z \cdot k - x \cdot j\\ t_4 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot t\_3\right)\\ t_5 := y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot t\_1\right)\\ t_6 := b \cdot y4 - i \cdot y5\\ \mathbf{if}\;y1 \leq -1.95 \cdot 10^{+133}:\\ \;\;\;\;\left(z \cdot y1\right) \cdot \left(a \cdot y3 - i \cdot k\right)\\ \mathbf{elif}\;y1 \leq -2.85 \cdot 10^{+88}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot t\_3\right)\\ \mathbf{elif}\;y1 \leq -1.65 \cdot 10^{+78}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot t\_2\right)\\ \mathbf{elif}\;y1 \leq -4.5 \cdot 10^{-54}:\\ \;\;\;\;j \cdot \left(\left(t \cdot t\_6 + y3 \cdot t\_1\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq -5 \cdot 10^{-184}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y1 \leq 3 \cdot 10^{-228}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y1 \leq 6.6 \cdot 10^{-129}:\\ \;\;\;\;t \cdot \left(\left(j \cdot t\_6 + c \cdot \left(z \cdot i\right)\right) + y2 \cdot t\_2\right)\\ \mathbf{elif}\;y1 \leq 2.7 \cdot 10^{+153}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y0 y5) (* y1 y4)))
        (t_2 (- (* a y5) (* c y4)))
        (t_3 (- (* z k) (* x j)))
        (t_4
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 t_3))))
        (t_5 (* y3 (+ (* y (- (* c y4) (* a y5))) (* j t_1))))
        (t_6 (- (* b y4) (* i y5))))
   (if (<= y1 -1.95e+133)
     (* (* z y1) (- (* a y3) (* i k)))
     (if (<= y1 -2.85e+88)
       (*
        y0
        (+
         (+ (* c (- (* x y2) (* z y3))) (* y5 (- (* j y3) (* k y2))))
         (* b t_3)))
       (if (<= y1 -1.65e+78)
         (* y2 (+ (* k (- (* y1 y4) (* y0 y5))) (* t t_2)))
         (if (<= y1 -4.5e-54)
           (* j (+ (+ (* t t_6) (* y3 t_1)) (* x (- (* i y1) (* b y0)))))
           (if (<= y1 -5e-184)
             t_5
             (if (<= y1 3e-228)
               t_4
               (if (<= y1 6.6e-129)
                 (* t (+ (+ (* j t_6) (* c (* z i))) (* y2 t_2)))
                 (if (<= y1 2.7e+153) t_4 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 = (y0 * y5) - (y1 * y4);
	double t_2 = (a * y5) - (c * y4);
	double t_3 = (z * k) - (x * j);
	double t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * t_3));
	double t_5 = y3 * ((y * ((c * y4) - (a * y5))) + (j * t_1));
	double t_6 = (b * y4) - (i * y5);
	double tmp;
	if (y1 <= -1.95e+133) {
		tmp = (z * y1) * ((a * y3) - (i * k));
	} else if (y1 <= -2.85e+88) {
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * t_3));
	} else if (y1 <= -1.65e+78) {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + (t * t_2));
	} else if (y1 <= -4.5e-54) {
		tmp = j * (((t * t_6) + (y3 * t_1)) + (x * ((i * y1) - (b * y0))));
	} else if (y1 <= -5e-184) {
		tmp = t_5;
	} else if (y1 <= 3e-228) {
		tmp = t_4;
	} else if (y1 <= 6.6e-129) {
		tmp = t * (((j * t_6) + (c * (z * i))) + (y2 * t_2));
	} else if (y1 <= 2.7e+153) {
		tmp = t_4;
	} else {
		tmp = 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_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = (y0 * y5) - (y1 * y4)
    t_2 = (a * y5) - (c * y4)
    t_3 = (z * k) - (x * j)
    t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * t_3))
    t_5 = y3 * ((y * ((c * y4) - (a * y5))) + (j * t_1))
    t_6 = (b * y4) - (i * y5)
    if (y1 <= (-1.95d+133)) then
        tmp = (z * y1) * ((a * y3) - (i * k))
    else if (y1 <= (-2.85d+88)) then
        tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * t_3))
    else if (y1 <= (-1.65d+78)) then
        tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + (t * t_2))
    else if (y1 <= (-4.5d-54)) then
        tmp = j * (((t * t_6) + (y3 * t_1)) + (x * ((i * y1) - (b * y0))))
    else if (y1 <= (-5d-184)) then
        tmp = t_5
    else if (y1 <= 3d-228) then
        tmp = t_4
    else if (y1 <= 6.6d-129) then
        tmp = t * (((j * t_6) + (c * (z * i))) + (y2 * t_2))
    else if (y1 <= 2.7d+153) then
        tmp = t_4
    else
        tmp = 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 = (y0 * y5) - (y1 * y4);
	double t_2 = (a * y5) - (c * y4);
	double t_3 = (z * k) - (x * j);
	double t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * t_3));
	double t_5 = y3 * ((y * ((c * y4) - (a * y5))) + (j * t_1));
	double t_6 = (b * y4) - (i * y5);
	double tmp;
	if (y1 <= -1.95e+133) {
		tmp = (z * y1) * ((a * y3) - (i * k));
	} else if (y1 <= -2.85e+88) {
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * t_3));
	} else if (y1 <= -1.65e+78) {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + (t * t_2));
	} else if (y1 <= -4.5e-54) {
		tmp = j * (((t * t_6) + (y3 * t_1)) + (x * ((i * y1) - (b * y0))));
	} else if (y1 <= -5e-184) {
		tmp = t_5;
	} else if (y1 <= 3e-228) {
		tmp = t_4;
	} else if (y1 <= 6.6e-129) {
		tmp = t * (((j * t_6) + (c * (z * i))) + (y2 * t_2));
	} else if (y1 <= 2.7e+153) {
		tmp = t_4;
	} else {
		tmp = 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 = (y0 * y5) - (y1 * y4)
	t_2 = (a * y5) - (c * y4)
	t_3 = (z * k) - (x * j)
	t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * t_3))
	t_5 = y3 * ((y * ((c * y4) - (a * y5))) + (j * t_1))
	t_6 = (b * y4) - (i * y5)
	tmp = 0
	if y1 <= -1.95e+133:
		tmp = (z * y1) * ((a * y3) - (i * k))
	elif y1 <= -2.85e+88:
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * t_3))
	elif y1 <= -1.65e+78:
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + (t * t_2))
	elif y1 <= -4.5e-54:
		tmp = j * (((t * t_6) + (y3 * t_1)) + (x * ((i * y1) - (b * y0))))
	elif y1 <= -5e-184:
		tmp = t_5
	elif y1 <= 3e-228:
		tmp = t_4
	elif y1 <= 6.6e-129:
		tmp = t * (((j * t_6) + (c * (z * i))) + (y2 * t_2))
	elif y1 <= 2.7e+153:
		tmp = t_4
	else:
		tmp = 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(y0 * y5) - Float64(y1 * y4))
	t_2 = Float64(Float64(a * y5) - Float64(c * y4))
	t_3 = Float64(Float64(z * k) - Float64(x * j))
	t_4 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * t_3)))
	t_5 = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(j * t_1)))
	t_6 = Float64(Float64(b * y4) - Float64(i * y5))
	tmp = 0.0
	if (y1 <= -1.95e+133)
		tmp = Float64(Float64(z * y1) * Float64(Float64(a * y3) - Float64(i * k)));
	elseif (y1 <= -2.85e+88)
		tmp = Float64(y0 * Float64(Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2)))) + Float64(b * t_3)));
	elseif (y1 <= -1.65e+78)
		tmp = Float64(y2 * Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(t * t_2)));
	elseif (y1 <= -4.5e-54)
		tmp = Float64(j * Float64(Float64(Float64(t * t_6) + Float64(y3 * t_1)) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y1 <= -5e-184)
		tmp = t_5;
	elseif (y1 <= 3e-228)
		tmp = t_4;
	elseif (y1 <= 6.6e-129)
		tmp = Float64(t * Float64(Float64(Float64(j * t_6) + Float64(c * Float64(z * i))) + Float64(y2 * t_2)));
	elseif (y1 <= 2.7e+153)
		tmp = t_4;
	else
		tmp = 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 = (y0 * y5) - (y1 * y4);
	t_2 = (a * y5) - (c * y4);
	t_3 = (z * k) - (x * j);
	t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * t_3));
	t_5 = y3 * ((y * ((c * y4) - (a * y5))) + (j * t_1));
	t_6 = (b * y4) - (i * y5);
	tmp = 0.0;
	if (y1 <= -1.95e+133)
		tmp = (z * y1) * ((a * y3) - (i * k));
	elseif (y1 <= -2.85e+88)
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * t_3));
	elseif (y1 <= -1.65e+78)
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + (t * t_2));
	elseif (y1 <= -4.5e-54)
		tmp = j * (((t * t_6) + (y3 * t_1)) + (x * ((i * y1) - (b * y0))));
	elseif (y1 <= -5e-184)
		tmp = t_5;
	elseif (y1 <= 3e-228)
		tmp = t_4;
	elseif (y1 <= 6.6e-129)
		tmp = t * (((j * t_6) + (c * (z * i))) + (y2 * t_2));
	elseif (y1 <= 2.7e+153)
		tmp = t_4;
	else
		tmp = 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[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -1.95e+133], N[(N[(z * y1), $MachinePrecision] * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.85e+88], N[(y0 * N[(N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.65e+78], N[(y2 * N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -4.5e-54], N[(j * N[(N[(N[(t * t$95$6), $MachinePrecision] + N[(y3 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -5e-184], t$95$5, If[LessEqual[y1, 3e-228], t$95$4, If[LessEqual[y1, 6.6e-129], N[(t * N[(N[(N[(j * t$95$6), $MachinePrecision] + N[(c * N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.7e+153], t$95$4, t$95$5]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y1 < -1.95000000000000007e133

   1. Initial program 16.8%

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

   3. Simplified 16.8%

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

   5. Taylor expanded in y1 around inf 64.2%

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

      1. +-commutative 64.2%

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

      2. mul-1-neg 64.2%

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

      3. unsub-neg 64.2%

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

      4. *-commutative 64.2%

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

      5. *-commutative 64.2%

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

      6. *-commutative 64.2%

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

      7. mul-1-neg 64.2%

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

      8. *-commutative 64.2%

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

   7. Simplified 64.2%

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

   8. Taylor expanded in z around -inf 56.0%

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

      1. mul-1-neg 56.0%

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

      2. associate-*r* 56.0%

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

   10. Simplified 56.0%

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

   if -1.95000000000000007e133 < y1 < -2.85000000000000011e88

   1. Initial program 44.4%

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

   3. Simplified 44.4%

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

   5. Taylor expanded in y0 around inf 88.9%

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

      1. +-commutative 88.9%

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

      2. mul-1-neg 88.9%

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

      3. unsub-neg 88.9%

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

      4. *-commutative 88.9%

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

      5. *-commutative 88.9%

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

      6. *-commutative 88.9%

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

      7. *-commutative 88.9%

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

   7. Simplified 88.9%

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

   if -2.85000000000000011e88 < y1 < -1.65e78

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in i around -inf 50.0%

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

      1. mul-1-neg 50.0%

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

      2. *-commutative 50.0%

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

      3. *-commutative 50.0%

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

   7. Simplified 50.0%

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

   8. Taylor expanded in y2 around inf 100.0%

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

   if -1.65e78 < y1 < -4.4999999999999998e-54

   1. Initial program 33.2%

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

   3. Simplified 33.2%

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

   5. Taylor expanded in j around inf 62.8%

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

      1. +-commutative 62.8%

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

      2. mul-1-neg 62.8%

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

      3. unsub-neg 62.8%

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

      4. *-commutative 62.8%

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

   7. Simplified 62.8%

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

   if -4.4999999999999998e-54 < y1 < -5.00000000000000003e-184 or 2.7000000000000001e153 < y1

   1. Initial program 20.3%

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

   3. Simplified 20.3%

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

   5. Taylor expanded in i around -inf 26.8%

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

      1. mul-1-neg 26.8%

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

      2. *-commutative 26.8%

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

      3. *-commutative 26.8%

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

   7. Simplified 26.8%

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

   8. Taylor expanded in y3 around -inf 54.9%

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

   if -5.00000000000000003e-184 < y1 < 3e-228 or 6.59999999999999977e-129 < y1 < 2.7000000000000001e153

   1. Initial program 29.6%

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

   3. Simplified 29.6%

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

   5. Taylor expanded in b around inf 53.7%

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

   if 3e-228 < y1 < 6.59999999999999977e-129

   1. Initial program 40.0%

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

   3. Simplified 40.0%

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

   5. Taylor expanded in i around -inf 40.0%

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

      1. mul-1-neg 40.0%

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

      2. *-commutative 40.0%

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

      3. *-commutative 40.0%

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

   7. Simplified 40.0%

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

   8. Taylor expanded in t around inf 60.6%

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

      1. associate--r+ 60.6%

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

      2. mul-1-neg 60.6%

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

   10. Simplified 60.6%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.95 \cdot 10^{+133}:\\ \;\;\;\;\left(z \cdot y1\right) \cdot \left(a \cdot y3 - i \cdot k\right)\\ \mathbf{elif}\;y1 \leq -2.85 \cdot 10^{+88}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq -1.65 \cdot 10^{+78}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -4.5 \cdot 10^{-54}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq -5 \cdot 10^{-184}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 3 \cdot 10^{-228}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 6.6 \cdot 10^{-129}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + c \cdot \left(z \cdot i\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 2.7 \cdot 10^{+153}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 29.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ t_2 := b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ t_3 := y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{if}\;j \leq -3.2 \cdot 10^{+171}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -1.95 \cdot 10^{+148}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -26:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -1.5 \cdot 10^{-222}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -9.8 \cdot 10^{-292}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 5.3 \cdot 10^{-252}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{-99}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{+99}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (* y3 (+ (* y (- (* c y4) (* a y5))) (* j (- (* y0 y5) (* y1 y4))))))
        (t_2 (* b (* a (- (* x y) (* z t)))))
        (t_3 (* y2 (* y4 (- (* k y1) (* t c))))))
   (if (<= j -3.2e+171)
     (* y0 (* y2 (- (* x c) (* k y5))))
     (if (<= j -1.95e+148)
       t_2
       (if (<= j -26.0)
         (* b (* x (- (* y a) (* j y0))))
         (if (<= j -1.5e-222)
           t_3
           (if (<= j -9.8e-292)
             t_1
             (if (<= j 5.3e-252)
               t_3
               (if (<= j 4.2e-99)
                 t_2
                 (if (<= j 3.7e+99)
                   (* y1 (* z (- (* a y3) (* i k))))
                   t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	double t_2 = b * (a * ((x * y) - (z * t)));
	double t_3 = y2 * (y4 * ((k * y1) - (t * c)));
	double tmp;
	if (j <= -3.2e+171) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (j <= -1.95e+148) {
		tmp = t_2;
	} else if (j <= -26.0) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (j <= -1.5e-222) {
		tmp = t_3;
	} else if (j <= -9.8e-292) {
		tmp = t_1;
	} else if (j <= 5.3e-252) {
		tmp = t_3;
	} else if (j <= 4.2e-99) {
		tmp = t_2;
	} else if (j <= 3.7e+99) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))))
    t_2 = b * (a * ((x * y) - (z * t)))
    t_3 = y2 * (y4 * ((k * y1) - (t * c)))
    if (j <= (-3.2d+171)) then
        tmp = y0 * (y2 * ((x * c) - (k * y5)))
    else if (j <= (-1.95d+148)) then
        tmp = t_2
    else if (j <= (-26.0d0)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (j <= (-1.5d-222)) then
        tmp = t_3
    else if (j <= (-9.8d-292)) then
        tmp = t_1
    else if (j <= 5.3d-252) then
        tmp = t_3
    else if (j <= 4.2d-99) then
        tmp = t_2
    else if (j <= 3.7d+99) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	double t_2 = b * (a * ((x * y) - (z * t)));
	double t_3 = y2 * (y4 * ((k * y1) - (t * c)));
	double tmp;
	if (j <= -3.2e+171) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (j <= -1.95e+148) {
		tmp = t_2;
	} else if (j <= -26.0) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (j <= -1.5e-222) {
		tmp = t_3;
	} else if (j <= -9.8e-292) {
		tmp = t_1;
	} else if (j <= 5.3e-252) {
		tmp = t_3;
	} else if (j <= 4.2e-99) {
		tmp = t_2;
	} else if (j <= 3.7e+99) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))))
	t_2 = b * (a * ((x * y) - (z * t)))
	t_3 = y2 * (y4 * ((k * y1) - (t * c)))
	tmp = 0
	if j <= -3.2e+171:
		tmp = y0 * (y2 * ((x * c) - (k * y5)))
	elif j <= -1.95e+148:
		tmp = t_2
	elif j <= -26.0:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif j <= -1.5e-222:
		tmp = t_3
	elif j <= -9.8e-292:
		tmp = t_1
	elif j <= 5.3e-252:
		tmp = t_3
	elif j <= 4.2e-99:
		tmp = t_2
	elif j <= 3.7e+99:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4)))))
	t_2 = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))))
	t_3 = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))))
	tmp = 0.0
	if (j <= -3.2e+171)
		tmp = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))));
	elseif (j <= -1.95e+148)
		tmp = t_2;
	elseif (j <= -26.0)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (j <= -1.5e-222)
		tmp = t_3;
	elseif (j <= -9.8e-292)
		tmp = t_1;
	elseif (j <= 5.3e-252)
		tmp = t_3;
	elseif (j <= 4.2e-99)
		tmp = t_2;
	elseif (j <= 3.7e+99)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	t_2 = b * (a * ((x * y) - (z * t)));
	t_3 = y2 * (y4 * ((k * y1) - (t * c)));
	tmp = 0.0;
	if (j <= -3.2e+171)
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	elseif (j <= -1.95e+148)
		tmp = t_2;
	elseif (j <= -26.0)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (j <= -1.5e-222)
		tmp = t_3;
	elseif (j <= -9.8e-292)
		tmp = t_1;
	elseif (j <= 5.3e-252)
		tmp = t_3;
	elseif (j <= 4.2e-99)
		tmp = t_2;
	elseif (j <= 3.7e+99)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.2e+171], N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.95e+148], t$95$2, If[LessEqual[j, -26.0], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.5e-222], t$95$3, If[LessEqual[j, -9.8e-292], t$95$1, If[LessEqual[j, 5.3e-252], t$95$3, If[LessEqual[j, 4.2e-99], t$95$2, If[LessEqual[j, 3.7e+99], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -3.20000000000000011e171

   1. Initial program 17.4%

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

   3. Simplified 17.4%

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

   5. Taylor expanded in y0 around inf 44.1%

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

      1. +-commutative 44.1%

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

      2. mul-1-neg 44.1%

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

      3. unsub-neg 44.1%

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

      4. *-commutative 44.1%

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

      5. *-commutative 44.1%

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

      6. *-commutative 44.1%

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

      7. *-commutative 44.1%

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

   7. Simplified 44.1%

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

   8. Taylor expanded in y2 around inf 57.0%

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

   if -3.20000000000000011e171 < j < -1.95000000000000001e148 or 5.30000000000000022e-252 < j < 4.19999999999999968e-99

   1. Initial program 32.7%

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

   3. Simplified 32.7%

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

   5. Taylor expanded in b around inf 56.2%

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

   6. Taylor expanded in a around inf 56.2%

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

   if -1.95000000000000001e148 < j < -26

   1. Initial program 19.3%

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

   3. Simplified 19.3%

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

   5. Taylor expanded in b around inf 32.9%

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

   6. Taylor expanded in x around inf 46.5%

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

   if -26 < j < -1.50000000000000015e-222 or -9.7999999999999992e-292 < j < 5.30000000000000022e-252

   1. Initial program 29.3%

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

   3. Simplified 29.3%

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

   5. Taylor expanded in y4 around inf 58.2%

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

   6. Taylor expanded in y2 around inf 59.7%

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

   if -1.50000000000000015e-222 < j < -9.7999999999999992e-292 or 3.7000000000000001e99 < j

   1. Initial program 19.1%

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

   3. Simplified 19.1%

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

   5. Taylor expanded in i around -inf 30.5%

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

      1. mul-1-neg 30.5%

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

      2. *-commutative 30.5%

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

      3. *-commutative 30.5%

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

   7. Simplified 30.5%

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

   8. Taylor expanded in y3 around -inf 59.3%

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

   if 4.19999999999999968e-99 < j < 3.7000000000000001e99

   1. Initial program 36.5%

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

   3. Simplified 36.5%

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

   5. Taylor expanded in y1 around inf 42.2%

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

      1. +-commutative 42.2%

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

      2. mul-1-neg 42.2%

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

      3. unsub-neg 42.2%

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

      4. *-commutative 42.2%

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

      5. *-commutative 42.2%

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

      6. *-commutative 42.2%

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

      7. mul-1-neg 42.2%

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

      8. *-commutative 42.2%

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

   7. Simplified 42.2%

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

   8. Taylor expanded in z around -inf 49.9%

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

      1. mul-1-neg 49.9%

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

   10. Simplified 49.9%

       \[\leadsto y1 \cdot \color{blue}{\left(-z \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.2 \cdot 10^{+171}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -1.95 \cdot 10^{+148}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq -26:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -1.5 \cdot 10^{-222}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq -9.8 \cdot 10^{-292}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 5.3 \cdot 10^{-252}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{-99}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{+99}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_2 := b \cdot y4 - i \cdot y5\\ t_3 := y0 \cdot y5 - y1 \cdot y4\\ t_4 := y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot t\_3\right)\\ \mathbf{if}\;y1 \leq -5.6 \cdot 10^{+77}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -1.25 \cdot 10^{-53}:\\ \;\;\;\;j \cdot \left(\left(t \cdot t\_2 + y3 \cdot t\_3\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq -3.8 \cdot 10^{-191}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y1 \leq 1.95 \cdot 10^{-227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq 2.7 \cdot 10^{-128}:\\ \;\;\;\;t \cdot \left(\left(j \cdot t\_2 + c \cdot \left(z \cdot i\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 2.45 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j))))))
        (t_2 (- (* b y4) (* i y5)))
        (t_3 (- (* y0 y5) (* y1 y4)))
        (t_4 (* y3 (+ (* y (- (* c y4) (* a y5))) (* j t_3)))))
   (if (<= y1 -5.6e+77)
     (* y1 (* a (- (* z y3) (* x y2))))
     (if (<= y1 -1.25e-53)
       (* j (+ (+ (* t t_2) (* y3 t_3)) (* x (- (* i y1) (* b y0)))))
       (if (<= y1 -3.8e-191)
         t_4
         (if (<= y1 1.95e-227)
           t_1
           (if (<= y1 2.7e-128)
             (* t (+ (+ (* j t_2) (* c (* z i))) (* y2 (- (* a y5) (* c y4)))))
             (if (<= y1 2.45e+153) t_1 t_4))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_2 = (b * y4) - (i * y5);
	double t_3 = (y0 * y5) - (y1 * y4);
	double t_4 = y3 * ((y * ((c * y4) - (a * y5))) + (j * t_3));
	double tmp;
	if (y1 <= -5.6e+77) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (y1 <= -1.25e-53) {
		tmp = j * (((t * t_2) + (y3 * t_3)) + (x * ((i * y1) - (b * y0))));
	} else if (y1 <= -3.8e-191) {
		tmp = t_4;
	} else if (y1 <= 1.95e-227) {
		tmp = t_1;
	} else if (y1 <= 2.7e-128) {
		tmp = t * (((j * t_2) + (c * (z * i))) + (y2 * ((a * y5) - (c * y4))));
	} else if (y1 <= 2.45e+153) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    t_2 = (b * y4) - (i * y5)
    t_3 = (y0 * y5) - (y1 * y4)
    t_4 = y3 * ((y * ((c * y4) - (a * y5))) + (j * t_3))
    if (y1 <= (-5.6d+77)) then
        tmp = y1 * (a * ((z * y3) - (x * y2)))
    else if (y1 <= (-1.25d-53)) then
        tmp = j * (((t * t_2) + (y3 * t_3)) + (x * ((i * y1) - (b * y0))))
    else if (y1 <= (-3.8d-191)) then
        tmp = t_4
    else if (y1 <= 1.95d-227) then
        tmp = t_1
    else if (y1 <= 2.7d-128) then
        tmp = t * (((j * t_2) + (c * (z * i))) + (y2 * ((a * y5) - (c * y4))))
    else if (y1 <= 2.45d+153) then
        tmp = t_1
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_2 = (b * y4) - (i * y5);
	double t_3 = (y0 * y5) - (y1 * y4);
	double t_4 = y3 * ((y * ((c * y4) - (a * y5))) + (j * t_3));
	double tmp;
	if (y1 <= -5.6e+77) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (y1 <= -1.25e-53) {
		tmp = j * (((t * t_2) + (y3 * t_3)) + (x * ((i * y1) - (b * y0))));
	} else if (y1 <= -3.8e-191) {
		tmp = t_4;
	} else if (y1 <= 1.95e-227) {
		tmp = t_1;
	} else if (y1 <= 2.7e-128) {
		tmp = t * (((j * t_2) + (c * (z * i))) + (y2 * ((a * y5) - (c * y4))));
	} else if (y1 <= 2.45e+153) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	t_2 = (b * y4) - (i * y5)
	t_3 = (y0 * y5) - (y1 * y4)
	t_4 = y3 * ((y * ((c * y4) - (a * y5))) + (j * t_3))
	tmp = 0
	if y1 <= -5.6e+77:
		tmp = y1 * (a * ((z * y3) - (x * y2)))
	elif y1 <= -1.25e-53:
		tmp = j * (((t * t_2) + (y3 * t_3)) + (x * ((i * y1) - (b * y0))))
	elif y1 <= -3.8e-191:
		tmp = t_4
	elif y1 <= 1.95e-227:
		tmp = t_1
	elif y1 <= 2.7e-128:
		tmp = t * (((j * t_2) + (c * (z * i))) + (y2 * ((a * y5) - (c * y4))))
	elif y1 <= 2.45e+153:
		tmp = t_1
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	t_2 = Float64(Float64(b * y4) - Float64(i * y5))
	t_3 = Float64(Float64(y0 * y5) - Float64(y1 * y4))
	t_4 = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(j * t_3)))
	tmp = 0.0
	if (y1 <= -5.6e+77)
		tmp = Float64(y1 * Float64(a * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (y1 <= -1.25e-53)
		tmp = Float64(j * Float64(Float64(Float64(t * t_2) + Float64(y3 * t_3)) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y1 <= -3.8e-191)
		tmp = t_4;
	elseif (y1 <= 1.95e-227)
		tmp = t_1;
	elseif (y1 <= 2.7e-128)
		tmp = Float64(t * Float64(Float64(Float64(j * t_2) + Float64(c * Float64(z * i))) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y1 <= 2.45e+153)
		tmp = t_1;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	t_2 = (b * y4) - (i * y5);
	t_3 = (y0 * y5) - (y1 * y4);
	t_4 = y3 * ((y * ((c * y4) - (a * y5))) + (j * t_3));
	tmp = 0.0;
	if (y1 <= -5.6e+77)
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	elseif (y1 <= -1.25e-53)
		tmp = j * (((t * t_2) + (y3 * t_3)) + (x * ((i * y1) - (b * y0))));
	elseif (y1 <= -3.8e-191)
		tmp = t_4;
	elseif (y1 <= 1.95e-227)
		tmp = t_1;
	elseif (y1 <= 2.7e-128)
		tmp = t * (((j * t_2) + (c * (z * i))) + (y2 * ((a * y5) - (c * y4))));
	elseif (y1 <= 2.45e+153)
		tmp = t_1;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -5.6e+77], N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.25e-53], N[(j * N[(N[(N[(t * t$95$2), $MachinePrecision] + N[(y3 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3.8e-191], t$95$4, If[LessEqual[y1, 1.95e-227], t$95$1, If[LessEqual[y1, 2.7e-128], N[(t * N[(N[(N[(j * t$95$2), $MachinePrecision] + N[(c * N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.45e+153], t$95$1, t$95$4]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y1 < -5.60000000000000001e77

   1. Initial program 21.4%

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

   3. Simplified 21.4%

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

   5. Taylor expanded in y1 around inf 60.1%

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

      1. +-commutative 60.1%

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

      2. mul-1-neg 60.1%

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

      3. unsub-neg 60.1%

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

      4. *-commutative 60.1%

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

      5. *-commutative 60.1%

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

      6. *-commutative 60.1%

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

      7. mul-1-neg 60.1%

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

      8. *-commutative 60.1%

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

   7. Simplified 60.1%

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

   8. Taylor expanded in a around inf 52.4%

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

   if -5.60000000000000001e77 < y1 < -1.25e-53

   1. Initial program 33.2%

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

   3. Simplified 33.2%

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

   5. Taylor expanded in j around inf 62.8%

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

      1. +-commutative 62.8%

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

      2. mul-1-neg 62.8%

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

      3. unsub-neg 62.8%

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

      4. *-commutative 62.8%

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

   7. Simplified 62.8%

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

   if -1.25e-53 < y1 < -3.7999999999999998e-191 or 2.45000000000000001e153 < y1

   1. Initial program 20.3%

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

   3. Simplified 20.3%

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

   5. Taylor expanded in i around -inf 26.8%

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

      1. mul-1-neg 26.8%

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

      2. *-commutative 26.8%

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

      3. *-commutative 26.8%

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

   7. Simplified 26.8%

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

   8. Taylor expanded in y3 around -inf 54.9%

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

   if -3.7999999999999998e-191 < y1 < 1.95e-227 or 2.70000000000000006e-128 < y1 < 2.45000000000000001e153

   1. Initial program 29.6%

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

   3. Simplified 29.6%

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

   5. Taylor expanded in b around inf 53.7%

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

   if 1.95e-227 < y1 < 2.70000000000000006e-128

   1. Initial program 40.0%

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

   3. Simplified 40.0%

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

   5. Taylor expanded in i around -inf 40.0%

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

      1. mul-1-neg 40.0%

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

      2. *-commutative 40.0%

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

      3. *-commutative 40.0%

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

   7. Simplified 40.0%

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

   8. Taylor expanded in t around inf 60.6%

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

      1. associate--r+ 60.6%

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

      2. mul-1-neg 60.6%

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

   10. Simplified 60.6%

       \[\leadsto \color{blue}{t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(-c \cdot \left(i \cdot z\right)\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -5.6 \cdot 10^{+77}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -1.25 \cdot 10^{-53}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq -3.8 \cdot 10^{-191}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 1.95 \cdot 10^{-227}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 2.7 \cdot 10^{-128}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + c \cdot \left(z \cdot i\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 2.45 \cdot 10^{+153}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 32.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ t_2 := i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{if}\;a \leq -8.5 \cdot 10^{+252}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{+94}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-29}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-76}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-132}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-216}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-164}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+83}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* a (- (* x y) (* z t)))))
        (t_2 (* i (* z (- (* t c) (* k y1))))))
   (if (<= a -8.5e+252)
     (* y1 (* a (- (* z y3) (* x y2))))
     (if (<= a -5.5e+147)
       t_1
       (if (<= a -6.5e+94)
         (* b (* x (- (* y a) (* j y0))))
         (if (<= a -1.3e-29)
           (* b (* y4 (- (* t j) (* y k))))
           (if (<= a -1e-76)
             (* c (* y4 (- (* y y3) (* t y2))))
             (if (<= a -1.8e-132)
               t_2
               (if (<= a -6.8e-216)
                 (* y0 (* y2 (- (* x c) (* k y5))))
                 (if (<= a 1.35e-164)
                   (* b (* y0 (- (* z k) (* x j))))
                   (if (<= a 6.2e+83) 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 = b * (a * ((x * y) - (z * t)));
	double t_2 = i * (z * ((t * c) - (k * y1)));
	double tmp;
	if (a <= -8.5e+252) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (a <= -5.5e+147) {
		tmp = t_1;
	} else if (a <= -6.5e+94) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (a <= -1.3e-29) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (a <= -1e-76) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (a <= -1.8e-132) {
		tmp = t_2;
	} else if (a <= -6.8e-216) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (a <= 1.35e-164) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (a <= 6.2e+83) {
		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 = b * (a * ((x * y) - (z * t)))
    t_2 = i * (z * ((t * c) - (k * y1)))
    if (a <= (-8.5d+252)) then
        tmp = y1 * (a * ((z * y3) - (x * y2)))
    else if (a <= (-5.5d+147)) then
        tmp = t_1
    else if (a <= (-6.5d+94)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (a <= (-1.3d-29)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (a <= (-1d-76)) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (a <= (-1.8d-132)) then
        tmp = t_2
    else if (a <= (-6.8d-216)) then
        tmp = y0 * (y2 * ((x * c) - (k * y5)))
    else if (a <= 1.35d-164) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (a <= 6.2d+83) 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 = b * (a * ((x * y) - (z * t)));
	double t_2 = i * (z * ((t * c) - (k * y1)));
	double tmp;
	if (a <= -8.5e+252) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (a <= -5.5e+147) {
		tmp = t_1;
	} else if (a <= -6.5e+94) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (a <= -1.3e-29) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (a <= -1e-76) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (a <= -1.8e-132) {
		tmp = t_2;
	} else if (a <= -6.8e-216) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (a <= 1.35e-164) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (a <= 6.2e+83) {
		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 = b * (a * ((x * y) - (z * t)))
	t_2 = i * (z * ((t * c) - (k * y1)))
	tmp = 0
	if a <= -8.5e+252:
		tmp = y1 * (a * ((z * y3) - (x * y2)))
	elif a <= -5.5e+147:
		tmp = t_1
	elif a <= -6.5e+94:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif a <= -1.3e-29:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif a <= -1e-76:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif a <= -1.8e-132:
		tmp = t_2
	elif a <= -6.8e-216:
		tmp = y0 * (y2 * ((x * c) - (k * y5)))
	elif a <= 1.35e-164:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif a <= 6.2e+83:
		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(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))))
	t_2 = Float64(i * Float64(z * Float64(Float64(t * c) - Float64(k * y1))))
	tmp = 0.0
	if (a <= -8.5e+252)
		tmp = Float64(y1 * Float64(a * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (a <= -5.5e+147)
		tmp = t_1;
	elseif (a <= -6.5e+94)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (a <= -1.3e-29)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (a <= -1e-76)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (a <= -1.8e-132)
		tmp = t_2;
	elseif (a <= -6.8e-216)
		tmp = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))));
	elseif (a <= 1.35e-164)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (a <= 6.2e+83)
		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 = b * (a * ((x * y) - (z * t)));
	t_2 = i * (z * ((t * c) - (k * y1)));
	tmp = 0.0;
	if (a <= -8.5e+252)
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	elseif (a <= -5.5e+147)
		tmp = t_1;
	elseif (a <= -6.5e+94)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (a <= -1.3e-29)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (a <= -1e-76)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (a <= -1.8e-132)
		tmp = t_2;
	elseif (a <= -6.8e-216)
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	elseif (a <= 1.35e-164)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (a <= 6.2e+83)
		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[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(z * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.5e+252], N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.5e+147], t$95$1, If[LessEqual[a, -6.5e+94], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.3e-29], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1e-76], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.8e-132], t$95$2, If[LessEqual[a, -6.8e-216], N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e-164], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e+83], t$95$2, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -8.50000000000000044e252

   1. Initial program 17.6%

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

   3. Simplified 17.6%

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

   5. Taylor expanded in y1 around inf 47.2%

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

      1. +-commutative 47.2%

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

      2. mul-1-neg 47.2%

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

      3. unsub-neg 47.2%

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

      4. *-commutative 47.2%

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

      5. *-commutative 47.2%

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

      6. *-commutative 47.2%

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

      7. mul-1-neg 47.2%

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

      8. *-commutative 47.2%

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

   7. Simplified 47.2%

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

   8. Taylor expanded in a around inf 70.7%

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

   if -8.50000000000000044e252 < a < -5.4999999999999997e147 or 6.19999999999999984e83 < a

   1. Initial program 24.2%

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

   3. Simplified 24.2%

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

   5. Taylor expanded in b around inf 57.2%

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

   6. Taylor expanded in a around inf 64.3%

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

   if -5.4999999999999997e147 < a < -6.49999999999999976e94

   1. Initial program 19.5%

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

   3. Simplified 19.5%

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

   5. Taylor expanded in b around inf 19.0%

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

   6. Taylor expanded in x around inf 62.9%

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

   if -6.49999999999999976e94 < a < -1.3000000000000001e-29

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in y4 around inf 52.0%

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

   6. Taylor expanded in b around inf 52.2%

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

   if -1.3000000000000001e-29 < a < -9.99999999999999927e-77

   1. Initial program 22.0%

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

   3. Simplified 22.0%

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

   5. Taylor expanded in y4 around inf 33.5%

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

   6. Taylor expanded in c around inf 67.0%

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

   if -9.99999999999999927e-77 < a < -1.80000000000000004e-132 or 1.3500000000000001e-164 < a < 6.19999999999999984e83

   1. Initial program 30.5%

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

   3. Simplified 30.5%

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

   5. Taylor expanded in i around -inf 36.7%

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

      1. mul-1-neg 36.7%

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

      2. *-commutative 36.7%

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

      3. *-commutative 36.7%

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

   7. Simplified 36.7%

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

   8. Taylor expanded in z around -inf 46.4%

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

   if -1.80000000000000004e-132 < a < -6.7999999999999995e-216

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in y0 around inf 56.2%

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

      1. +-commutative 56.2%

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

      2. mul-1-neg 56.2%

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

      3. unsub-neg 56.2%

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

      4. *-commutative 56.2%

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

      5. *-commutative 56.2%

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

      6. *-commutative 56.2%

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

      7. *-commutative 56.2%

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

   7. Simplified 56.2%

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

   8. Taylor expanded in y2 around inf 55.9%

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

   if -6.7999999999999995e-216 < a < 1.3500000000000001e-164

   1. Initial program 33.6%

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

   3. Simplified 33.6%

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

   5. Taylor expanded in b around inf 45.9%

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

   6. Taylor expanded in y0 around inf 48.9%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+252}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{+94}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-29}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-76}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-132}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-216}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-164}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+83}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 32.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ t_2 := i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{+209}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -9 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-32}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-73}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-131}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-216}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{-167}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+86}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* a (- (* x y) (* z t)))))
        (t_2 (* i (* z (- (* t c) (* k y1))))))
   (if (<= a -5.2e+209)
     (* a (* y5 (- (* t y2) (* y y3))))
     (if (<= a -2.65e+149)
       t_1
       (if (<= a -9e+95)
         (* b (* x (- (* y a) (* j y0))))
         (if (<= a -2.05e-32)
           (* b (* y4 (- (* t j) (* y k))))
           (if (<= a -2.9e-73)
             (* c (* y4 (- (* y y3) (* t y2))))
             (if (<= a -1e-131)
               t_2
               (if (<= a -8.2e-216)
                 (* y0 (* y2 (- (* x c) (* k y5))))
                 (if (<= a 3.05e-167)
                   (* b (* y0 (- (* z k) (* x j))))
                   (if (<= a 4.6e+86) 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 = b * (a * ((x * y) - (z * t)));
	double t_2 = i * (z * ((t * c) - (k * y1)));
	double tmp;
	if (a <= -5.2e+209) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (a <= -2.65e+149) {
		tmp = t_1;
	} else if (a <= -9e+95) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (a <= -2.05e-32) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (a <= -2.9e-73) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (a <= -1e-131) {
		tmp = t_2;
	} else if (a <= -8.2e-216) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (a <= 3.05e-167) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (a <= 4.6e+86) {
		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 = b * (a * ((x * y) - (z * t)))
    t_2 = i * (z * ((t * c) - (k * y1)))
    if (a <= (-5.2d+209)) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (a <= (-2.65d+149)) then
        tmp = t_1
    else if (a <= (-9d+95)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (a <= (-2.05d-32)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (a <= (-2.9d-73)) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (a <= (-1d-131)) then
        tmp = t_2
    else if (a <= (-8.2d-216)) then
        tmp = y0 * (y2 * ((x * c) - (k * y5)))
    else if (a <= 3.05d-167) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (a <= 4.6d+86) 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 = b * (a * ((x * y) - (z * t)));
	double t_2 = i * (z * ((t * c) - (k * y1)));
	double tmp;
	if (a <= -5.2e+209) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (a <= -2.65e+149) {
		tmp = t_1;
	} else if (a <= -9e+95) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (a <= -2.05e-32) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (a <= -2.9e-73) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (a <= -1e-131) {
		tmp = t_2;
	} else if (a <= -8.2e-216) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (a <= 3.05e-167) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (a <= 4.6e+86) {
		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 = b * (a * ((x * y) - (z * t)))
	t_2 = i * (z * ((t * c) - (k * y1)))
	tmp = 0
	if a <= -5.2e+209:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif a <= -2.65e+149:
		tmp = t_1
	elif a <= -9e+95:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif a <= -2.05e-32:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif a <= -2.9e-73:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif a <= -1e-131:
		tmp = t_2
	elif a <= -8.2e-216:
		tmp = y0 * (y2 * ((x * c) - (k * y5)))
	elif a <= 3.05e-167:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif a <= 4.6e+86:
		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(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))))
	t_2 = Float64(i * Float64(z * Float64(Float64(t * c) - Float64(k * y1))))
	tmp = 0.0
	if (a <= -5.2e+209)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (a <= -2.65e+149)
		tmp = t_1;
	elseif (a <= -9e+95)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (a <= -2.05e-32)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (a <= -2.9e-73)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (a <= -1e-131)
		tmp = t_2;
	elseif (a <= -8.2e-216)
		tmp = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))));
	elseif (a <= 3.05e-167)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (a <= 4.6e+86)
		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 = b * (a * ((x * y) - (z * t)));
	t_2 = i * (z * ((t * c) - (k * y1)));
	tmp = 0.0;
	if (a <= -5.2e+209)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (a <= -2.65e+149)
		tmp = t_1;
	elseif (a <= -9e+95)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (a <= -2.05e-32)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (a <= -2.9e-73)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (a <= -1e-131)
		tmp = t_2;
	elseif (a <= -8.2e-216)
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	elseif (a <= 3.05e-167)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (a <= 4.6e+86)
		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[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(z * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.2e+209], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.65e+149], t$95$1, If[LessEqual[a, -9e+95], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.05e-32], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.9e-73], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1e-131], t$95$2, If[LessEqual[a, -8.2e-216], N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.05e-167], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.6e+86], t$95$2, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -5.2000000000000001e209

   1. Initial program 20.0%

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

   3. Simplified 20.0%

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

   5. Taylor expanded in i around -inf 28.6%

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

      1. mul-1-neg 28.6%

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

      2. *-commutative 28.6%

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

      3. *-commutative 28.6%

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

   7. Simplified 28.6%

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

   8. Taylor expanded in a around inf 56.8%

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

   if -5.2000000000000001e209 < a < -2.65000000000000016e149 or 4.59999999999999979e86 < a

   1. Initial program 24.1%

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

   3. Simplified 24.1%

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

   5. Taylor expanded in b around inf 60.3%

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

   6. Taylor expanded in a around inf 66.5%

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

   if -2.65000000000000016e149 < a < -9.00000000000000033e95

   1. Initial program 19.5%

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

   3. Simplified 19.5%

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

   5. Taylor expanded in b around inf 19.0%

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

   6. Taylor expanded in x around inf 62.9%

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

   if -9.00000000000000033e95 < a < -2.04999999999999988e-32

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in y4 around inf 52.0%

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

   6. Taylor expanded in b around inf 52.2%

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

   if -2.04999999999999988e-32 < a < -2.9e-73

   1. Initial program 22.0%

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

   3. Simplified 22.0%

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

   5. Taylor expanded in y4 around inf 33.5%

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

   6. Taylor expanded in c around inf 67.0%

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

   if -2.9e-73 < a < -9.9999999999999999e-132 or 3.0499999999999999e-167 < a < 4.59999999999999979e86

   1. Initial program 30.5%

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

   3. Simplified 30.5%

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

   5. Taylor expanded in i around -inf 36.7%

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

      1. mul-1-neg 36.7%

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

      2. *-commutative 36.7%

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

      3. *-commutative 36.7%

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

   7. Simplified 36.7%

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

   8. Taylor expanded in z around -inf 46.4%

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

   if -9.9999999999999999e-132 < a < -8.20000000000000047e-216

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in y0 around inf 56.2%

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

      1. +-commutative 56.2%

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

      2. mul-1-neg 56.2%

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

      3. unsub-neg 56.2%

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

      4. *-commutative 56.2%

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

      5. *-commutative 56.2%

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

      6. *-commutative 56.2%

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

      7. *-commutative 56.2%

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

   7. Simplified 56.2%

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

   8. Taylor expanded in y2 around inf 55.9%

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

   if -8.20000000000000047e-216 < a < 3.0499999999999999e-167

   1. Initial program 33.6%

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

   3. Simplified 33.6%

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

   5. Taylor expanded in b around inf 45.9%

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

   6. Taylor expanded in y0 around inf 48.9%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+209}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{+149}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq -9 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-32}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-73}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-131}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-216}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{-167}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+86}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 32.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{+253}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{+83}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{-21}:\\ \;\;\;\;y1 \cdot \left(x \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-86}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-217}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-169}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+219}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* a (- (* x y) (* z t))))))
   (if (<= a -1.15e+253)
     (* y1 (* a (- (* z y3) (* x y2))))
     (if (<= a -6.8e+141)
       t_1
       (if (<= a -6.8e+83)
         (* b (* x (- (* y a) (* j y0))))
         (if (<= a -2.65e-21)
           (* y1 (* x (- (* i j) (* a y2))))
           (if (<= a -6.2e-86)
             (* k (* y (- (* i y5) (* b y4))))
             (if (<= a -7e-217)
               (*
                y2
                (+ (* k (- (* y1 y4) (* y0 y5))) (* t (- (* a y5) (* c y4)))))
               (if (<= a 4e-169)
                 (* b (* y0 (- (* z k) (* x j))))
                 (if (<= a 4.2e+219)
                   (* y1 (* z (- (* a y3) (* i k))))
                   t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (a * ((x * y) - (z * t)));
	double tmp;
	if (a <= -1.15e+253) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (a <= -6.8e+141) {
		tmp = t_1;
	} else if (a <= -6.8e+83) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (a <= -2.65e-21) {
		tmp = y1 * (x * ((i * j) - (a * y2)));
	} else if (a <= -6.2e-86) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (a <= -7e-217) {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + (t * ((a * y5) - (c * y4))));
	} else if (a <= 4e-169) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (a <= 4.2e+219) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * ((x * y) - (z * t)))
    if (a <= (-1.15d+253)) then
        tmp = y1 * (a * ((z * y3) - (x * y2)))
    else if (a <= (-6.8d+141)) then
        tmp = t_1
    else if (a <= (-6.8d+83)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (a <= (-2.65d-21)) then
        tmp = y1 * (x * ((i * j) - (a * y2)))
    else if (a <= (-6.2d-86)) then
        tmp = k * (y * ((i * y5) - (b * y4)))
    else if (a <= (-7d-217)) then
        tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + (t * ((a * y5) - (c * y4))))
    else if (a <= 4d-169) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (a <= 4.2d+219) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (a * ((x * y) - (z * t)));
	double tmp;
	if (a <= -1.15e+253) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (a <= -6.8e+141) {
		tmp = t_1;
	} else if (a <= -6.8e+83) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (a <= -2.65e-21) {
		tmp = y1 * (x * ((i * j) - (a * y2)));
	} else if (a <= -6.2e-86) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (a <= -7e-217) {
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + (t * ((a * y5) - (c * y4))));
	} else if (a <= 4e-169) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (a <= 4.2e+219) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (a * ((x * y) - (z * t)))
	tmp = 0
	if a <= -1.15e+253:
		tmp = y1 * (a * ((z * y3) - (x * y2)))
	elif a <= -6.8e+141:
		tmp = t_1
	elif a <= -6.8e+83:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif a <= -2.65e-21:
		tmp = y1 * (x * ((i * j) - (a * y2)))
	elif a <= -6.2e-86:
		tmp = k * (y * ((i * y5) - (b * y4)))
	elif a <= -7e-217:
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + (t * ((a * y5) - (c * y4))))
	elif a <= 4e-169:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif a <= 4.2e+219:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (a <= -1.15e+253)
		tmp = Float64(y1 * Float64(a * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (a <= -6.8e+141)
		tmp = t_1;
	elseif (a <= -6.8e+83)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (a <= -2.65e-21)
		tmp = Float64(y1 * Float64(x * Float64(Float64(i * j) - Float64(a * y2))));
	elseif (a <= -6.2e-86)
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))));
	elseif (a <= -7e-217)
		tmp = Float64(y2 * Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (a <= 4e-169)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (a <= 4.2e+219)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (a * ((x * y) - (z * t)));
	tmp = 0.0;
	if (a <= -1.15e+253)
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	elseif (a <= -6.8e+141)
		tmp = t_1;
	elseif (a <= -6.8e+83)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (a <= -2.65e-21)
		tmp = y1 * (x * ((i * j) - (a * y2)));
	elseif (a <= -6.2e-86)
		tmp = k * (y * ((i * y5) - (b * y4)));
	elseif (a <= -7e-217)
		tmp = y2 * ((k * ((y1 * y4) - (y0 * y5))) + (t * ((a * y5) - (c * y4))));
	elseif (a <= 4e-169)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (a <= 4.2e+219)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.15e+253], N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.8e+141], t$95$1, If[LessEqual[a, -6.8e+83], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.65e-21], N[(y1 * N[(x * N[(N[(i * j), $MachinePrecision] - N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.2e-86], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7e-217], N[(y2 * N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e-169], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e+219], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -1.15e253

   1. Initial program 17.6%

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

   3. Simplified 17.6%

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

   5. Taylor expanded in y1 around inf 47.2%

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

      1. +-commutative 47.2%

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

      2. mul-1-neg 47.2%

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

      3. unsub-neg 47.2%

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

      4. *-commutative 47.2%

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

      5. *-commutative 47.2%

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

      6. *-commutative 47.2%

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

      7. mul-1-neg 47.2%

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

      8. *-commutative 47.2%

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

   7. Simplified 47.2%

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

   8. Taylor expanded in a around inf 70.7%

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

   if -1.15e253 < a < -6.7999999999999996e141 or 4.19999999999999976e219 < a

   1. Initial program 19.7%

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

   3. Simplified 19.7%

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

   5. Taylor expanded in b around inf 56.4%

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

   6. Taylor expanded in a around inf 73.5%

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

   if -6.7999999999999996e141 < a < -6.7999999999999996e83

   1. Initial program 21.7%

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

   3. Simplified 21.7%

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

   5. Taylor expanded in b around inf 31.8%

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

   6. Taylor expanded in x around inf 58.2%

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

   if -6.7999999999999996e83 < a < -2.65e-21

   1. Initial program 17.4%

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

   3. Simplified 17.4%

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

   5. Taylor expanded in y1 around inf 39.8%

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

      1. +-commutative 39.8%

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

      2. mul-1-neg 39.8%

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

      3. unsub-neg 39.8%

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

      4. *-commutative 39.8%

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

      5. *-commutative 39.8%

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

      6. *-commutative 39.8%

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

      7. mul-1-neg 39.8%

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

      8. *-commutative 39.8%

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

   7. Simplified 39.8%

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

   8. Taylor expanded in x around inf 53.5%

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

   if -2.65e-21 < a < -6.19999999999999977e-86

   1. Initial program 26.8%

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

   3. Simplified 26.8%

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

   5. Taylor expanded in i around -inf 13.3%

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

      1. mul-1-neg 13.3%

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

      2. *-commutative 13.3%

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

      3. *-commutative 13.3%

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

   7. Simplified 13.3%

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

   8. Taylor expanded in y around inf 62.4%

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

      1. associate-*r* 62.4%

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

      2. neg-mul-1 62.4%

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

      3. mul-1-neg 62.4%

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

   10. Simplified 62.4%

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

   11. Taylor expanded in k around inf 49.8%

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

   if -6.19999999999999977e-86 < a < -7e-217

   1. Initial program 24.1%

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

   3. Simplified 24.1%

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

   5. Taylor expanded in i around -inf 24.3%

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

      1. mul-1-neg 24.3%

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

      2. *-commutative 24.3%

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

      3. *-commutative 24.3%

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

   7. Simplified 24.3%

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

   8. Taylor expanded in y2 around inf 62.7%

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

   if -7e-217 < a < 4.00000000000000008e-169

   1. Initial program 34.4%

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

   3. Simplified 34.4%

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

   5. Taylor expanded in b around inf 44.7%

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

   6. Taylor expanded in y0 around inf 49.9%

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

   if 4.00000000000000008e-169 < a < 4.19999999999999976e219

   1. Initial program 32.5%

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

   3. Simplified 32.5%

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

   5. Taylor expanded in y1 around inf 38.9%

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

      1. +-commutative 38.9%

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

      2. mul-1-neg 38.9%

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

      3. unsub-neg 38.9%

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

      4. *-commutative 38.9%

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

      5. *-commutative 38.9%

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

      6. *-commutative 38.9%

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

      7. mul-1-neg 38.9%

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

      8. *-commutative 38.9%

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

   7. Simplified 38.9%

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

   8. Taylor expanded in z around -inf 42.6%

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

      1. mul-1-neg 42.6%

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

   10. Simplified 42.6%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+253}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{+141}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{+83}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{-21}:\\ \;\;\;\;y1 \cdot \left(x \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-86}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-217}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-169}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+219}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 32.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ t_2 := i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{if}\;a \leq -3.15 \cdot 10^{+209}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{+91}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-31}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{-76}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-168}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-167}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+86}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* a (- (* x y) (* z t)))))
        (t_2 (* i (* z (- (* t c) (* k y1))))))
   (if (<= a -3.15e+209)
     (* a (* y5 (- (* t y2) (* y y3))))
     (if (<= a -9.5e+149)
       t_1
       (if (<= a -7.5e+91)
         (* b (* x (- (* y a) (* j y0))))
         (if (<= a -3.7e-31)
           (* b (* y4 (- (* t j) (* y k))))
           (if (<= a -9.8e-76)
             (* c (* y4 (- (* y y3) (* t y2))))
             (if (<= a -1.35e-168)
               t_2
               (if (<= a 1.05e-167)
                 (* b (* j (- (* t y4) (* x y0))))
                 (if (<= a 4.5e+86) 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 = b * (a * ((x * y) - (z * t)));
	double t_2 = i * (z * ((t * c) - (k * y1)));
	double tmp;
	if (a <= -3.15e+209) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (a <= -9.5e+149) {
		tmp = t_1;
	} else if (a <= -7.5e+91) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (a <= -3.7e-31) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (a <= -9.8e-76) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (a <= -1.35e-168) {
		tmp = t_2;
	} else if (a <= 1.05e-167) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (a <= 4.5e+86) {
		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 = b * (a * ((x * y) - (z * t)))
    t_2 = i * (z * ((t * c) - (k * y1)))
    if (a <= (-3.15d+209)) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (a <= (-9.5d+149)) then
        tmp = t_1
    else if (a <= (-7.5d+91)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (a <= (-3.7d-31)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (a <= (-9.8d-76)) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (a <= (-1.35d-168)) then
        tmp = t_2
    else if (a <= 1.05d-167) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (a <= 4.5d+86) 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 = b * (a * ((x * y) - (z * t)));
	double t_2 = i * (z * ((t * c) - (k * y1)));
	double tmp;
	if (a <= -3.15e+209) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (a <= -9.5e+149) {
		tmp = t_1;
	} else if (a <= -7.5e+91) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (a <= -3.7e-31) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (a <= -9.8e-76) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (a <= -1.35e-168) {
		tmp = t_2;
	} else if (a <= 1.05e-167) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (a <= 4.5e+86) {
		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 = b * (a * ((x * y) - (z * t)))
	t_2 = i * (z * ((t * c) - (k * y1)))
	tmp = 0
	if a <= -3.15e+209:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif a <= -9.5e+149:
		tmp = t_1
	elif a <= -7.5e+91:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif a <= -3.7e-31:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif a <= -9.8e-76:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif a <= -1.35e-168:
		tmp = t_2
	elif a <= 1.05e-167:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif a <= 4.5e+86:
		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(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))))
	t_2 = Float64(i * Float64(z * Float64(Float64(t * c) - Float64(k * y1))))
	tmp = 0.0
	if (a <= -3.15e+209)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (a <= -9.5e+149)
		tmp = t_1;
	elseif (a <= -7.5e+91)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (a <= -3.7e-31)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (a <= -9.8e-76)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (a <= -1.35e-168)
		tmp = t_2;
	elseif (a <= 1.05e-167)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (a <= 4.5e+86)
		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 = b * (a * ((x * y) - (z * t)));
	t_2 = i * (z * ((t * c) - (k * y1)));
	tmp = 0.0;
	if (a <= -3.15e+209)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (a <= -9.5e+149)
		tmp = t_1;
	elseif (a <= -7.5e+91)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (a <= -3.7e-31)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (a <= -9.8e-76)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (a <= -1.35e-168)
		tmp = t_2;
	elseif (a <= 1.05e-167)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (a <= 4.5e+86)
		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[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(z * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.15e+209], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9.5e+149], t$95$1, If[LessEqual[a, -7.5e+91], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.7e-31], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9.8e-76], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.35e-168], t$95$2, If[LessEqual[a, 1.05e-167], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e+86], t$95$2, t$95$1]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -3.15000000000000001e209

   1. Initial program 20.0%

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

   3. Simplified 20.0%

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

   5. Taylor expanded in i around -inf 28.6%

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

      1. mul-1-neg 28.6%

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

      2. *-commutative 28.6%

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

      3. *-commutative 28.6%

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

   7. Simplified 28.6%

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

   8. Taylor expanded in a around inf 56.8%

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

   if -3.15000000000000001e209 < a < -9.49999999999999973e149 or 4.49999999999999993e86 < a

   1. Initial program 24.1%

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

   3. Simplified 24.1%

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

   5. Taylor expanded in b around inf 60.3%

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

   6. Taylor expanded in a around inf 66.5%

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

   if -9.49999999999999973e149 < a < -7.50000000000000033e91

   1. Initial program 19.5%

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

   3. Simplified 19.5%

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

   5. Taylor expanded in b around inf 19.0%

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

   6. Taylor expanded in x around inf 62.9%

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

   if -7.50000000000000033e91 < a < -3.6999999999999998e-31

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in y4 around inf 52.0%

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

   6. Taylor expanded in b around inf 52.2%

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

   if -3.6999999999999998e-31 < a < -9.79999999999999944e-76

   1. Initial program 22.0%

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

   3. Simplified 22.0%

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

   5. Taylor expanded in y4 around inf 33.5%

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

   6. Taylor expanded in c around inf 67.0%

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

   if -9.79999999999999944e-76 < a < -1.35000000000000008e-168 or 1.05000000000000009e-167 < a < 4.49999999999999993e86

   1. Initial program 28.5%

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

   3. Simplified 28.5%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 34.1%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 34.1%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 34.1%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 34.1%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 34.1%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in z around -inf 45.5%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   if -1.35000000000000008e-168 < a < 1.05000000000000009e-167

   1. Initial program 33.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.0%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 46.9%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.15 \cdot 10^{+209}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{+149}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{+91}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-31}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{-76}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-168}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-167}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+86}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 22.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot b\right) \cdot \left(x \cdot a\right)\\ t_2 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;a \leq -6.4 \cdot 10^{+210}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.56 \cdot 10^{+22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-21}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(x \cdot y1\right)\\ \mathbf{elif}\;a \leq -2.95 \cdot 10^{-83}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-137}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c\right)\right)\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-297}:\\ \;\;\;\;b \cdot \left(j \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-72}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(z \cdot \left(-k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* y b) (* x a))) (t_2 (* a (* y5 (- (* t y2) (* y y3))))))
   (if (<= a -6.4e+210)
     t_2
     (if (<= a -1.45e+98)
       t_1
       (if (<= a -1.56e+22)
         t_2
         (if (<= a -5.4e-21)
           (* (* i j) (* x y1))
           (if (<= a -2.95e-83)
             (* b (* k (* y (- y4))))
             (if (<= a -2.05e-137)
               (* i (* z (* t c)))
               (if (<= a -1.45e-297)
                 (* b (* j (* x (- y0))))
                 (if (<= a 2.1e-72) (* i (* y1 (* z (- k)))) t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * b) * (x * a);
	double t_2 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (a <= -6.4e+210) {
		tmp = t_2;
	} else if (a <= -1.45e+98) {
		tmp = t_1;
	} else if (a <= -1.56e+22) {
		tmp = t_2;
	} else if (a <= -5.4e-21) {
		tmp = (i * j) * (x * y1);
	} else if (a <= -2.95e-83) {
		tmp = b * (k * (y * -y4));
	} else if (a <= -2.05e-137) {
		tmp = i * (z * (t * c));
	} else if (a <= -1.45e-297) {
		tmp = b * (j * (x * -y0));
	} else if (a <= 2.1e-72) {
		tmp = i * (y1 * (z * -k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * b) * (x * a)
    t_2 = a * (y5 * ((t * y2) - (y * y3)))
    if (a <= (-6.4d+210)) then
        tmp = t_2
    else if (a <= (-1.45d+98)) then
        tmp = t_1
    else if (a <= (-1.56d+22)) then
        tmp = t_2
    else if (a <= (-5.4d-21)) then
        tmp = (i * j) * (x * y1)
    else if (a <= (-2.95d-83)) then
        tmp = b * (k * (y * -y4))
    else if (a <= (-2.05d-137)) then
        tmp = i * (z * (t * c))
    else if (a <= (-1.45d-297)) then
        tmp = b * (j * (x * -y0))
    else if (a <= 2.1d-72) then
        tmp = i * (y1 * (z * -k))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * b) * (x * a);
	double t_2 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (a <= -6.4e+210) {
		tmp = t_2;
	} else if (a <= -1.45e+98) {
		tmp = t_1;
	} else if (a <= -1.56e+22) {
		tmp = t_2;
	} else if (a <= -5.4e-21) {
		tmp = (i * j) * (x * y1);
	} else if (a <= -2.95e-83) {
		tmp = b * (k * (y * -y4));
	} else if (a <= -2.05e-137) {
		tmp = i * (z * (t * c));
	} else if (a <= -1.45e-297) {
		tmp = b * (j * (x * -y0));
	} else if (a <= 2.1e-72) {
		tmp = i * (y1 * (z * -k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y * b) * (x * a)
	t_2 = a * (y5 * ((t * y2) - (y * y3)))
	tmp = 0
	if a <= -6.4e+210:
		tmp = t_2
	elif a <= -1.45e+98:
		tmp = t_1
	elif a <= -1.56e+22:
		tmp = t_2
	elif a <= -5.4e-21:
		tmp = (i * j) * (x * y1)
	elif a <= -2.95e-83:
		tmp = b * (k * (y * -y4))
	elif a <= -2.05e-137:
		tmp = i * (z * (t * c))
	elif a <= -1.45e-297:
		tmp = b * (j * (x * -y0))
	elif a <= 2.1e-72:
		tmp = i * (y1 * (z * -k))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * b) * Float64(x * a))
	t_2 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	tmp = 0.0
	if (a <= -6.4e+210)
		tmp = t_2;
	elseif (a <= -1.45e+98)
		tmp = t_1;
	elseif (a <= -1.56e+22)
		tmp = t_2;
	elseif (a <= -5.4e-21)
		tmp = Float64(Float64(i * j) * Float64(x * y1));
	elseif (a <= -2.95e-83)
		tmp = Float64(b * Float64(k * Float64(y * Float64(-y4))));
	elseif (a <= -2.05e-137)
		tmp = Float64(i * Float64(z * Float64(t * c)));
	elseif (a <= -1.45e-297)
		tmp = Float64(b * Float64(j * Float64(x * Float64(-y0))));
	elseif (a <= 2.1e-72)
		tmp = Float64(i * Float64(y1 * Float64(z * Float64(-k))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y * b) * (x * a);
	t_2 = a * (y5 * ((t * y2) - (y * y3)));
	tmp = 0.0;
	if (a <= -6.4e+210)
		tmp = t_2;
	elseif (a <= -1.45e+98)
		tmp = t_1;
	elseif (a <= -1.56e+22)
		tmp = t_2;
	elseif (a <= -5.4e-21)
		tmp = (i * j) * (x * y1);
	elseif (a <= -2.95e-83)
		tmp = b * (k * (y * -y4));
	elseif (a <= -2.05e-137)
		tmp = i * (z * (t * c));
	elseif (a <= -1.45e-297)
		tmp = b * (j * (x * -y0));
	elseif (a <= 2.1e-72)
		tmp = i * (y1 * (z * -k));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] * N[(x * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.4e+210], t$95$2, If[LessEqual[a, -1.45e+98], t$95$1, If[LessEqual[a, -1.56e+22], t$95$2, If[LessEqual[a, -5.4e-21], N[(N[(i * j), $MachinePrecision] * N[(x * y1), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.95e-83], N[(b * N[(k * N[(y * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.05e-137], N[(i * N[(z * N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.45e-297], N[(b * N[(j * N[(x * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.1e-72], N[(i * N[(y1 * N[(z * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -6.4000000000000005e210 or -1.45000000000000005e98 < a < -1.56e22

   1. Initial program 23.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.8%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 33.7%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 33.7%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 33.7%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 33.7%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 33.7%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 51.0%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -6.4000000000000005e210 < a < -1.45000000000000005e98 or 2.1e-72 < a

   1. Initial program 26.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.2%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 44.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y around -inf 44.6%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 44.6%

         \[\leadsto \color{blue}{-b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]

      2. associate-*r* 39.6%

         \[\leadsto -\color{blue}{\left(b \cdot y\right) \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)} \]

      3. mul-1-neg 39.6%

         \[\leadsto -\left(b \cdot y\right) \cdot \left(\color{blue}{\left(-a \cdot x\right)} + k \cdot y4\right) \]

   8. Simplified 39.6%

      \[\leadsto \color{blue}{-\left(b \cdot y\right) \cdot \left(\left(-a \cdot x\right) + k \cdot y4\right)} \]

   9. Taylor expanded in a around inf 39.5%

      \[\leadsto -\left(b \cdot y\right) \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 39.5%

          \[\leadsto -\left(b \cdot y\right) \cdot \color{blue}{\left(-a \cdot x\right)} \]

       2. distribute-rgt-neg-out 39.5%

          \[\leadsto -\left(b \cdot y\right) \cdot \color{blue}{\left(a \cdot \left(-x\right)\right)} \]

   11. Simplified 39.5%

       \[\leadsto -\left(b \cdot y\right) \cdot \color{blue}{\left(a \cdot \left(-x\right)\right)} \]

   if -1.56e22 < a < -5.4000000000000002e-21

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y1 around inf 66.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 66.9%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 66.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 66.9%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 66.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 66.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 66.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 66.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 66.9%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   7. Simplified 66.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   8. Taylor expanded in i around inf 66.9%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 55.8%

         \[\leadsto \color{blue}{\left(i \cdot y1\right) \cdot \left(j \cdot x - k \cdot z\right)} \]

   10. Simplified 55.8%

       \[\leadsto \color{blue}{\left(i \cdot y1\right) \cdot \left(j \cdot x - k \cdot z\right)} \]

   11. Taylor expanded in j around inf 56.1%

       \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 56.1%

          \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(x \cdot y1\right)} \]

       2. *-commutative 56.1%

          \[\leadsto \left(i \cdot j\right) \cdot \color{blue}{\left(y1 \cdot x\right)} \]

   13. Simplified 56.1%

       \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(y1 \cdot x\right)} \]

   if -5.4000000000000002e-21 < a < -2.9499999999999998e-83

   1. Initial program 23.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.4%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 47.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y around -inf 40.5%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 40.5%

         \[\leadsto \color{blue}{-b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]

      2. associate-*r* 33.1%

         \[\leadsto -\color{blue}{\left(b \cdot y\right) \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)} \]

      3. mul-1-neg 33.1%

         \[\leadsto -\left(b \cdot y\right) \cdot \left(\color{blue}{\left(-a \cdot x\right)} + k \cdot y4\right) \]

   8. Simplified 33.1%

      \[\leadsto \color{blue}{-\left(b \cdot y\right) \cdot \left(\left(-a \cdot x\right) + k \cdot y4\right)} \]

   9. Taylor expanded in a around 0 40.4%

      \[\leadsto -\color{blue}{b \cdot \left(k \cdot \left(y \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 40.4%

          \[\leadsto -b \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot k\right)} \]

   11. Simplified 40.4%

       \[\leadsto -\color{blue}{b \cdot \left(\left(y \cdot y4\right) \cdot k\right)} \]

   if -2.9499999999999998e-83 < a < -2.0499999999999999e-137

   1. Initial program 30.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.5%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 30.7%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 30.7%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 30.7%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 30.7%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 30.7%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in z around -inf 61.9%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   9. Taylor expanded in c around inf 47.3%

      \[\leadsto i \cdot \left(z \cdot \color{blue}{\left(c \cdot t\right)}\right) \]

   if -2.0499999999999999e-137 < a < -1.44999999999999995e-297

   1. Initial program 25.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.3%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 35.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 51.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around 0 39.0%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot \left(x \cdot y0\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 39.0%

         \[\leadsto \color{blue}{-b \cdot \left(j \cdot \left(x \cdot y0\right)\right)} \]

      2. *-commutative 39.0%

         \[\leadsto -\color{blue}{\left(j \cdot \left(x \cdot y0\right)\right) \cdot b} \]

      3. distribute-rgt-neg-in 39.0%

         \[\leadsto \color{blue}{\left(j \cdot \left(x \cdot y0\right)\right) \cdot \left(-b\right)} \]

   9. Simplified 39.0%

      \[\leadsto \color{blue}{\left(j \cdot \left(x \cdot y0\right)\right) \cdot \left(-b\right)} \]

   if -1.44999999999999995e-297 < a < 2.1e-72

   1. Initial program 33.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.6%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 41.7%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 41.7%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 41.7%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 41.7%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 41.7%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in z around -inf 39.0%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   9. Taylor expanded in c around 0 34.7%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 34.7%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. distribute-rgt-neg-in 34.7%

          \[\leadsto \color{blue}{i \cdot \left(-k \cdot \left(y1 \cdot z\right)\right)} \]

       3. distribute-rgt-neg-in 34.7%

          \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(-y1 \cdot z\right)\right)} \]

       4. distribute-rgt-neg-in 34.7%

          \[\leadsto i \cdot \left(k \cdot \color{blue}{\left(y1 \cdot \left(-z\right)\right)}\right) \]

   11. Simplified 34.7%

       \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y1 \cdot \left(-z\right)\right)\right)} \]

   12. Taylor expanded in i around 0 34.7%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   13. Step-by-step derivation

       1. mul-1-neg 34.7%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. distribute-rgt-neg-in 34.7%

          \[\leadsto \color{blue}{i \cdot \left(-k \cdot \left(y1 \cdot z\right)\right)} \]

       3. *-commutative 34.7%

          \[\leadsto i \cdot \left(-\color{blue}{\left(y1 \cdot z\right) \cdot k}\right) \]

       4. distribute-lft-neg-in 34.7%

          \[\leadsto i \cdot \color{blue}{\left(\left(-y1 \cdot z\right) \cdot k\right)} \]

       5. distribute-rgt-neg-out 34.7%

          \[\leadsto i \cdot \left(\color{blue}{\left(y1 \cdot \left(-z\right)\right)} \cdot k\right) \]

       6. associate-*l* 40.2%

          \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \left(\left(-z\right) \cdot k\right)\right)} \]

       7. distribute-lft-neg-in 40.2%

          \[\leadsto i \cdot \left(y1 \cdot \color{blue}{\left(-z \cdot k\right)}\right) \]

       8. *-commutative 40.2%

          \[\leadsto i \cdot \left(y1 \cdot \left(-\color{blue}{k \cdot z}\right)\right) \]

       9. distribute-rgt-neg-in 40.2%

          \[\leadsto i \cdot \left(y1 \cdot \color{blue}{\left(k \cdot \left(-z\right)\right)}\right) \]

   14. Simplified 40.2%

       \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(k \cdot \left(-z\right)\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{+210}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{+98}:\\ \;\;\;\;\left(y \cdot b\right) \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;a \leq -1.56 \cdot 10^{+22}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-21}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(x \cdot y1\right)\\ \mathbf{elif}\;a \leq -2.95 \cdot 10^{-83}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-137}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c\right)\right)\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-297}:\\ \;\;\;\;b \cdot \left(j \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-72}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(z \cdot \left(-k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot b\right) \cdot \left(x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;a \leq -9.4 \cdot 10^{+210}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-170}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 1.38 \cdot 10^{-73}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(z \cdot \left(-k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* a (- (* x y) (* z t))))))
   (if (<= a -9.4e+210)
     (* a (* y5 (- (* t y2) (* y y3))))
     (if (<= a -4.4e+154)
       t_1
       (if (<= a -7e+95)
         (* b (* x (- (* y a) (* j y0))))
         (if (<= a -3.9e-44)
           (* b (* y4 (- (* t j) (* y k))))
           (if (<= a -8.5e-135)
             (* i (* z (* t c)))
             (if (<= a 9e-170)
               (* b (* y0 (- (* z k) (* x j))))
               (if (<= a 1.38e-73) (* i (* y1 (* z (- k)))) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (a * ((x * y) - (z * t)));
	double tmp;
	if (a <= -9.4e+210) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (a <= -4.4e+154) {
		tmp = t_1;
	} else if (a <= -7e+95) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (a <= -3.9e-44) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (a <= -8.5e-135) {
		tmp = i * (z * (t * c));
	} else if (a <= 9e-170) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (a <= 1.38e-73) {
		tmp = i * (y1 * (z * -k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * ((x * y) - (z * t)))
    if (a <= (-9.4d+210)) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (a <= (-4.4d+154)) then
        tmp = t_1
    else if (a <= (-7d+95)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (a <= (-3.9d-44)) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (a <= (-8.5d-135)) then
        tmp = i * (z * (t * c))
    else if (a <= 9d-170) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (a <= 1.38d-73) then
        tmp = i * (y1 * (z * -k))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (a * ((x * y) - (z * t)));
	double tmp;
	if (a <= -9.4e+210) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (a <= -4.4e+154) {
		tmp = t_1;
	} else if (a <= -7e+95) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (a <= -3.9e-44) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (a <= -8.5e-135) {
		tmp = i * (z * (t * c));
	} else if (a <= 9e-170) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (a <= 1.38e-73) {
		tmp = i * (y1 * (z * -k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (a * ((x * y) - (z * t)))
	tmp = 0
	if a <= -9.4e+210:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif a <= -4.4e+154:
		tmp = t_1
	elif a <= -7e+95:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif a <= -3.9e-44:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif a <= -8.5e-135:
		tmp = i * (z * (t * c))
	elif a <= 9e-170:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif a <= 1.38e-73:
		tmp = i * (y1 * (z * -k))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (a <= -9.4e+210)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (a <= -4.4e+154)
		tmp = t_1;
	elseif (a <= -7e+95)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (a <= -3.9e-44)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (a <= -8.5e-135)
		tmp = Float64(i * Float64(z * Float64(t * c)));
	elseif (a <= 9e-170)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (a <= 1.38e-73)
		tmp = Float64(i * Float64(y1 * Float64(z * Float64(-k))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (a * ((x * y) - (z * t)));
	tmp = 0.0;
	if (a <= -9.4e+210)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (a <= -4.4e+154)
		tmp = t_1;
	elseif (a <= -7e+95)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (a <= -3.9e-44)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (a <= -8.5e-135)
		tmp = i * (z * (t * c));
	elseif (a <= 9e-170)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (a <= 1.38e-73)
		tmp = i * (y1 * (z * -k));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.4e+210], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.4e+154], t$95$1, If[LessEqual[a, -7e+95], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.9e-44], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.5e-135], N[(i * N[(z * N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e-170], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.38e-73], N[(i * N[(y1 * N[(z * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -9.4000000000000001e210

   1. Initial program 20.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 20.0%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 28.6%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 28.6%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 28.6%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 28.6%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 28.6%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 56.8%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -9.4000000000000001e210 < a < -4.4000000000000002e154 or 1.37999999999999996e-73 < a

   1. Initial program 27.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.6%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 49.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 51.9%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -4.4000000000000002e154 < a < -6.99999999999999999e95

   1. Initial program 19.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 19.5%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 19.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 62.9%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if -6.99999999999999999e95 < a < -3.9000000000000002e-44

   1. Initial program 20.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 20.7%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y4 around inf 48.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   6. Taylor expanded in b around inf 48.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if -3.9000000000000002e-44 < a < -8.49999999999999942e-135

   1. Initial program 26.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.1%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 21.6%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 21.6%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 21.6%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 21.6%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 21.6%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in z around -inf 44.1%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   9. Taylor expanded in c around inf 36.2%

      \[\leadsto i \cdot \left(z \cdot \color{blue}{\left(c \cdot t\right)}\right) \]

   if -8.49999999999999942e-135 < a < 9.00000000000000003e-170

   1. Initial program 30.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.8%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 38.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y0 around inf 45.4%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if 9.00000000000000003e-170 < a < 1.37999999999999996e-73

   1. Initial program 29.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.0%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 48.4%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 48.4%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 48.4%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 48.4%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 48.4%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in z around -inf 48.9%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   9. Taylor expanded in c around 0 48.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 48.6%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. distribute-rgt-neg-in 48.6%

          \[\leadsto \color{blue}{i \cdot \left(-k \cdot \left(y1 \cdot z\right)\right)} \]

       3. distribute-rgt-neg-in 48.6%

          \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(-y1 \cdot z\right)\right)} \]

       4. distribute-rgt-neg-in 48.6%

          \[\leadsto i \cdot \left(k \cdot \color{blue}{\left(y1 \cdot \left(-z\right)\right)}\right) \]

   11. Simplified 48.6%

       \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y1 \cdot \left(-z\right)\right)\right)} \]

   12. Taylor expanded in i around 0 48.6%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   13. Step-by-step derivation

       1. mul-1-neg 48.6%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. distribute-rgt-neg-in 48.6%

          \[\leadsto \color{blue}{i \cdot \left(-k \cdot \left(y1 \cdot z\right)\right)} \]

       3. *-commutative 48.6%

          \[\leadsto i \cdot \left(-\color{blue}{\left(y1 \cdot z\right) \cdot k}\right) \]

       4. distribute-lft-neg-in 48.6%

          \[\leadsto i \cdot \color{blue}{\left(\left(-y1 \cdot z\right) \cdot k\right)} \]

       5. distribute-rgt-neg-out 48.6%

          \[\leadsto i \cdot \left(\color{blue}{\left(y1 \cdot \left(-z\right)\right)} \cdot k\right) \]

       6. associate-*l* 48.6%

          \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \left(\left(-z\right) \cdot k\right)\right)} \]

       7. distribute-lft-neg-in 48.6%

          \[\leadsto i \cdot \left(y1 \cdot \color{blue}{\left(-z \cdot k\right)}\right) \]

       8. *-commutative 48.6%

          \[\leadsto i \cdot \left(y1 \cdot \left(-\color{blue}{k \cdot z}\right)\right) \]

       9. distribute-rgt-neg-in 48.6%

          \[\leadsto i \cdot \left(y1 \cdot \color{blue}{\left(k \cdot \left(-z\right)\right)}\right) \]

   14. Simplified 48.6%

       \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(k \cdot \left(-z\right)\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.4 \cdot 10^{+210}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{+154}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-170}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 1.38 \cdot 10^{-73}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(z \cdot \left(-k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 19.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -1.1 \cdot 10^{-21}:\\ \;\;\;\;\left(y \cdot b\right) \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y2 \leq -3.8 \cdot 10^{-79}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -9 \cdot 10^{-171}:\\ \;\;\;\;y3 \cdot \left(c \cdot \left(y \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 4.3 \cdot 10^{-249}:\\ \;\;\;\;a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 4.9 \cdot 10^{-133}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(z \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.7 \cdot 10^{-22}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y2 \leq 5 \cdot 10^{+163}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -1.1e-21)
   (* (* y b) (* x a))
   (if (<= y2 -3.8e-79)
     (* j (* y0 (* y3 y5)))
     (if (<= y2 -9e-171)
       (* y3 (* c (* y y4)))
       (if (<= y2 4.3e-249)
         (* a (* y (* y3 (- y5))))
         (if (<= y2 4.9e-133)
           (* i (* y1 (* z (- k))))
           (if (<= y2 1.7e-22)
             (* a (* (* x y) b))
             (if (<= y2 5e+163)
               (* b (* k (* y (- y4))))
               (* a (* t (* y2 y5)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.1e-21) {
		tmp = (y * b) * (x * a);
	} else if (y2 <= -3.8e-79) {
		tmp = j * (y0 * (y3 * y5));
	} else if (y2 <= -9e-171) {
		tmp = y3 * (c * (y * y4));
	} else if (y2 <= 4.3e-249) {
		tmp = a * (y * (y3 * -y5));
	} else if (y2 <= 4.9e-133) {
		tmp = i * (y1 * (z * -k));
	} else if (y2 <= 1.7e-22) {
		tmp = a * ((x * y) * b);
	} else if (y2 <= 5e+163) {
		tmp = b * (k * (y * -y4));
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-1.1d-21)) then
        tmp = (y * b) * (x * a)
    else if (y2 <= (-3.8d-79)) then
        tmp = j * (y0 * (y3 * y5))
    else if (y2 <= (-9d-171)) then
        tmp = y3 * (c * (y * y4))
    else if (y2 <= 4.3d-249) then
        tmp = a * (y * (y3 * -y5))
    else if (y2 <= 4.9d-133) then
        tmp = i * (y1 * (z * -k))
    else if (y2 <= 1.7d-22) then
        tmp = a * ((x * y) * b)
    else if (y2 <= 5d+163) then
        tmp = b * (k * (y * -y4))
    else
        tmp = a * (t * (y2 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.1e-21) {
		tmp = (y * b) * (x * a);
	} else if (y2 <= -3.8e-79) {
		tmp = j * (y0 * (y3 * y5));
	} else if (y2 <= -9e-171) {
		tmp = y3 * (c * (y * y4));
	} else if (y2 <= 4.3e-249) {
		tmp = a * (y * (y3 * -y5));
	} else if (y2 <= 4.9e-133) {
		tmp = i * (y1 * (z * -k));
	} else if (y2 <= 1.7e-22) {
		tmp = a * ((x * y) * b);
	} else if (y2 <= 5e+163) {
		tmp = b * (k * (y * -y4));
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -1.1e-21:
		tmp = (y * b) * (x * a)
	elif y2 <= -3.8e-79:
		tmp = j * (y0 * (y3 * y5))
	elif y2 <= -9e-171:
		tmp = y3 * (c * (y * y4))
	elif y2 <= 4.3e-249:
		tmp = a * (y * (y3 * -y5))
	elif y2 <= 4.9e-133:
		tmp = i * (y1 * (z * -k))
	elif y2 <= 1.7e-22:
		tmp = a * ((x * y) * b)
	elif y2 <= 5e+163:
		tmp = b * (k * (y * -y4))
	else:
		tmp = a * (t * (y2 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -1.1e-21)
		tmp = Float64(Float64(y * b) * Float64(x * a));
	elseif (y2 <= -3.8e-79)
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	elseif (y2 <= -9e-171)
		tmp = Float64(y3 * Float64(c * Float64(y * y4)));
	elseif (y2 <= 4.3e-249)
		tmp = Float64(a * Float64(y * Float64(y3 * Float64(-y5))));
	elseif (y2 <= 4.9e-133)
		tmp = Float64(i * Float64(y1 * Float64(z * Float64(-k))));
	elseif (y2 <= 1.7e-22)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (y2 <= 5e+163)
		tmp = Float64(b * Float64(k * Float64(y * Float64(-y4))));
	else
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -1.1e-21)
		tmp = (y * b) * (x * a);
	elseif (y2 <= -3.8e-79)
		tmp = j * (y0 * (y3 * y5));
	elseif (y2 <= -9e-171)
		tmp = y3 * (c * (y * y4));
	elseif (y2 <= 4.3e-249)
		tmp = a * (y * (y3 * -y5));
	elseif (y2 <= 4.9e-133)
		tmp = i * (y1 * (z * -k));
	elseif (y2 <= 1.7e-22)
		tmp = a * ((x * y) * b);
	elseif (y2 <= 5e+163)
		tmp = b * (k * (y * -y4));
	else
		tmp = a * (t * (y2 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -1.1e-21], N[(N[(y * b), $MachinePrecision] * N[(x * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -3.8e-79], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -9e-171], N[(y3 * N[(c * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.3e-249], N[(a * N[(y * N[(y3 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.9e-133], N[(i * N[(y1 * N[(z * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.7e-22], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5e+163], N[(b * N[(k * N[(y * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y2 < -1.1e-21

   1. Initial program 28.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.4%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 30.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y around -inf 35.9%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 35.9%

         \[\leadsto \color{blue}{-b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]

      2. associate-*r* 34.4%

         \[\leadsto -\color{blue}{\left(b \cdot y\right) \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)} \]

      3. mul-1-neg 34.4%

         \[\leadsto -\left(b \cdot y\right) \cdot \left(\color{blue}{\left(-a \cdot x\right)} + k \cdot y4\right) \]

   8. Simplified 34.4%

      \[\leadsto \color{blue}{-\left(b \cdot y\right) \cdot \left(\left(-a \cdot x\right) + k \cdot y4\right)} \]

   9. Taylor expanded in a around inf 27.8%

      \[\leadsto -\left(b \cdot y\right) \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 27.8%

          \[\leadsto -\left(b \cdot y\right) \cdot \color{blue}{\left(-a \cdot x\right)} \]

       2. distribute-rgt-neg-out 27.8%

          \[\leadsto -\left(b \cdot y\right) \cdot \color{blue}{\left(a \cdot \left(-x\right)\right)} \]

   11. Simplified 27.8%

       \[\leadsto -\left(b \cdot y\right) \cdot \color{blue}{\left(a \cdot \left(-x\right)\right)} \]

   if -1.1e-21 < y2 < -3.8000000000000001e-79

   1. Initial program 23.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.1%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 38.5%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 38.5%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 38.5%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 38.5%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 38.5%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in y3 around -inf 70.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   9. Taylor expanded in y0 around inf 47.7%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 47.7%

          \[\leadsto -1 \cdot \color{blue}{\left(-j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       2. *-commutative 47.7%

          \[\leadsto -1 \cdot \left(-\color{blue}{\left(y0 \cdot \left(y3 \cdot y5\right)\right) \cdot j}\right) \]

       3. distribute-rgt-neg-in 47.7%

          \[\leadsto -1 \cdot \color{blue}{\left(\left(y0 \cdot \left(y3 \cdot y5\right)\right) \cdot \left(-j\right)\right)} \]

   11. Simplified 47.7%

       \[\leadsto -1 \cdot \color{blue}{\left(\left(y0 \cdot \left(y3 \cdot y5\right)\right) \cdot \left(-j\right)\right)} \]

   if -3.8000000000000001e-79 < y2 < -9.0000000000000008e-171

   1. Initial program 30.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.2%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 35.2%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 35.2%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 35.2%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 35.2%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 35.2%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in y3 around -inf 30.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   9. Taylor expanded in c around inf 35.7%

      \[\leadsto -1 \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(y \cdot y4\right)\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 35.7%

          \[\leadsto -1 \cdot \left(y3 \cdot \color{blue}{\left(-c \cdot \left(y \cdot y4\right)\right)}\right) \]

       2. *-commutative 35.7%

          \[\leadsto -1 \cdot \left(y3 \cdot \left(-\color{blue}{\left(y \cdot y4\right) \cdot c}\right)\right) \]

       3. distribute-rgt-neg-in 35.7%

          \[\leadsto -1 \cdot \left(y3 \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot \left(-c\right)\right)}\right) \]

   11. Simplified 35.7%

       \[\leadsto -1 \cdot \left(y3 \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot \left(-c\right)\right)}\right) \]

   if -9.0000000000000008e-171 < y2 < 4.3000000000000002e-249

   1. Initial program 28.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.0%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 28.3%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 28.3%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 28.3%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 28.3%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 28.3%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 37.8%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around 0 40.4%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 40.4%

          \[\leadsto a \cdot \color{blue}{\left(-y \cdot \left(y3 \cdot y5\right)\right)} \]

       2. *-commutative 40.4%

          \[\leadsto a \cdot \left(-\color{blue}{\left(y3 \cdot y5\right) \cdot y}\right) \]

       3. distribute-rgt-neg-in 40.4%

          \[\leadsto a \cdot \color{blue}{\left(\left(y3 \cdot y5\right) \cdot \left(-y\right)\right)} \]

   11. Simplified 40.4%

       \[\leadsto a \cdot \color{blue}{\left(\left(y3 \cdot y5\right) \cdot \left(-y\right)\right)} \]

   if 4.3000000000000002e-249 < y2 < 4.89999999999999996e-133

   1. Initial program 22.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 22.8%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 30.2%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 30.2%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 30.2%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 30.2%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 30.2%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in z around -inf 46.1%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   9. Taylor expanded in c around 0 38.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 38.6%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. distribute-rgt-neg-in 38.6%

          \[\leadsto \color{blue}{i \cdot \left(-k \cdot \left(y1 \cdot z\right)\right)} \]

       3. distribute-rgt-neg-in 38.6%

          \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(-y1 \cdot z\right)\right)} \]

       4. distribute-rgt-neg-in 38.6%

          \[\leadsto i \cdot \left(k \cdot \color{blue}{\left(y1 \cdot \left(-z\right)\right)}\right) \]

   11. Simplified 38.6%

       \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y1 \cdot \left(-z\right)\right)\right)} \]

   12. Taylor expanded in i around 0 38.6%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   13. Step-by-step derivation

       1. mul-1-neg 38.6%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. distribute-rgt-neg-in 38.6%

          \[\leadsto \color{blue}{i \cdot \left(-k \cdot \left(y1 \cdot z\right)\right)} \]

       3. *-commutative 38.6%

          \[\leadsto i \cdot \left(-\color{blue}{\left(y1 \cdot z\right) \cdot k}\right) \]

       4. distribute-lft-neg-in 38.6%

          \[\leadsto i \cdot \color{blue}{\left(\left(-y1 \cdot z\right) \cdot k\right)} \]

       5. distribute-rgt-neg-out 38.6%

          \[\leadsto i \cdot \left(\color{blue}{\left(y1 \cdot \left(-z\right)\right)} \cdot k\right) \]

       6. associate-*l* 45.4%

          \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \left(\left(-z\right) \cdot k\right)\right)} \]

       7. distribute-lft-neg-in 45.4%

          \[\leadsto i \cdot \left(y1 \cdot \color{blue}{\left(-z \cdot k\right)}\right) \]

       8. *-commutative 45.4%

          \[\leadsto i \cdot \left(y1 \cdot \left(-\color{blue}{k \cdot z}\right)\right) \]

       9. distribute-rgt-neg-in 45.4%

          \[\leadsto i \cdot \left(y1 \cdot \color{blue}{\left(k \cdot \left(-z\right)\right)}\right) \]

   14. Simplified 45.4%

       \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(k \cdot \left(-z\right)\right)\right)} \]

   if 4.89999999999999996e-133 < y2 < 1.6999999999999999e-22

   1. Initial program 36.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 36.9%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 41.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y around -inf 41.8%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 41.8%

         \[\leadsto \color{blue}{-b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]

      2. associate-*r* 34.7%

         \[\leadsto -\color{blue}{\left(b \cdot y\right) \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)} \]

      3. mul-1-neg 34.7%

         \[\leadsto -\left(b \cdot y\right) \cdot \left(\color{blue}{\left(-a \cdot x\right)} + k \cdot y4\right) \]

   8. Simplified 34.7%

      \[\leadsto \color{blue}{-\left(b \cdot y\right) \cdot \left(\left(-a \cdot x\right) + k \cdot y4\right)} \]

   9. Taylor expanded in a around inf 49.1%

      \[\leadsto -\color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(x \cdot y\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 49.1%

          \[\leadsto -\color{blue}{\left(-a \cdot \left(b \cdot \left(x \cdot y\right)\right)\right)} \]

       2. *-commutative 49.1%

          \[\leadsto -\left(-\color{blue}{\left(b \cdot \left(x \cdot y\right)\right) \cdot a}\right) \]

       3. distribute-rgt-neg-in 49.1%

          \[\leadsto -\color{blue}{\left(b \cdot \left(x \cdot y\right)\right) \cdot \left(-a\right)} \]

       4. *-commutative 49.1%

          \[\leadsto -\left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \cdot \left(-a\right) \]

   11. Simplified 49.1%

       \[\leadsto -\color{blue}{\left(b \cdot \left(y \cdot x\right)\right) \cdot \left(-a\right)} \]

   if 1.6999999999999999e-22 < y2 < 5e163

   1. Initial program 28.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.3%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 45.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y around -inf 43.0%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 43.0%

         \[\leadsto \color{blue}{-b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]

      2. associate-*r* 33.1%

         \[\leadsto -\color{blue}{\left(b \cdot y\right) \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)} \]

      3. mul-1-neg 33.1%

         \[\leadsto -\left(b \cdot y\right) \cdot \left(\color{blue}{\left(-a \cdot x\right)} + k \cdot y4\right) \]

   8. Simplified 33.1%

      \[\leadsto \color{blue}{-\left(b \cdot y\right) \cdot \left(\left(-a \cdot x\right) + k \cdot y4\right)} \]

   9. Taylor expanded in a around 0 32.8%

      \[\leadsto -\color{blue}{b \cdot \left(k \cdot \left(y \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 32.8%

          \[\leadsto -b \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot k\right)} \]

   11. Simplified 32.8%

       \[\leadsto -\color{blue}{b \cdot \left(\left(y \cdot y4\right) \cdot k\right)} \]

   if 5e163 < y2

   1. Initial program 12.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 12.1%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 12.3%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 12.3%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 12.3%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 12.3%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 12.3%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 41.9%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf 44.5%

      \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 44.5%

          \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   11. Simplified 44.5%

       \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(y5 \cdot y2\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.1 \cdot 10^{-21}:\\ \;\;\;\;\left(y \cdot b\right) \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y2 \leq -3.8 \cdot 10^{-79}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -9 \cdot 10^{-171}:\\ \;\;\;\;y3 \cdot \left(c \cdot \left(y \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 4.3 \cdot 10^{-249}:\\ \;\;\;\;a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 4.9 \cdot 10^{-133}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(z \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.7 \cdot 10^{-22}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y2 \leq 5 \cdot 10^{+163}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 23.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{if}\;x \leq -10000000000000:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{-154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-283}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-152}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+50}:\\ \;\;\;\;y3 \cdot \left(a \cdot \left(y \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+177}:\\ \;\;\;\;y \cdot \left(c \cdot \left(x \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* k (* z y0)))))
   (if (<= x -10000000000000.0)
     (* a (* (* x y) b))
     (if (<= x -1.22e-154)
       t_1
       (if (<= x 1.3e-283)
         (* b (* k (* y (- y4))))
         (if (<= x 1.35e-152)
           (* a (* y5 (* y (- y3))))
           (if (<= x 9e-109)
             t_1
             (if (<= x 3.7e+50)
               (* y3 (* a (* y (- y5))))
               (if (<= x 6e+177)
                 (* y (* c (* x (- i))))
                 (* b (* j (* 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 t_1 = b * (k * (z * y0));
	double tmp;
	if (x <= -10000000000000.0) {
		tmp = a * ((x * y) * b);
	} else if (x <= -1.22e-154) {
		tmp = t_1;
	} else if (x <= 1.3e-283) {
		tmp = b * (k * (y * -y4));
	} else if (x <= 1.35e-152) {
		tmp = a * (y5 * (y * -y3));
	} else if (x <= 9e-109) {
		tmp = t_1;
	} else if (x <= 3.7e+50) {
		tmp = y3 * (a * (y * -y5));
	} else if (x <= 6e+177) {
		tmp = y * (c * (x * -i));
	} else {
		tmp = b * (j * (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) :: t_1
    real(8) :: tmp
    t_1 = b * (k * (z * y0))
    if (x <= (-10000000000000.0d0)) then
        tmp = a * ((x * y) * b)
    else if (x <= (-1.22d-154)) then
        tmp = t_1
    else if (x <= 1.3d-283) then
        tmp = b * (k * (y * -y4))
    else if (x <= 1.35d-152) then
        tmp = a * (y5 * (y * -y3))
    else if (x <= 9d-109) then
        tmp = t_1
    else if (x <= 3.7d+50) then
        tmp = y3 * (a * (y * -y5))
    else if (x <= 6d+177) then
        tmp = y * (c * (x * -i))
    else
        tmp = b * (j * (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 t_1 = b * (k * (z * y0));
	double tmp;
	if (x <= -10000000000000.0) {
		tmp = a * ((x * y) * b);
	} else if (x <= -1.22e-154) {
		tmp = t_1;
	} else if (x <= 1.3e-283) {
		tmp = b * (k * (y * -y4));
	} else if (x <= 1.35e-152) {
		tmp = a * (y5 * (y * -y3));
	} else if (x <= 9e-109) {
		tmp = t_1;
	} else if (x <= 3.7e+50) {
		tmp = y3 * (a * (y * -y5));
	} else if (x <= 6e+177) {
		tmp = y * (c * (x * -i));
	} else {
		tmp = b * (j * (x * -y0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (k * (z * y0))
	tmp = 0
	if x <= -10000000000000.0:
		tmp = a * ((x * y) * b)
	elif x <= -1.22e-154:
		tmp = t_1
	elif x <= 1.3e-283:
		tmp = b * (k * (y * -y4))
	elif x <= 1.35e-152:
		tmp = a * (y5 * (y * -y3))
	elif x <= 9e-109:
		tmp = t_1
	elif x <= 3.7e+50:
		tmp = y3 * (a * (y * -y5))
	elif x <= 6e+177:
		tmp = y * (c * (x * -i))
	else:
		tmp = b * (j * (x * -y0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(k * Float64(z * y0)))
	tmp = 0.0
	if (x <= -10000000000000.0)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (x <= -1.22e-154)
		tmp = t_1;
	elseif (x <= 1.3e-283)
		tmp = Float64(b * Float64(k * Float64(y * Float64(-y4))));
	elseif (x <= 1.35e-152)
		tmp = Float64(a * Float64(y5 * Float64(y * Float64(-y3))));
	elseif (x <= 9e-109)
		tmp = t_1;
	elseif (x <= 3.7e+50)
		tmp = Float64(y3 * Float64(a * Float64(y * Float64(-y5))));
	elseif (x <= 6e+177)
		tmp = Float64(y * Float64(c * Float64(x * Float64(-i))));
	else
		tmp = Float64(b * Float64(j * Float64(x * Float64(-y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (k * (z * y0));
	tmp = 0.0;
	if (x <= -10000000000000.0)
		tmp = a * ((x * y) * b);
	elseif (x <= -1.22e-154)
		tmp = t_1;
	elseif (x <= 1.3e-283)
		tmp = b * (k * (y * -y4));
	elseif (x <= 1.35e-152)
		tmp = a * (y5 * (y * -y3));
	elseif (x <= 9e-109)
		tmp = t_1;
	elseif (x <= 3.7e+50)
		tmp = y3 * (a * (y * -y5));
	elseif (x <= 6e+177)
		tmp = y * (c * (x * -i));
	else
		tmp = b * (j * (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_] := Block[{t$95$1 = N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -10000000000000.0], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.22e-154], t$95$1, If[LessEqual[x, 1.3e-283], N[(b * N[(k * N[(y * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.35e-152], N[(a * N[(y5 * N[(y * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e-109], t$95$1, If[LessEqual[x, 3.7e+50], N[(y3 * N[(a * N[(y * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e+177], N[(y * N[(c * N[(x * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(j * N[(x * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -1e13

   1. Initial program 18.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 18.6%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 40.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y around -inf 48.3%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 48.3%

         \[\leadsto \color{blue}{-b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]

      2. associate-*r* 44.7%

         \[\leadsto -\color{blue}{\left(b \cdot y\right) \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)} \]

      3. mul-1-neg 44.7%

         \[\leadsto -\left(b \cdot y\right) \cdot \left(\color{blue}{\left(-a \cdot x\right)} + k \cdot y4\right) \]

   8. Simplified 44.7%

      \[\leadsto \color{blue}{-\left(b \cdot y\right) \cdot \left(\left(-a \cdot x\right) + k \cdot y4\right)} \]

   9. Taylor expanded in a around inf 42.9%

      \[\leadsto -\color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(x \cdot y\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 42.9%

          \[\leadsto -\color{blue}{\left(-a \cdot \left(b \cdot \left(x \cdot y\right)\right)\right)} \]

       2. *-commutative 42.9%

          \[\leadsto -\left(-\color{blue}{\left(b \cdot \left(x \cdot y\right)\right) \cdot a}\right) \]

       3. distribute-rgt-neg-in 42.9%

          \[\leadsto -\color{blue}{\left(b \cdot \left(x \cdot y\right)\right) \cdot \left(-a\right)} \]

       4. *-commutative 42.9%

          \[\leadsto -\left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \cdot \left(-a\right) \]

   11. Simplified 42.9%

       \[\leadsto -\color{blue}{\left(b \cdot \left(y \cdot x\right)\right) \cdot \left(-a\right)} \]

   if -1e13 < x < -1.22000000000000005e-154 or 1.34999999999999999e-152 < x < 9.0000000000000002e-109

   1. Initial program 23.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.0%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 34.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 42.0%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 42.0%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 42.0%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 42.0%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 42.1%

      \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 42.1%

          \[\leadsto b \cdot \left(k \cdot \color{blue}{\left(z \cdot y0\right)}\right) \]

   11. Simplified 42.1%

       \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(z \cdot y0\right)\right)} \]

   if -1.22000000000000005e-154 < x < 1.3000000000000001e-283

   1. Initial program 30.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.3%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 43.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y around -inf 31.6%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 31.6%

         \[\leadsto \color{blue}{-b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]

      2. associate-*r* 33.3%

         \[\leadsto -\color{blue}{\left(b \cdot y\right) \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)} \]

      3. mul-1-neg 33.3%

         \[\leadsto -\left(b \cdot y\right) \cdot \left(\color{blue}{\left(-a \cdot x\right)} + k \cdot y4\right) \]

   8. Simplified 33.3%

      \[\leadsto \color{blue}{-\left(b \cdot y\right) \cdot \left(\left(-a \cdot x\right) + k \cdot y4\right)} \]

   9. Taylor expanded in a around 0 29.2%

      \[\leadsto -\color{blue}{b \cdot \left(k \cdot \left(y \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 29.2%

          \[\leadsto -b \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot k\right)} \]

   11. Simplified 29.2%

       \[\leadsto -\color{blue}{b \cdot \left(\left(y \cdot y4\right) \cdot k\right)} \]

   if 1.3000000000000001e-283 < x < 1.34999999999999999e-152

   1. Initial program 50.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 50.1%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 56.8%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 56.8%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 56.8%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 56.8%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 56.8%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 35.5%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around 0 35.7%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y3\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 35.7%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(-y \cdot y3\right)}\right) \]

       2. distribute-lft-neg-out 35.7%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(\left(-y\right) \cdot y3\right)}\right) \]

       3. *-commutative 35.7%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y3 \cdot \left(-y\right)\right)}\right) \]

   11. Simplified 35.7%

       \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y3 \cdot \left(-y\right)\right)}\right) \]

   if 9.0000000000000002e-109 < x < 3.7000000000000001e50

   1. Initial program 21.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.9%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 29.4%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 29.4%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 29.4%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 29.4%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 29.4%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in y3 around -inf 39.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   9. Taylor expanded in a around inf 37.7%

      \[\leadsto -1 \cdot \left(y3 \cdot \color{blue}{\left(a \cdot \left(y \cdot y5\right)\right)}\right) \]

   if 3.7000000000000001e50 < x < 6e177

   1. Initial program 27.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.8%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 25.1%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 25.1%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 25.1%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 25.1%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 25.1%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in y around inf 45.4%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 45.4%

         \[\leadsto y \cdot \left(\color{blue}{\left(-1 \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)} - \left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right) \]

      2. neg-mul-1 45.4%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right) \]

      3. mul-1-neg 45.4%

         \[\leadsto y \cdot \left(\left(-k\right) \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(\color{blue}{\left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + c \cdot \left(i \cdot x\right)\right)\right) \]

   10. Simplified 45.4%

       \[\leadsto \color{blue}{y \cdot \left(\left(-k\right) \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(\left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right)} \]

   11. Taylor expanded in x around inf 39.1%

       \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot x\right)\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg 39.1%

          \[\leadsto y \cdot \color{blue}{\left(-c \cdot \left(i \cdot x\right)\right)} \]

       2. distribute-rgt-neg-in 39.1%

          \[\leadsto y \cdot \color{blue}{\left(c \cdot \left(-i \cdot x\right)\right)} \]

       3. distribute-rgt-neg-in 39.1%

          \[\leadsto y \cdot \left(c \cdot \color{blue}{\left(i \cdot \left(-x\right)\right)}\right) \]

   13. Simplified 39.1%

       \[\leadsto y \cdot \color{blue}{\left(c \cdot \left(i \cdot \left(-x\right)\right)\right)} \]

   if 6e177 < x

   1. Initial program 14.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 14.9%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 40.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 60.2%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around 0 50.2%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot \left(x \cdot y0\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 50.2%

         \[\leadsto \color{blue}{-b \cdot \left(j \cdot \left(x \cdot y0\right)\right)} \]

      2. *-commutative 50.2%

         \[\leadsto -\color{blue}{\left(j \cdot \left(x \cdot y0\right)\right) \cdot b} \]

      3. distribute-rgt-neg-in 50.2%

         \[\leadsto \color{blue}{\left(j \cdot \left(x \cdot y0\right)\right) \cdot \left(-b\right)} \]

   9. Simplified 50.2%

      \[\leadsto \color{blue}{\left(j \cdot \left(x \cdot y0\right)\right) \cdot \left(-b\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -10000000000000:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{-154}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-283}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-152}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-109}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+50}:\\ \;\;\;\;y3 \cdot \left(a \cdot \left(y \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+177}:\\ \;\;\;\;y \cdot \left(c \cdot \left(x \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 28.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;j \leq -1.55 \cdot 10^{+172}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -2.4 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -700:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{-251}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.35 \cdot 10^{+111}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* a (- (* x y) (* z t))))))
   (if (<= j -1.55e+172)
     (* y0 (* y2 (- (* x c) (* k y5))))
     (if (<= j -2.4e+148)
       t_1
       (if (<= j -700.0)
         (* b (* x (- (* y a) (* j y0))))
         (if (<= j 6.4e-251)
           (* y2 (* y4 (- (* k y1) (* t c))))
           (if (<= j 6.2e-99)
             t_1
             (if (<= j 2.35e+111)
               (* y1 (* z (- (* a y3) (* i k))))
               (* y1 (* y4 (- (* k y2) (* j y3))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (a * ((x * y) - (z * t)));
	double tmp;
	if (j <= -1.55e+172) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (j <= -2.4e+148) {
		tmp = t_1;
	} else if (j <= -700.0) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (j <= 6.4e-251) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (j <= 6.2e-99) {
		tmp = t_1;
	} else if (j <= 2.35e+111) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * ((x * y) - (z * t)))
    if (j <= (-1.55d+172)) then
        tmp = y0 * (y2 * ((x * c) - (k * y5)))
    else if (j <= (-2.4d+148)) then
        tmp = t_1
    else if (j <= (-700.0d0)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (j <= 6.4d-251) then
        tmp = y2 * (y4 * ((k * y1) - (t * c)))
    else if (j <= 6.2d-99) then
        tmp = t_1
    else if (j <= 2.35d+111) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (a * ((x * y) - (z * t)));
	double tmp;
	if (j <= -1.55e+172) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (j <= -2.4e+148) {
		tmp = t_1;
	} else if (j <= -700.0) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (j <= 6.4e-251) {
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	} else if (j <= 6.2e-99) {
		tmp = t_1;
	} else if (j <= 2.35e+111) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (a * ((x * y) - (z * t)))
	tmp = 0
	if j <= -1.55e+172:
		tmp = y0 * (y2 * ((x * c) - (k * y5)))
	elif j <= -2.4e+148:
		tmp = t_1
	elif j <= -700.0:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif j <= 6.4e-251:
		tmp = y2 * (y4 * ((k * y1) - (t * c)))
	elif j <= 6.2e-99:
		tmp = t_1
	elif j <= 2.35e+111:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	else:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (j <= -1.55e+172)
		tmp = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))));
	elseif (j <= -2.4e+148)
		tmp = t_1;
	elseif (j <= -700.0)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (j <= 6.4e-251)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (j <= 6.2e-99)
		tmp = t_1;
	elseif (j <= 2.35e+111)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	else
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (a * ((x * y) - (z * t)));
	tmp = 0.0;
	if (j <= -1.55e+172)
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	elseif (j <= -2.4e+148)
		tmp = t_1;
	elseif (j <= -700.0)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (j <= 6.4e-251)
		tmp = y2 * (y4 * ((k * y1) - (t * c)));
	elseif (j <= 6.2e-99)
		tmp = t_1;
	elseif (j <= 2.35e+111)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	else
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.55e+172], N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.4e+148], t$95$1, If[LessEqual[j, -700.0], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.4e-251], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.2e-99], t$95$1, If[LessEqual[j, 2.35e+111], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -1.54999999999999994e172

   1. Initial program 17.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 17.4%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y0 around inf 44.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 44.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 44.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 44.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 44.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 44.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 44.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 44.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   7. Simplified 44.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   8. Taylor expanded in y2 around inf 57.0%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(c \cdot x - k \cdot y5\right)\right)} \]

   if -1.54999999999999994e172 < j < -2.39999999999999995e148 or 6.39999999999999963e-251 < j < 6.1999999999999997e-99

   1. Initial program 32.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.7%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 56.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 56.2%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -2.39999999999999995e148 < j < -700

   1. Initial program 19.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 19.3%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 32.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 46.5%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if -700 < j < 6.39999999999999963e-251

   1. Initial program 30.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.5%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y4 around inf 48.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   6. Taylor expanded in y2 around inf 52.8%

      \[\leadsto \color{blue}{y2 \cdot \left(y4 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]

   if 6.1999999999999997e-99 < j < 2.35000000000000004e111

   1. Initial program 35.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.7%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y1 around inf 41.2%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 41.2%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 41.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 41.2%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 41.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 41.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 41.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 41.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 41.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   7. Simplified 41.2%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   8. Taylor expanded in z around -inf 51.1%

      \[\leadsto y1 \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(i \cdot k - a \cdot y3\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 51.1%

         \[\leadsto y1 \cdot \color{blue}{\left(-z \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]

   10. Simplified 51.1%

       \[\leadsto y1 \cdot \color{blue}{\left(-z \cdot \left(i \cdot k - a \cdot y3\right)\right)} \]

   if 2.35000000000000004e111 < j

   1. Initial program 13.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 13.6%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y4 around inf 50.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   6. Taylor expanded in y1 around inf 46.5%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.55 \cdot 10^{+172}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -2.4 \cdot 10^{+148}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq -700:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{-251}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-99}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 2.35 \cdot 10^{+111}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 21.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{if}\;x \leq -1350000000000:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-284}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-139}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 96000000000:\\ \;\;\;\;y \cdot \left(a \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot b\right) \cdot \left(x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* k (* z y0)))))
   (if (<= x -1350000000000.0)
     (* a (* (* x y) b))
     (if (<= x -4.6e-155)
       t_1
       (if (<= x 7e-284)
         (* b (* k (* y (- y4))))
         (if (<= x 5.3e-139)
           (* a (* y5 (* y (- y3))))
           (if (<= x 3e-108)
             t_1
             (if (<= x 96000000000.0)
               (* y (* a (* y3 (- y5))))
               (* (* y b) (* x a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (k * (z * y0));
	double tmp;
	if (x <= -1350000000000.0) {
		tmp = a * ((x * y) * b);
	} else if (x <= -4.6e-155) {
		tmp = t_1;
	} else if (x <= 7e-284) {
		tmp = b * (k * (y * -y4));
	} else if (x <= 5.3e-139) {
		tmp = a * (y5 * (y * -y3));
	} else if (x <= 3e-108) {
		tmp = t_1;
	} else if (x <= 96000000000.0) {
		tmp = y * (a * (y3 * -y5));
	} else {
		tmp = (y * b) * (x * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (k * (z * y0))
    if (x <= (-1350000000000.0d0)) then
        tmp = a * ((x * y) * b)
    else if (x <= (-4.6d-155)) then
        tmp = t_1
    else if (x <= 7d-284) then
        tmp = b * (k * (y * -y4))
    else if (x <= 5.3d-139) then
        tmp = a * (y5 * (y * -y3))
    else if (x <= 3d-108) then
        tmp = t_1
    else if (x <= 96000000000.0d0) then
        tmp = y * (a * (y3 * -y5))
    else
        tmp = (y * b) * (x * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (k * (z * y0));
	double tmp;
	if (x <= -1350000000000.0) {
		tmp = a * ((x * y) * b);
	} else if (x <= -4.6e-155) {
		tmp = t_1;
	} else if (x <= 7e-284) {
		tmp = b * (k * (y * -y4));
	} else if (x <= 5.3e-139) {
		tmp = a * (y5 * (y * -y3));
	} else if (x <= 3e-108) {
		tmp = t_1;
	} else if (x <= 96000000000.0) {
		tmp = y * (a * (y3 * -y5));
	} else {
		tmp = (y * b) * (x * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (k * (z * y0))
	tmp = 0
	if x <= -1350000000000.0:
		tmp = a * ((x * y) * b)
	elif x <= -4.6e-155:
		tmp = t_1
	elif x <= 7e-284:
		tmp = b * (k * (y * -y4))
	elif x <= 5.3e-139:
		tmp = a * (y5 * (y * -y3))
	elif x <= 3e-108:
		tmp = t_1
	elif x <= 96000000000.0:
		tmp = y * (a * (y3 * -y5))
	else:
		tmp = (y * b) * (x * a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(k * Float64(z * y0)))
	tmp = 0.0
	if (x <= -1350000000000.0)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (x <= -4.6e-155)
		tmp = t_1;
	elseif (x <= 7e-284)
		tmp = Float64(b * Float64(k * Float64(y * Float64(-y4))));
	elseif (x <= 5.3e-139)
		tmp = Float64(a * Float64(y5 * Float64(y * Float64(-y3))));
	elseif (x <= 3e-108)
		tmp = t_1;
	elseif (x <= 96000000000.0)
		tmp = Float64(y * Float64(a * Float64(y3 * Float64(-y5))));
	else
		tmp = Float64(Float64(y * b) * Float64(x * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (k * (z * y0));
	tmp = 0.0;
	if (x <= -1350000000000.0)
		tmp = a * ((x * y) * b);
	elseif (x <= -4.6e-155)
		tmp = t_1;
	elseif (x <= 7e-284)
		tmp = b * (k * (y * -y4));
	elseif (x <= 5.3e-139)
		tmp = a * (y5 * (y * -y3));
	elseif (x <= 3e-108)
		tmp = t_1;
	elseif (x <= 96000000000.0)
		tmp = y * (a * (y3 * -y5));
	else
		tmp = (y * b) * (x * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1350000000000.0], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.6e-155], t$95$1, If[LessEqual[x, 7e-284], N[(b * N[(k * N[(y * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.3e-139], N[(a * N[(y5 * N[(y * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e-108], t$95$1, If[LessEqual[x, 96000000000.0], N[(y * N[(a * N[(y3 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * b), $MachinePrecision] * N[(x * a), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.35e12

   1. Initial program 18.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 18.6%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 40.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y around -inf 48.3%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 48.3%

         \[\leadsto \color{blue}{-b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]

      2. associate-*r* 44.7%

         \[\leadsto -\color{blue}{\left(b \cdot y\right) \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)} \]

      3. mul-1-neg 44.7%

         \[\leadsto -\left(b \cdot y\right) \cdot \left(\color{blue}{\left(-a \cdot x\right)} + k \cdot y4\right) \]

   8. Simplified 44.7%

      \[\leadsto \color{blue}{-\left(b \cdot y\right) \cdot \left(\left(-a \cdot x\right) + k \cdot y4\right)} \]

   9. Taylor expanded in a around inf 42.9%

      \[\leadsto -\color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(x \cdot y\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 42.9%

          \[\leadsto -\color{blue}{\left(-a \cdot \left(b \cdot \left(x \cdot y\right)\right)\right)} \]

       2. *-commutative 42.9%

          \[\leadsto -\left(-\color{blue}{\left(b \cdot \left(x \cdot y\right)\right) \cdot a}\right) \]

       3. distribute-rgt-neg-in 42.9%

          \[\leadsto -\color{blue}{\left(b \cdot \left(x \cdot y\right)\right) \cdot \left(-a\right)} \]

       4. *-commutative 42.9%

          \[\leadsto -\left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \cdot \left(-a\right) \]

   11. Simplified 42.9%

       \[\leadsto -\color{blue}{\left(b \cdot \left(y \cdot x\right)\right) \cdot \left(-a\right)} \]

   if -1.35e12 < x < -4.60000000000000011e-155 or 5.2999999999999997e-139 < x < 2.99999999999999993e-108

   1. Initial program 23.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.0%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 34.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 42.0%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 42.0%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 42.0%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 42.0%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 42.1%

      \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 42.1%

          \[\leadsto b \cdot \left(k \cdot \color{blue}{\left(z \cdot y0\right)}\right) \]

   11. Simplified 42.1%

       \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(z \cdot y0\right)\right)} \]

   if -4.60000000000000011e-155 < x < 6.99999999999999951e-284

   1. Initial program 30.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.3%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 43.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y around -inf 31.6%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 31.6%

         \[\leadsto \color{blue}{-b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]

      2. associate-*r* 33.3%

         \[\leadsto -\color{blue}{\left(b \cdot y\right) \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)} \]

      3. mul-1-neg 33.3%

         \[\leadsto -\left(b \cdot y\right) \cdot \left(\color{blue}{\left(-a \cdot x\right)} + k \cdot y4\right) \]

   8. Simplified 33.3%

      \[\leadsto \color{blue}{-\left(b \cdot y\right) \cdot \left(\left(-a \cdot x\right) + k \cdot y4\right)} \]

   9. Taylor expanded in a around 0 29.2%

      \[\leadsto -\color{blue}{b \cdot \left(k \cdot \left(y \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 29.2%

          \[\leadsto -b \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot k\right)} \]

   11. Simplified 29.2%

       \[\leadsto -\color{blue}{b \cdot \left(\left(y \cdot y4\right) \cdot k\right)} \]

   if 6.99999999999999951e-284 < x < 5.2999999999999997e-139

   1. Initial program 50.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 50.1%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 56.8%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 56.8%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 56.8%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 56.8%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 56.8%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 35.5%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around 0 35.7%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y3\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 35.7%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(-y \cdot y3\right)}\right) \]

       2. distribute-lft-neg-out 35.7%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(\left(-y\right) \cdot y3\right)}\right) \]

       3. *-commutative 35.7%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y3 \cdot \left(-y\right)\right)}\right) \]

   11. Simplified 35.7%

       \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y3 \cdot \left(-y\right)\right)}\right) \]

   if 2.99999999999999993e-108 < x < 9.6e10

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.0%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 25.2%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 25.2%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 25.2%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 25.2%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 25.2%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in y around inf 38.7%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 38.7%

         \[\leadsto y \cdot \left(\color{blue}{\left(-1 \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)} - \left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right) \]

      2. neg-mul-1 38.7%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right) \]

      3. mul-1-neg 38.7%

         \[\leadsto y \cdot \left(\left(-k\right) \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(\color{blue}{\left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + c \cdot \left(i \cdot x\right)\right)\right) \]

   10. Simplified 38.7%

       \[\leadsto \color{blue}{y \cdot \left(\left(-k\right) \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(\left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right)} \]

   11. Taylor expanded in a around inf 36.2%

       \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg 36.2%

          \[\leadsto y \cdot \color{blue}{\left(-a \cdot \left(y3 \cdot y5\right)\right)} \]

       2. distribute-rgt-neg-in 36.2%

          \[\leadsto y \cdot \color{blue}{\left(a \cdot \left(-y3 \cdot y5\right)\right)} \]

       3. distribute-rgt-neg-in 36.2%

          \[\leadsto y \cdot \left(a \cdot \color{blue}{\left(y3 \cdot \left(-y5\right)\right)}\right) \]

   13. Simplified 36.2%

       \[\leadsto y \cdot \color{blue}{\left(a \cdot \left(y3 \cdot \left(-y5\right)\right)\right)} \]

   if 9.6e10 < x

   1. Initial program 20.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 20.8%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 43.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y around -inf 40.4%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 40.4%

         \[\leadsto \color{blue}{-b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]

      2. associate-*r* 32.3%

         \[\leadsto -\color{blue}{\left(b \cdot y\right) \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)} \]

      3. mul-1-neg 32.3%

         \[\leadsto -\left(b \cdot y\right) \cdot \left(\color{blue}{\left(-a \cdot x\right)} + k \cdot y4\right) \]

   8. Simplified 32.3%

      \[\leadsto \color{blue}{-\left(b \cdot y\right) \cdot \left(\left(-a \cdot x\right) + k \cdot y4\right)} \]

   9. Taylor expanded in a around inf 35.7%

      \[\leadsto -\left(b \cdot y\right) \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 35.7%

          \[\leadsto -\left(b \cdot y\right) \cdot \color{blue}{\left(-a \cdot x\right)} \]

       2. distribute-rgt-neg-out 35.7%

          \[\leadsto -\left(b \cdot y\right) \cdot \color{blue}{\left(a \cdot \left(-x\right)\right)} \]

   11. Simplified 35.7%

       \[\leadsto -\left(b \cdot y\right) \cdot \color{blue}{\left(a \cdot \left(-x\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1350000000000:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-155}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-284}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-139}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-108}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 96000000000:\\ \;\;\;\;y \cdot \left(a \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot b\right) \cdot \left(x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 21.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot b\right) \cdot \left(x \cdot a\right)\\ t_2 := b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{if}\;x \leq -1750000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{-154}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-284}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-151}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-109}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 235000000000:\\ \;\;\;\;y \cdot \left(a \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* y b) (* x a))) (t_2 (* b (* k (* z y0)))))
   (if (<= x -1750000000000.0)
     t_1
     (if (<= x -2.45e-154)
       t_2
       (if (<= x 5.1e-284)
         (* b (* k (* y (- y4))))
         (if (<= x 6.5e-151)
           (* a (* y5 (* y (- y3))))
           (if (<= x 7e-109)
             t_2
             (if (<= x 235000000000.0) (* y (* a (* y3 (- y5)))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * b) * (x * a);
	double t_2 = b * (k * (z * y0));
	double tmp;
	if (x <= -1750000000000.0) {
		tmp = t_1;
	} else if (x <= -2.45e-154) {
		tmp = t_2;
	} else if (x <= 5.1e-284) {
		tmp = b * (k * (y * -y4));
	} else if (x <= 6.5e-151) {
		tmp = a * (y5 * (y * -y3));
	} else if (x <= 7e-109) {
		tmp = t_2;
	} else if (x <= 235000000000.0) {
		tmp = y * (a * (y3 * -y5));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * b) * (x * a)
    t_2 = b * (k * (z * y0))
    if (x <= (-1750000000000.0d0)) then
        tmp = t_1
    else if (x <= (-2.45d-154)) then
        tmp = t_2
    else if (x <= 5.1d-284) then
        tmp = b * (k * (y * -y4))
    else if (x <= 6.5d-151) then
        tmp = a * (y5 * (y * -y3))
    else if (x <= 7d-109) then
        tmp = t_2
    else if (x <= 235000000000.0d0) then
        tmp = y * (a * (y3 * -y5))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * b) * (x * a);
	double t_2 = b * (k * (z * y0));
	double tmp;
	if (x <= -1750000000000.0) {
		tmp = t_1;
	} else if (x <= -2.45e-154) {
		tmp = t_2;
	} else if (x <= 5.1e-284) {
		tmp = b * (k * (y * -y4));
	} else if (x <= 6.5e-151) {
		tmp = a * (y5 * (y * -y3));
	} else if (x <= 7e-109) {
		tmp = t_2;
	} else if (x <= 235000000000.0) {
		tmp = y * (a * (y3 * -y5));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y * b) * (x * a)
	t_2 = b * (k * (z * y0))
	tmp = 0
	if x <= -1750000000000.0:
		tmp = t_1
	elif x <= -2.45e-154:
		tmp = t_2
	elif x <= 5.1e-284:
		tmp = b * (k * (y * -y4))
	elif x <= 6.5e-151:
		tmp = a * (y5 * (y * -y3))
	elif x <= 7e-109:
		tmp = t_2
	elif x <= 235000000000.0:
		tmp = y * (a * (y3 * -y5))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * b) * Float64(x * a))
	t_2 = Float64(b * Float64(k * Float64(z * y0)))
	tmp = 0.0
	if (x <= -1750000000000.0)
		tmp = t_1;
	elseif (x <= -2.45e-154)
		tmp = t_2;
	elseif (x <= 5.1e-284)
		tmp = Float64(b * Float64(k * Float64(y * Float64(-y4))));
	elseif (x <= 6.5e-151)
		tmp = Float64(a * Float64(y5 * Float64(y * Float64(-y3))));
	elseif (x <= 7e-109)
		tmp = t_2;
	elseif (x <= 235000000000.0)
		tmp = Float64(y * Float64(a * Float64(y3 * Float64(-y5))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y * b) * (x * a);
	t_2 = b * (k * (z * y0));
	tmp = 0.0;
	if (x <= -1750000000000.0)
		tmp = t_1;
	elseif (x <= -2.45e-154)
		tmp = t_2;
	elseif (x <= 5.1e-284)
		tmp = b * (k * (y * -y4));
	elseif (x <= 6.5e-151)
		tmp = a * (y5 * (y * -y3));
	elseif (x <= 7e-109)
		tmp = t_2;
	elseif (x <= 235000000000.0)
		tmp = y * (a * (y3 * -y5));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] * N[(x * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1750000000000.0], t$95$1, If[LessEqual[x, -2.45e-154], t$95$2, If[LessEqual[x, 5.1e-284], N[(b * N[(k * N[(y * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e-151], N[(a * N[(y5 * N[(y * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e-109], t$95$2, If[LessEqual[x, 235000000000.0], N[(y * N[(a * N[(y3 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.75e12 or 2.35e11 < x

   1. Initial program 19.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 19.7%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 42.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y around -inf 44.2%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 44.2%

         \[\leadsto \color{blue}{-b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]

      2. associate-*r* 38.3%

         \[\leadsto -\color{blue}{\left(b \cdot y\right) \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)} \]

      3. mul-1-neg 38.3%

         \[\leadsto -\left(b \cdot y\right) \cdot \left(\color{blue}{\left(-a \cdot x\right)} + k \cdot y4\right) \]

   8. Simplified 38.3%

      \[\leadsto \color{blue}{-\left(b \cdot y\right) \cdot \left(\left(-a \cdot x\right) + k \cdot y4\right)} \]

   9. Taylor expanded in a around inf 39.2%

      \[\leadsto -\left(b \cdot y\right) \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 39.2%

          \[\leadsto -\left(b \cdot y\right) \cdot \color{blue}{\left(-a \cdot x\right)} \]

       2. distribute-rgt-neg-out 39.2%

          \[\leadsto -\left(b \cdot y\right) \cdot \color{blue}{\left(a \cdot \left(-x\right)\right)} \]

   11. Simplified 39.2%

       \[\leadsto -\left(b \cdot y\right) \cdot \color{blue}{\left(a \cdot \left(-x\right)\right)} \]

   if -1.75e12 < x < -2.44999999999999998e-154 or 6.4999999999999994e-151 < x < 7e-109

   1. Initial program 23.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.0%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 34.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 42.0%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 42.0%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 42.0%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 42.0%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 42.1%

      \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 42.1%

          \[\leadsto b \cdot \left(k \cdot \color{blue}{\left(z \cdot y0\right)}\right) \]

   11. Simplified 42.1%

       \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(z \cdot y0\right)\right)} \]

   if -2.44999999999999998e-154 < x < 5.1000000000000002e-284

   1. Initial program 30.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.3%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 43.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y around -inf 31.6%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 31.6%

         \[\leadsto \color{blue}{-b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]

      2. associate-*r* 33.3%

         \[\leadsto -\color{blue}{\left(b \cdot y\right) \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)} \]

      3. mul-1-neg 33.3%

         \[\leadsto -\left(b \cdot y\right) \cdot \left(\color{blue}{\left(-a \cdot x\right)} + k \cdot y4\right) \]

   8. Simplified 33.3%

      \[\leadsto \color{blue}{-\left(b \cdot y\right) \cdot \left(\left(-a \cdot x\right) + k \cdot y4\right)} \]

   9. Taylor expanded in a around 0 29.2%

      \[\leadsto -\color{blue}{b \cdot \left(k \cdot \left(y \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 29.2%

          \[\leadsto -b \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot k\right)} \]

   11. Simplified 29.2%

       \[\leadsto -\color{blue}{b \cdot \left(\left(y \cdot y4\right) \cdot k\right)} \]

   if 5.1000000000000002e-284 < x < 6.4999999999999994e-151

   1. Initial program 50.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 50.1%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 56.8%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 56.8%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 56.8%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 56.8%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 56.8%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 35.5%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around 0 35.7%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y3\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 35.7%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(-y \cdot y3\right)}\right) \]

       2. distribute-lft-neg-out 35.7%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(\left(-y\right) \cdot y3\right)}\right) \]

       3. *-commutative 35.7%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y3 \cdot \left(-y\right)\right)}\right) \]

   11. Simplified 35.7%

       \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y3 \cdot \left(-y\right)\right)}\right) \]

   if 7e-109 < x < 2.35e11

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.0%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 25.2%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 25.2%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 25.2%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 25.2%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 25.2%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in y around inf 38.7%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 38.7%

         \[\leadsto y \cdot \left(\color{blue}{\left(-1 \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)} - \left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right) \]

      2. neg-mul-1 38.7%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right) \]

      3. mul-1-neg 38.7%

         \[\leadsto y \cdot \left(\left(-k\right) \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(\color{blue}{\left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + c \cdot \left(i \cdot x\right)\right)\right) \]

   10. Simplified 38.7%

       \[\leadsto \color{blue}{y \cdot \left(\left(-k\right) \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(\left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right)} \]

   11. Taylor expanded in a around inf 36.2%

       \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg 36.2%

          \[\leadsto y \cdot \color{blue}{\left(-a \cdot \left(y3 \cdot y5\right)\right)} \]

       2. distribute-rgt-neg-in 36.2%

          \[\leadsto y \cdot \color{blue}{\left(a \cdot \left(-y3 \cdot y5\right)\right)} \]

       3. distribute-rgt-neg-in 36.2%

          \[\leadsto y \cdot \left(a \cdot \color{blue}{\left(y3 \cdot \left(-y5\right)\right)}\right) \]

   13. Simplified 36.2%

       \[\leadsto y \cdot \color{blue}{\left(a \cdot \left(y3 \cdot \left(-y5\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1750000000000:\\ \;\;\;\;\left(y \cdot b\right) \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{-154}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-284}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-151}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-109}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 235000000000:\\ \;\;\;\;y \cdot \left(a \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot b\right) \cdot \left(x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 22.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y3 \cdot \left(-y5\right)\\ \mathbf{if}\;y2 \leq -9.5 \cdot 10^{+96}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 6.5 \cdot 10^{-248}:\\ \;\;\;\;y \cdot \left(a \cdot t\_1\right)\\ \mathbf{elif}\;y2 \leq 10^{-132}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(z \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.45 \cdot 10^{-81}:\\ \;\;\;\;\left(y \cdot a\right) \cdot t\_1\\ \mathbf{elif}\;y2 \leq 2.55 \cdot 10^{-39}:\\ \;\;\;\;b \cdot \left(j \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.14 \cdot 10^{+164}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y3 (- y5))))
   (if (<= y2 -9.5e+96)
     (* a (* y5 (* t y2)))
     (if (<= y2 6.5e-248)
       (* y (* a t_1))
       (if (<= y2 1e-132)
         (* i (* y1 (* z (- k))))
         (if (<= y2 1.45e-81)
           (* (* y a) t_1)
           (if (<= y2 2.55e-39)
             (* b (* j (* x (- y0))))
             (if (<= y2 1.14e+164)
               (* b (* k (* y (- y4))))
               (* a (* t (* y2 y5)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y3 * -y5;
	double tmp;
	if (y2 <= -9.5e+96) {
		tmp = a * (y5 * (t * y2));
	} else if (y2 <= 6.5e-248) {
		tmp = y * (a * t_1);
	} else if (y2 <= 1e-132) {
		tmp = i * (y1 * (z * -k));
	} else if (y2 <= 1.45e-81) {
		tmp = (y * a) * t_1;
	} else if (y2 <= 2.55e-39) {
		tmp = b * (j * (x * -y0));
	} else if (y2 <= 1.14e+164) {
		tmp = b * (k * (y * -y4));
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y3 * -y5
    if (y2 <= (-9.5d+96)) then
        tmp = a * (y5 * (t * y2))
    else if (y2 <= 6.5d-248) then
        tmp = y * (a * t_1)
    else if (y2 <= 1d-132) then
        tmp = i * (y1 * (z * -k))
    else if (y2 <= 1.45d-81) then
        tmp = (y * a) * t_1
    else if (y2 <= 2.55d-39) then
        tmp = b * (j * (x * -y0))
    else if (y2 <= 1.14d+164) then
        tmp = b * (k * (y * -y4))
    else
        tmp = a * (t * (y2 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y3 * -y5;
	double tmp;
	if (y2 <= -9.5e+96) {
		tmp = a * (y5 * (t * y2));
	} else if (y2 <= 6.5e-248) {
		tmp = y * (a * t_1);
	} else if (y2 <= 1e-132) {
		tmp = i * (y1 * (z * -k));
	} else if (y2 <= 1.45e-81) {
		tmp = (y * a) * t_1;
	} else if (y2 <= 2.55e-39) {
		tmp = b * (j * (x * -y0));
	} else if (y2 <= 1.14e+164) {
		tmp = b * (k * (y * -y4));
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y3 * -y5
	tmp = 0
	if y2 <= -9.5e+96:
		tmp = a * (y5 * (t * y2))
	elif y2 <= 6.5e-248:
		tmp = y * (a * t_1)
	elif y2 <= 1e-132:
		tmp = i * (y1 * (z * -k))
	elif y2 <= 1.45e-81:
		tmp = (y * a) * t_1
	elif y2 <= 2.55e-39:
		tmp = b * (j * (x * -y0))
	elif y2 <= 1.14e+164:
		tmp = b * (k * (y * -y4))
	else:
		tmp = a * (t * (y2 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y3 * Float64(-y5))
	tmp = 0.0
	if (y2 <= -9.5e+96)
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	elseif (y2 <= 6.5e-248)
		tmp = Float64(y * Float64(a * t_1));
	elseif (y2 <= 1e-132)
		tmp = Float64(i * Float64(y1 * Float64(z * Float64(-k))));
	elseif (y2 <= 1.45e-81)
		tmp = Float64(Float64(y * a) * t_1);
	elseif (y2 <= 2.55e-39)
		tmp = Float64(b * Float64(j * Float64(x * Float64(-y0))));
	elseif (y2 <= 1.14e+164)
		tmp = Float64(b * Float64(k * Float64(y * Float64(-y4))));
	else
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y3 * -y5;
	tmp = 0.0;
	if (y2 <= -9.5e+96)
		tmp = a * (y5 * (t * y2));
	elseif (y2 <= 6.5e-248)
		tmp = y * (a * t_1);
	elseif (y2 <= 1e-132)
		tmp = i * (y1 * (z * -k));
	elseif (y2 <= 1.45e-81)
		tmp = (y * a) * t_1;
	elseif (y2 <= 2.55e-39)
		tmp = b * (j * (x * -y0));
	elseif (y2 <= 1.14e+164)
		tmp = b * (k * (y * -y4));
	else
		tmp = a * (t * (y2 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y3 * (-y5)), $MachinePrecision]}, If[LessEqual[y2, -9.5e+96], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 6.5e-248], N[(y * N[(a * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1e-132], N[(i * N[(y1 * N[(z * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.45e-81], N[(N[(y * a), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[y2, 2.55e-39], N[(b * N[(j * N[(x * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.14e+164], N[(b * N[(k * N[(y * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y2 < -9.50000000000000089e96

   1. Initial program 14.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 14.2%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 14.4%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 14.4%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 14.4%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 14.4%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 14.4%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 34.8%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf 32.0%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]

   if -9.50000000000000089e96 < y2 < 6.5e-248

   1. Initial program 33.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.1%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 32.4%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 32.4%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 32.4%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 32.4%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 32.4%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in y around inf 35.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 35.1%

         \[\leadsto y \cdot \left(\color{blue}{\left(-1 \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)} - \left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right) \]

      2. neg-mul-1 35.1%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right) \]

      3. mul-1-neg 35.1%

         \[\leadsto y \cdot \left(\left(-k\right) \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(\color{blue}{\left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + c \cdot \left(i \cdot x\right)\right)\right) \]

   10. Simplified 35.1%

       \[\leadsto \color{blue}{y \cdot \left(\left(-k\right) \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(\left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right)} \]

   11. Taylor expanded in a around inf 26.0%

       \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg 26.0%

          \[\leadsto y \cdot \color{blue}{\left(-a \cdot \left(y3 \cdot y5\right)\right)} \]

       2. distribute-rgt-neg-in 26.0%

          \[\leadsto y \cdot \color{blue}{\left(a \cdot \left(-y3 \cdot y5\right)\right)} \]

       3. distribute-rgt-neg-in 26.0%

          \[\leadsto y \cdot \left(a \cdot \color{blue}{\left(y3 \cdot \left(-y5\right)\right)}\right) \]

   13. Simplified 26.0%

       \[\leadsto y \cdot \color{blue}{\left(a \cdot \left(y3 \cdot \left(-y5\right)\right)\right)} \]

   if 6.5e-248 < y2 < 9.9999999999999999e-133

   1. Initial program 22.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 22.8%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 30.2%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 30.2%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 30.2%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 30.2%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 30.2%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in z around -inf 46.1%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   9. Taylor expanded in c around 0 38.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 38.6%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. distribute-rgt-neg-in 38.6%

          \[\leadsto \color{blue}{i \cdot \left(-k \cdot \left(y1 \cdot z\right)\right)} \]

       3. distribute-rgt-neg-in 38.6%

          \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(-y1 \cdot z\right)\right)} \]

       4. distribute-rgt-neg-in 38.6%

          \[\leadsto i \cdot \left(k \cdot \color{blue}{\left(y1 \cdot \left(-z\right)\right)}\right) \]

   11. Simplified 38.6%

       \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y1 \cdot \left(-z\right)\right)\right)} \]

   12. Taylor expanded in i around 0 38.6%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   13. Step-by-step derivation

       1. mul-1-neg 38.6%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. distribute-rgt-neg-in 38.6%

          \[\leadsto \color{blue}{i \cdot \left(-k \cdot \left(y1 \cdot z\right)\right)} \]

       3. *-commutative 38.6%

          \[\leadsto i \cdot \left(-\color{blue}{\left(y1 \cdot z\right) \cdot k}\right) \]

       4. distribute-lft-neg-in 38.6%

          \[\leadsto i \cdot \color{blue}{\left(\left(-y1 \cdot z\right) \cdot k\right)} \]

       5. distribute-rgt-neg-out 38.6%

          \[\leadsto i \cdot \left(\color{blue}{\left(y1 \cdot \left(-z\right)\right)} \cdot k\right) \]

       6. associate-*l* 45.4%

          \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \left(\left(-z\right) \cdot k\right)\right)} \]

       7. distribute-lft-neg-in 45.4%

          \[\leadsto i \cdot \left(y1 \cdot \color{blue}{\left(-z \cdot k\right)}\right) \]

       8. *-commutative 45.4%

          \[\leadsto i \cdot \left(y1 \cdot \left(-\color{blue}{k \cdot z}\right)\right) \]

       9. distribute-rgt-neg-in 45.4%

          \[\leadsto i \cdot \left(y1 \cdot \color{blue}{\left(k \cdot \left(-z\right)\right)}\right) \]

   14. Simplified 45.4%

       \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(k \cdot \left(-z\right)\right)\right)} \]

   if 9.9999999999999999e-133 < y2 < 1.44999999999999994e-81

   1. Initial program 53.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 53.6%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 61.3%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 61.3%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 61.3%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 61.3%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 61.3%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 41.1%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around 0 33.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 33.3%

          \[\leadsto \color{blue}{-a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]

       2. associate-*r* 40.5%

          \[\leadsto -\color{blue}{\left(a \cdot y\right) \cdot \left(y3 \cdot y5\right)} \]

       3. distribute-lft-neg-in 40.5%

          \[\leadsto \color{blue}{\left(-a \cdot y\right) \cdot \left(y3 \cdot y5\right)} \]

       4. *-commutative 40.5%

          \[\leadsto \left(-\color{blue}{y \cdot a}\right) \cdot \left(y3 \cdot y5\right) \]

       5. distribute-rgt-neg-in 40.5%

          \[\leadsto \color{blue}{\left(y \cdot \left(-a\right)\right)} \cdot \left(y3 \cdot y5\right) \]

   11. Simplified 40.5%

       \[\leadsto \color{blue}{\left(y \cdot \left(-a\right)\right) \cdot \left(y3 \cdot y5\right)} \]

   if 1.44999999999999994e-81 < y2 < 2.54999999999999994e-39

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 25.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 75.0%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around 0 75.6%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot \left(x \cdot y0\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 75.6%

         \[\leadsto \color{blue}{-b \cdot \left(j \cdot \left(x \cdot y0\right)\right)} \]

      2. *-commutative 75.6%

         \[\leadsto -\color{blue}{\left(j \cdot \left(x \cdot y0\right)\right) \cdot b} \]

      3. distribute-rgt-neg-in 75.6%

         \[\leadsto \color{blue}{\left(j \cdot \left(x \cdot y0\right)\right) \cdot \left(-b\right)} \]

   9. Simplified 75.6%

      \[\leadsto \color{blue}{\left(j \cdot \left(x \cdot y0\right)\right) \cdot \left(-b\right)} \]

   if 2.54999999999999994e-39 < y2 < 1.14e164

   1. Initial program 31.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.1%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 50.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y around -inf 46.3%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 46.3%

         \[\leadsto \color{blue}{-b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]

      2. associate-*r* 35.6%

         \[\leadsto -\color{blue}{\left(b \cdot y\right) \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)} \]

      3. mul-1-neg 35.6%

         \[\leadsto -\left(b \cdot y\right) \cdot \left(\color{blue}{\left(-a \cdot x\right)} + k \cdot y4\right) \]

   8. Simplified 35.6%

      \[\leadsto \color{blue}{-\left(b \cdot y\right) \cdot \left(\left(-a \cdot x\right) + k \cdot y4\right)} \]

   9. Taylor expanded in a around 0 33.1%

      \[\leadsto -\color{blue}{b \cdot \left(k \cdot \left(y \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 33.1%

          \[\leadsto -b \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot k\right)} \]

   11. Simplified 33.1%

       \[\leadsto -\color{blue}{b \cdot \left(\left(y \cdot y4\right) \cdot k\right)} \]

   if 1.14e164 < y2

   1. Initial program 12.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 12.1%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 12.3%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 12.3%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 12.3%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 12.3%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 12.3%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 41.9%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf 44.5%

      \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 44.5%

          \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   11. Simplified 44.5%

       \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(y5 \cdot y2\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -9.5 \cdot 10^{+96}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 6.5 \cdot 10^{-248}:\\ \;\;\;\;y \cdot \left(a \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 10^{-132}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(z \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.45 \cdot 10^{-81}:\\ \;\;\;\;\left(y \cdot a\right) \cdot \left(y3 \cdot \left(-y5\right)\right)\\ \mathbf{elif}\;y2 \leq 2.55 \cdot 10^{-39}:\\ \;\;\;\;b \cdot \left(j \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.14 \cdot 10^{+164}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 22.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -1.02 \cdot 10^{+96}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 2.5 \cdot 10^{-248}:\\ \;\;\;\;y \cdot \left(a \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 6 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(z \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 5.8 \cdot 10^{-80}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.2 \cdot 10^{-39}:\\ \;\;\;\;b \cdot \left(j \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 2.8 \cdot 10^{+164}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -1.02e+96)
   (* a (* y5 (* t y2)))
   (if (<= y2 2.5e-248)
     (* y (* a (* y3 (- y5))))
     (if (<= y2 6e-135)
       (* i (* y1 (* z (- k))))
       (if (<= y2 5.8e-80)
         (* a (* y5 (* y (- y3))))
         (if (<= y2 1.2e-39)
           (* b (* j (* x (- y0))))
           (if (<= y2 2.8e+164)
             (* b (* k (* y (- y4))))
             (* a (* t (* y2 y5))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.02e+96) {
		tmp = a * (y5 * (t * y2));
	} else if (y2 <= 2.5e-248) {
		tmp = y * (a * (y3 * -y5));
	} else if (y2 <= 6e-135) {
		tmp = i * (y1 * (z * -k));
	} else if (y2 <= 5.8e-80) {
		tmp = a * (y5 * (y * -y3));
	} else if (y2 <= 1.2e-39) {
		tmp = b * (j * (x * -y0));
	} else if (y2 <= 2.8e+164) {
		tmp = b * (k * (y * -y4));
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-1.02d+96)) then
        tmp = a * (y5 * (t * y2))
    else if (y2 <= 2.5d-248) then
        tmp = y * (a * (y3 * -y5))
    else if (y2 <= 6d-135) then
        tmp = i * (y1 * (z * -k))
    else if (y2 <= 5.8d-80) then
        tmp = a * (y5 * (y * -y3))
    else if (y2 <= 1.2d-39) then
        tmp = b * (j * (x * -y0))
    else if (y2 <= 2.8d+164) then
        tmp = b * (k * (y * -y4))
    else
        tmp = a * (t * (y2 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.02e+96) {
		tmp = a * (y5 * (t * y2));
	} else if (y2 <= 2.5e-248) {
		tmp = y * (a * (y3 * -y5));
	} else if (y2 <= 6e-135) {
		tmp = i * (y1 * (z * -k));
	} else if (y2 <= 5.8e-80) {
		tmp = a * (y5 * (y * -y3));
	} else if (y2 <= 1.2e-39) {
		tmp = b * (j * (x * -y0));
	} else if (y2 <= 2.8e+164) {
		tmp = b * (k * (y * -y4));
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -1.02e+96:
		tmp = a * (y5 * (t * y2))
	elif y2 <= 2.5e-248:
		tmp = y * (a * (y3 * -y5))
	elif y2 <= 6e-135:
		tmp = i * (y1 * (z * -k))
	elif y2 <= 5.8e-80:
		tmp = a * (y5 * (y * -y3))
	elif y2 <= 1.2e-39:
		tmp = b * (j * (x * -y0))
	elif y2 <= 2.8e+164:
		tmp = b * (k * (y * -y4))
	else:
		tmp = a * (t * (y2 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -1.02e+96)
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	elseif (y2 <= 2.5e-248)
		tmp = Float64(y * Float64(a * Float64(y3 * Float64(-y5))));
	elseif (y2 <= 6e-135)
		tmp = Float64(i * Float64(y1 * Float64(z * Float64(-k))));
	elseif (y2 <= 5.8e-80)
		tmp = Float64(a * Float64(y5 * Float64(y * Float64(-y3))));
	elseif (y2 <= 1.2e-39)
		tmp = Float64(b * Float64(j * Float64(x * Float64(-y0))));
	elseif (y2 <= 2.8e+164)
		tmp = Float64(b * Float64(k * Float64(y * Float64(-y4))));
	else
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -1.02e+96)
		tmp = a * (y5 * (t * y2));
	elseif (y2 <= 2.5e-248)
		tmp = y * (a * (y3 * -y5));
	elseif (y2 <= 6e-135)
		tmp = i * (y1 * (z * -k));
	elseif (y2 <= 5.8e-80)
		tmp = a * (y5 * (y * -y3));
	elseif (y2 <= 1.2e-39)
		tmp = b * (j * (x * -y0));
	elseif (y2 <= 2.8e+164)
		tmp = b * (k * (y * -y4));
	else
		tmp = a * (t * (y2 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -1.02e+96], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.5e-248], N[(y * N[(a * N[(y3 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 6e-135], N[(i * N[(y1 * N[(z * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5.8e-80], N[(a * N[(y5 * N[(y * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.2e-39], N[(b * N[(j * N[(x * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.8e+164], N[(b * N[(k * N[(y * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y2 < -1.02000000000000001e96

   1. Initial program 14.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 14.2%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 14.4%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 14.4%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 14.4%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 14.4%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 14.4%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 34.8%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf 32.0%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]

   if -1.02000000000000001e96 < y2 < 2.5e-248

   1. Initial program 33.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.1%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 32.4%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 32.4%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 32.4%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 32.4%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 32.4%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in y around inf 35.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 35.1%

         \[\leadsto y \cdot \left(\color{blue}{\left(-1 \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)} - \left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right) \]

      2. neg-mul-1 35.1%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right) \]

      3. mul-1-neg 35.1%

         \[\leadsto y \cdot \left(\left(-k\right) \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(\color{blue}{\left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + c \cdot \left(i \cdot x\right)\right)\right) \]

   10. Simplified 35.1%

       \[\leadsto \color{blue}{y \cdot \left(\left(-k\right) \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(\left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right)} \]

   11. Taylor expanded in a around inf 26.0%

       \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg 26.0%

          \[\leadsto y \cdot \color{blue}{\left(-a \cdot \left(y3 \cdot y5\right)\right)} \]

       2. distribute-rgt-neg-in 26.0%

          \[\leadsto y \cdot \color{blue}{\left(a \cdot \left(-y3 \cdot y5\right)\right)} \]

       3. distribute-rgt-neg-in 26.0%

          \[\leadsto y \cdot \left(a \cdot \color{blue}{\left(y3 \cdot \left(-y5\right)\right)}\right) \]

   13. Simplified 26.0%

       \[\leadsto y \cdot \color{blue}{\left(a \cdot \left(y3 \cdot \left(-y5\right)\right)\right)} \]

   if 2.5e-248 < y2 < 6.00000000000000024e-135

   1. Initial program 22.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 22.8%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 30.2%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 30.2%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 30.2%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 30.2%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 30.2%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in z around -inf 46.1%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   9. Taylor expanded in c around 0 38.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 38.6%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. distribute-rgt-neg-in 38.6%

          \[\leadsto \color{blue}{i \cdot \left(-k \cdot \left(y1 \cdot z\right)\right)} \]

       3. distribute-rgt-neg-in 38.6%

          \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(-y1 \cdot z\right)\right)} \]

       4. distribute-rgt-neg-in 38.6%

          \[\leadsto i \cdot \left(k \cdot \color{blue}{\left(y1 \cdot \left(-z\right)\right)}\right) \]

   11. Simplified 38.6%

       \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y1 \cdot \left(-z\right)\right)\right)} \]

   12. Taylor expanded in i around 0 38.6%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   13. Step-by-step derivation

       1. mul-1-neg 38.6%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. distribute-rgt-neg-in 38.6%

          \[\leadsto \color{blue}{i \cdot \left(-k \cdot \left(y1 \cdot z\right)\right)} \]

       3. *-commutative 38.6%

          \[\leadsto i \cdot \left(-\color{blue}{\left(y1 \cdot z\right) \cdot k}\right) \]

       4. distribute-lft-neg-in 38.6%

          \[\leadsto i \cdot \color{blue}{\left(\left(-y1 \cdot z\right) \cdot k\right)} \]

       5. distribute-rgt-neg-out 38.6%

          \[\leadsto i \cdot \left(\color{blue}{\left(y1 \cdot \left(-z\right)\right)} \cdot k\right) \]

       6. associate-*l* 45.4%

          \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \left(\left(-z\right) \cdot k\right)\right)} \]

       7. distribute-lft-neg-in 45.4%

          \[\leadsto i \cdot \left(y1 \cdot \color{blue}{\left(-z \cdot k\right)}\right) \]

       8. *-commutative 45.4%

          \[\leadsto i \cdot \left(y1 \cdot \left(-\color{blue}{k \cdot z}\right)\right) \]

       9. distribute-rgt-neg-in 45.4%

          \[\leadsto i \cdot \left(y1 \cdot \color{blue}{\left(k \cdot \left(-z\right)\right)}\right) \]

   14. Simplified 45.4%

       \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(k \cdot \left(-z\right)\right)\right)} \]

   if 6.00000000000000024e-135 < y2 < 5.79999999999999996e-80

   1. Initial program 53.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 53.6%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 61.3%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 61.3%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 61.3%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 61.3%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 61.3%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 41.1%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around 0 40.5%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y3\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 40.5%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(-y \cdot y3\right)}\right) \]

       2. distribute-lft-neg-out 40.5%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(\left(-y\right) \cdot y3\right)}\right) \]

       3. *-commutative 40.5%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y3 \cdot \left(-y\right)\right)}\right) \]

   11. Simplified 40.5%

       \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y3 \cdot \left(-y\right)\right)}\right) \]

   if 5.79999999999999996e-80 < y2 < 1.20000000000000008e-39

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 25.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 75.0%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around 0 75.6%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot \left(x \cdot y0\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 75.6%

         \[\leadsto \color{blue}{-b \cdot \left(j \cdot \left(x \cdot y0\right)\right)} \]

      2. *-commutative 75.6%

         \[\leadsto -\color{blue}{\left(j \cdot \left(x \cdot y0\right)\right) \cdot b} \]

      3. distribute-rgt-neg-in 75.6%

         \[\leadsto \color{blue}{\left(j \cdot \left(x \cdot y0\right)\right) \cdot \left(-b\right)} \]

   9. Simplified 75.6%

      \[\leadsto \color{blue}{\left(j \cdot \left(x \cdot y0\right)\right) \cdot \left(-b\right)} \]

   if 1.20000000000000008e-39 < y2 < 2.8000000000000002e164

   1. Initial program 31.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.1%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 50.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y around -inf 46.3%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 46.3%

         \[\leadsto \color{blue}{-b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]

      2. associate-*r* 35.6%

         \[\leadsto -\color{blue}{\left(b \cdot y\right) \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)} \]

      3. mul-1-neg 35.6%

         \[\leadsto -\left(b \cdot y\right) \cdot \left(\color{blue}{\left(-a \cdot x\right)} + k \cdot y4\right) \]

   8. Simplified 35.6%

      \[\leadsto \color{blue}{-\left(b \cdot y\right) \cdot \left(\left(-a \cdot x\right) + k \cdot y4\right)} \]

   9. Taylor expanded in a around 0 33.1%

      \[\leadsto -\color{blue}{b \cdot \left(k \cdot \left(y \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 33.1%

          \[\leadsto -b \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot k\right)} \]

   11. Simplified 33.1%

       \[\leadsto -\color{blue}{b \cdot \left(\left(y \cdot y4\right) \cdot k\right)} \]

   if 2.8000000000000002e164 < y2

   1. Initial program 12.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 12.1%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 12.3%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 12.3%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 12.3%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 12.3%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 12.3%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 41.9%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf 44.5%

      \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 44.5%

          \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   11. Simplified 44.5%

       \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(y5 \cdot y2\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.02 \cdot 10^{+96}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 2.5 \cdot 10^{-248}:\\ \;\;\;\;y \cdot \left(a \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 6 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(z \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 5.8 \cdot 10^{-80}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.2 \cdot 10^{-39}:\\ \;\;\;\;b \cdot \left(j \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 2.8 \cdot 10^{+164}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 30.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ t_2 := c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;y4 \leq -6.4 \cdot 10^{+177}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y4 \leq -3.1 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq -1.85 \cdot 10^{-12}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y4 \leq 4.6 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 1.52 \cdot 10^{+174}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* x (- (* y a) (* j y0)))))
        (t_2 (* c (* y4 (- (* y y3) (* t y2))))))
   (if (<= y4 -6.4e+177)
     t_2
     (if (<= y4 -3.1e+38)
       t_1
       (if (<= y4 -1.85e-12)
         t_2
         (if (<= y4 4.6e-86)
           t_1
           (if (<= y4 1.52e+174) (* b (* a (- (* x y) (* z t)))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (x * ((y * a) - (j * y0)));
	double t_2 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (y4 <= -6.4e+177) {
		tmp = t_2;
	} else if (y4 <= -3.1e+38) {
		tmp = t_1;
	} else if (y4 <= -1.85e-12) {
		tmp = t_2;
	} else if (y4 <= 4.6e-86) {
		tmp = t_1;
	} else if (y4 <= 1.52e+174) {
		tmp = b * (a * ((x * y) - (z * t)));
	} 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 = b * (x * ((y * a) - (j * y0)))
    t_2 = c * (y4 * ((y * y3) - (t * y2)))
    if (y4 <= (-6.4d+177)) then
        tmp = t_2
    else if (y4 <= (-3.1d+38)) then
        tmp = t_1
    else if (y4 <= (-1.85d-12)) then
        tmp = t_2
    else if (y4 <= 4.6d-86) then
        tmp = t_1
    else if (y4 <= 1.52d+174) then
        tmp = b * (a * ((x * y) - (z * t)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (x * ((y * a) - (j * y0)));
	double t_2 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (y4 <= -6.4e+177) {
		tmp = t_2;
	} else if (y4 <= -3.1e+38) {
		tmp = t_1;
	} else if (y4 <= -1.85e-12) {
		tmp = t_2;
	} else if (y4 <= 4.6e-86) {
		tmp = t_1;
	} else if (y4 <= 1.52e+174) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (x * ((y * a) - (j * y0)))
	t_2 = c * (y4 * ((y * y3) - (t * y2)))
	tmp = 0
	if y4 <= -6.4e+177:
		tmp = t_2
	elif y4 <= -3.1e+38:
		tmp = t_1
	elif y4 <= -1.85e-12:
		tmp = t_2
	elif y4 <= 4.6e-86:
		tmp = t_1
	elif y4 <= 1.52e+174:
		tmp = b * (a * ((x * y) - (z * t)))
	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(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))))
	t_2 = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))
	tmp = 0.0
	if (y4 <= -6.4e+177)
		tmp = t_2;
	elseif (y4 <= -3.1e+38)
		tmp = t_1;
	elseif (y4 <= -1.85e-12)
		tmp = t_2;
	elseif (y4 <= 4.6e-86)
		tmp = t_1;
	elseif (y4 <= 1.52e+174)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (x * ((y * a) - (j * y0)));
	t_2 = c * (y4 * ((y * y3) - (t * y2)));
	tmp = 0.0;
	if (y4 <= -6.4e+177)
		tmp = t_2;
	elseif (y4 <= -3.1e+38)
		tmp = t_1;
	elseif (y4 <= -1.85e-12)
		tmp = t_2;
	elseif (y4 <= 4.6e-86)
		tmp = t_1;
	elseif (y4 <= 1.52e+174)
		tmp = b * (a * ((x * y) - (z * t)));
	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[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -6.4e+177], t$95$2, If[LessEqual[y4, -3.1e+38], t$95$1, If[LessEqual[y4, -1.85e-12], t$95$2, If[LessEqual[y4, 4.6e-86], t$95$1, If[LessEqual[y4, 1.52e+174], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y4 < -6.4e177 or -3.10000000000000018e38 < y4 < -1.84999999999999999e-12 or 1.52000000000000004e174 < y4

   1. Initial program 20.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 20.6%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y4 around inf 57.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   6. Taylor expanded in c around inf 64.6%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   if -6.4e177 < y4 < -3.10000000000000018e38 or -1.84999999999999999e-12 < y4 < 4.59999999999999992e-86

   1. Initial program 30.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.1%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 41.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 45.4%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if 4.59999999999999992e-86 < y4 < 1.52000000000000004e174

   1. Initial program 23.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.1%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 33.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 38.7%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -6.4 \cdot 10^{+177}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -3.1 \cdot 10^{+38}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq -1.85 \cdot 10^{-12}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq 4.6 \cdot 10^{-86}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 1.52 \cdot 10^{+174}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 30.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ t_2 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;a \leq -8.8 \cdot 10^{+209}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-111}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-164}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-77}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(z \cdot \left(-k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* a (- (* x y) (* z t)))))
        (t_2 (* a (* y5 (- (* t y2) (* y y3))))))
   (if (<= a -8.8e+209)
     t_2
     (if (<= a -2e-37)
       t_1
       (if (<= a -2.8e-111)
         t_2
         (if (<= a 1.55e-164)
           (* b (* j (- (* t y4) (* x y0))))
           (if (<= a 2.8e-77) (* i (* y1 (* z (- k)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (a * ((x * y) - (z * t)));
	double t_2 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (a <= -8.8e+209) {
		tmp = t_2;
	} else if (a <= -2e-37) {
		tmp = t_1;
	} else if (a <= -2.8e-111) {
		tmp = t_2;
	} else if (a <= 1.55e-164) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (a <= 2.8e-77) {
		tmp = i * (y1 * (z * -k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a * ((x * y) - (z * t)))
    t_2 = a * (y5 * ((t * y2) - (y * y3)))
    if (a <= (-8.8d+209)) then
        tmp = t_2
    else if (a <= (-2d-37)) then
        tmp = t_1
    else if (a <= (-2.8d-111)) then
        tmp = t_2
    else if (a <= 1.55d-164) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (a <= 2.8d-77) then
        tmp = i * (y1 * (z * -k))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (a * ((x * y) - (z * t)));
	double t_2 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (a <= -8.8e+209) {
		tmp = t_2;
	} else if (a <= -2e-37) {
		tmp = t_1;
	} else if (a <= -2.8e-111) {
		tmp = t_2;
	} else if (a <= 1.55e-164) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (a <= 2.8e-77) {
		tmp = i * (y1 * (z * -k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (a * ((x * y) - (z * t)))
	t_2 = a * (y5 * ((t * y2) - (y * y3)))
	tmp = 0
	if a <= -8.8e+209:
		tmp = t_2
	elif a <= -2e-37:
		tmp = t_1
	elif a <= -2.8e-111:
		tmp = t_2
	elif a <= 1.55e-164:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif a <= 2.8e-77:
		tmp = i * (y1 * (z * -k))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))))
	t_2 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	tmp = 0.0
	if (a <= -8.8e+209)
		tmp = t_2;
	elseif (a <= -2e-37)
		tmp = t_1;
	elseif (a <= -2.8e-111)
		tmp = t_2;
	elseif (a <= 1.55e-164)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (a <= 2.8e-77)
		tmp = Float64(i * Float64(y1 * Float64(z * Float64(-k))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (a * ((x * y) - (z * t)));
	t_2 = a * (y5 * ((t * y2) - (y * y3)));
	tmp = 0.0;
	if (a <= -8.8e+209)
		tmp = t_2;
	elseif (a <= -2e-37)
		tmp = t_1;
	elseif (a <= -2.8e-111)
		tmp = t_2;
	elseif (a <= 1.55e-164)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (a <= 2.8e-77)
		tmp = i * (y1 * (z * -k));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.8e+209], t$95$2, If[LessEqual[a, -2e-37], t$95$1, If[LessEqual[a, -2.8e-111], t$95$2, If[LessEqual[a, 1.55e-164], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e-77], N[(i * N[(y1 * N[(z * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.7999999999999995e209 or -2.00000000000000013e-37 < a < -2.79999999999999995e-111

   1. Initial program 19.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 19.1%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 21.8%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 21.8%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 21.8%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 21.8%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 21.8%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 48.7%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -8.7999999999999995e209 < a < -2.00000000000000013e-37 or 2.7999999999999999e-77 < a

   1. Initial program 25.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.1%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 41.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 46.9%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -2.79999999999999995e-111 < a < 1.55e-164

   1. Initial program 31.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.6%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 36.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 42.9%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if 1.55e-164 < a < 2.7999999999999999e-77

   1. Initial program 30.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.4%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 50.8%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 50.8%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 50.8%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 50.8%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 50.8%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in z around -inf 51.4%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   9. Taylor expanded in c around 0 50.8%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 50.8%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. distribute-rgt-neg-in 50.8%

          \[\leadsto \color{blue}{i \cdot \left(-k \cdot \left(y1 \cdot z\right)\right)} \]

       3. distribute-rgt-neg-in 50.8%

          \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(-y1 \cdot z\right)\right)} \]

       4. distribute-rgt-neg-in 50.8%

          \[\leadsto i \cdot \left(k \cdot \color{blue}{\left(y1 \cdot \left(-z\right)\right)}\right) \]

   11. Simplified 50.8%

       \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y1 \cdot \left(-z\right)\right)\right)} \]

   12. Taylor expanded in i around 0 50.8%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   13. Step-by-step derivation

       1. mul-1-neg 50.8%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. distribute-rgt-neg-in 50.8%

          \[\leadsto \color{blue}{i \cdot \left(-k \cdot \left(y1 \cdot z\right)\right)} \]

       3. *-commutative 50.8%

          \[\leadsto i \cdot \left(-\color{blue}{\left(y1 \cdot z\right) \cdot k}\right) \]

       4. distribute-lft-neg-in 50.8%

          \[\leadsto i \cdot \color{blue}{\left(\left(-y1 \cdot z\right) \cdot k\right)} \]

       5. distribute-rgt-neg-out 50.8%

          \[\leadsto i \cdot \left(\color{blue}{\left(y1 \cdot \left(-z\right)\right)} \cdot k\right) \]

       6. associate-*l* 50.9%

          \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \left(\left(-z\right) \cdot k\right)\right)} \]

       7. distribute-lft-neg-in 50.9%

          \[\leadsto i \cdot \left(y1 \cdot \color{blue}{\left(-z \cdot k\right)}\right) \]

       8. *-commutative 50.9%

          \[\leadsto i \cdot \left(y1 \cdot \left(-\color{blue}{k \cdot z}\right)\right) \]

       9. distribute-rgt-neg-in 50.9%

          \[\leadsto i \cdot \left(y1 \cdot \color{blue}{\left(k \cdot \left(-z\right)\right)}\right) \]

   14. Simplified 50.9%

       \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(k \cdot \left(-z\right)\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+209}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-37}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-111}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-164}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-77}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(z \cdot \left(-k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 27.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{+209}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c\right)\right)\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-297}:\\ \;\;\;\;b \cdot \left(j \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-74}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(z \cdot \left(-k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* a (- (* x y) (* z t))))))
   (if (<= a -4.8e+209)
     (* a (* y5 (- (* t y2) (* y y3))))
     (if (<= a -3.6e-41)
       t_1
       (if (<= a -2.8e-135)
         (* i (* z (* t c)))
         (if (<= a -6.5e-297)
           (* b (* j (* x (- y0))))
           (if (<= a 2.4e-74) (* i (* y1 (* z (- k)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (a * ((x * y) - (z * t)));
	double tmp;
	if (a <= -4.8e+209) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (a <= -3.6e-41) {
		tmp = t_1;
	} else if (a <= -2.8e-135) {
		tmp = i * (z * (t * c));
	} else if (a <= -6.5e-297) {
		tmp = b * (j * (x * -y0));
	} else if (a <= 2.4e-74) {
		tmp = i * (y1 * (z * -k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * ((x * y) - (z * t)))
    if (a <= (-4.8d+209)) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (a <= (-3.6d-41)) then
        tmp = t_1
    else if (a <= (-2.8d-135)) then
        tmp = i * (z * (t * c))
    else if (a <= (-6.5d-297)) then
        tmp = b * (j * (x * -y0))
    else if (a <= 2.4d-74) then
        tmp = i * (y1 * (z * -k))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (a * ((x * y) - (z * t)));
	double tmp;
	if (a <= -4.8e+209) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (a <= -3.6e-41) {
		tmp = t_1;
	} else if (a <= -2.8e-135) {
		tmp = i * (z * (t * c));
	} else if (a <= -6.5e-297) {
		tmp = b * (j * (x * -y0));
	} else if (a <= 2.4e-74) {
		tmp = i * (y1 * (z * -k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (a * ((x * y) - (z * t)))
	tmp = 0
	if a <= -4.8e+209:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif a <= -3.6e-41:
		tmp = t_1
	elif a <= -2.8e-135:
		tmp = i * (z * (t * c))
	elif a <= -6.5e-297:
		tmp = b * (j * (x * -y0))
	elif a <= 2.4e-74:
		tmp = i * (y1 * (z * -k))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (a <= -4.8e+209)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (a <= -3.6e-41)
		tmp = t_1;
	elseif (a <= -2.8e-135)
		tmp = Float64(i * Float64(z * Float64(t * c)));
	elseif (a <= -6.5e-297)
		tmp = Float64(b * Float64(j * Float64(x * Float64(-y0))));
	elseif (a <= 2.4e-74)
		tmp = Float64(i * Float64(y1 * Float64(z * Float64(-k))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (a * ((x * y) - (z * t)));
	tmp = 0.0;
	if (a <= -4.8e+209)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (a <= -3.6e-41)
		tmp = t_1;
	elseif (a <= -2.8e-135)
		tmp = i * (z * (t * c));
	elseif (a <= -6.5e-297)
		tmp = b * (j * (x * -y0));
	elseif (a <= 2.4e-74)
		tmp = i * (y1 * (z * -k));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.8e+209], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.6e-41], t$95$1, If[LessEqual[a, -2.8e-135], N[(i * N[(z * N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.5e-297], N[(b * N[(j * N[(x * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e-74], N[(i * N[(y1 * N[(z * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.79999999999999991e209

   1. Initial program 20.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 20.0%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 28.6%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 28.6%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 28.6%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 28.6%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 28.6%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 56.8%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -4.79999999999999991e209 < a < -3.6e-41 or 2.3999999999999999e-74 < a

   1. Initial program 25.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.1%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 41.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 46.9%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -3.6e-41 < a < -2.80000000000000023e-135

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.0%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 20.7%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 20.7%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 20.7%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 20.7%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 20.7%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in z around -inf 42.5%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   9. Taylor expanded in c around inf 34.8%

      \[\leadsto i \cdot \left(z \cdot \color{blue}{\left(c \cdot t\right)}\right) \]

   if -2.80000000000000023e-135 < a < -6.5000000000000002e-297

   1. Initial program 25.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.3%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 35.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 51.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around 0 39.0%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot \left(x \cdot y0\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 39.0%

         \[\leadsto \color{blue}{-b \cdot \left(j \cdot \left(x \cdot y0\right)\right)} \]

      2. *-commutative 39.0%

         \[\leadsto -\color{blue}{\left(j \cdot \left(x \cdot y0\right)\right) \cdot b} \]

      3. distribute-rgt-neg-in 39.0%

         \[\leadsto \color{blue}{\left(j \cdot \left(x \cdot y0\right)\right) \cdot \left(-b\right)} \]

   9. Simplified 39.0%

      \[\leadsto \color{blue}{\left(j \cdot \left(x \cdot y0\right)\right) \cdot \left(-b\right)} \]

   if -6.5000000000000002e-297 < a < 2.3999999999999999e-74

   1. Initial program 33.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.6%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 41.7%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 41.7%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 41.7%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 41.7%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 41.7%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in z around -inf 39.0%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   9. Taylor expanded in c around 0 34.7%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 34.7%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. distribute-rgt-neg-in 34.7%

          \[\leadsto \color{blue}{i \cdot \left(-k \cdot \left(y1 \cdot z\right)\right)} \]

       3. distribute-rgt-neg-in 34.7%

          \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(-y1 \cdot z\right)\right)} \]

       4. distribute-rgt-neg-in 34.7%

          \[\leadsto i \cdot \left(k \cdot \color{blue}{\left(y1 \cdot \left(-z\right)\right)}\right) \]

   11. Simplified 34.7%

       \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y1 \cdot \left(-z\right)\right)\right)} \]

   12. Taylor expanded in i around 0 34.7%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   13. Step-by-step derivation

       1. mul-1-neg 34.7%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. distribute-rgt-neg-in 34.7%

          \[\leadsto \color{blue}{i \cdot \left(-k \cdot \left(y1 \cdot z\right)\right)} \]

       3. *-commutative 34.7%

          \[\leadsto i \cdot \left(-\color{blue}{\left(y1 \cdot z\right) \cdot k}\right) \]

       4. distribute-lft-neg-in 34.7%

          \[\leadsto i \cdot \color{blue}{\left(\left(-y1 \cdot z\right) \cdot k\right)} \]

       5. distribute-rgt-neg-out 34.7%

          \[\leadsto i \cdot \left(\color{blue}{\left(y1 \cdot \left(-z\right)\right)} \cdot k\right) \]

       6. associate-*l* 40.2%

          \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \left(\left(-z\right) \cdot k\right)\right)} \]

       7. distribute-lft-neg-in 40.2%

          \[\leadsto i \cdot \left(y1 \cdot \color{blue}{\left(-z \cdot k\right)}\right) \]

       8. *-commutative 40.2%

          \[\leadsto i \cdot \left(y1 \cdot \left(-\color{blue}{k \cdot z}\right)\right) \]

       9. distribute-rgt-neg-in 40.2%

          \[\leadsto i \cdot \left(y1 \cdot \color{blue}{\left(k \cdot \left(-z\right)\right)}\right) \]

   14. Simplified 40.2%

       \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(k \cdot \left(-z\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+209}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-41}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c\right)\right)\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-297}:\\ \;\;\;\;b \cdot \left(j \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-74}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(z \cdot \left(-k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 22.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y1 \cdot \left(z \cdot \left(-k\right)\right)\right)\\ \mathbf{if}\;t \leq -1.65 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 7.7 \cdot 10^{-208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-104}:\\ \;\;\;\;c \cdot \left(\left(x \cdot y\right) \cdot \left(-i\right)\right)\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+95}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* y1 (* z (- k))))))
   (if (<= t -1.65e+81)
     (* b (* j (* t y4)))
     (if (<= t 7.7e-208)
       t_1
       (if (<= t 1.12e-104)
         (* c (* (* x y) (- i)))
         (if (<= t 9.8e-85)
           t_1
           (if (<= t 1.9e+95)
             (* a (* y5 (* y (- y3))))
             (* a (* y5 (* t y2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y1 * (z * -k));
	double tmp;
	if (t <= -1.65e+81) {
		tmp = b * (j * (t * y4));
	} else if (t <= 7.7e-208) {
		tmp = t_1;
	} else if (t <= 1.12e-104) {
		tmp = c * ((x * y) * -i);
	} else if (t <= 9.8e-85) {
		tmp = t_1;
	} else if (t <= 1.9e+95) {
		tmp = a * (y5 * (y * -y3));
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (y1 * (z * -k))
    if (t <= (-1.65d+81)) then
        tmp = b * (j * (t * y4))
    else if (t <= 7.7d-208) then
        tmp = t_1
    else if (t <= 1.12d-104) then
        tmp = c * ((x * y) * -i)
    else if (t <= 9.8d-85) then
        tmp = t_1
    else if (t <= 1.9d+95) then
        tmp = a * (y5 * (y * -y3))
    else
        tmp = a * (y5 * (t * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y1 * (z * -k));
	double tmp;
	if (t <= -1.65e+81) {
		tmp = b * (j * (t * y4));
	} else if (t <= 7.7e-208) {
		tmp = t_1;
	} else if (t <= 1.12e-104) {
		tmp = c * ((x * y) * -i);
	} else if (t <= 9.8e-85) {
		tmp = t_1;
	} else if (t <= 1.9e+95) {
		tmp = a * (y5 * (y * -y3));
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (y1 * (z * -k))
	tmp = 0
	if t <= -1.65e+81:
		tmp = b * (j * (t * y4))
	elif t <= 7.7e-208:
		tmp = t_1
	elif t <= 1.12e-104:
		tmp = c * ((x * y) * -i)
	elif t <= 9.8e-85:
		tmp = t_1
	elif t <= 1.9e+95:
		tmp = a * (y5 * (y * -y3))
	else:
		tmp = a * (y5 * (t * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(y1 * Float64(z * Float64(-k))))
	tmp = 0.0
	if (t <= -1.65e+81)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	elseif (t <= 7.7e-208)
		tmp = t_1;
	elseif (t <= 1.12e-104)
		tmp = Float64(c * Float64(Float64(x * y) * Float64(-i)));
	elseif (t <= 9.8e-85)
		tmp = t_1;
	elseif (t <= 1.9e+95)
		tmp = Float64(a * Float64(y5 * Float64(y * Float64(-y3))));
	else
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (y1 * (z * -k));
	tmp = 0.0;
	if (t <= -1.65e+81)
		tmp = b * (j * (t * y4));
	elseif (t <= 7.7e-208)
		tmp = t_1;
	elseif (t <= 1.12e-104)
		tmp = c * ((x * y) * -i);
	elseif (t <= 9.8e-85)
		tmp = t_1;
	elseif (t <= 1.9e+95)
		tmp = a * (y5 * (y * -y3));
	else
		tmp = a * (y5 * (t * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(y1 * N[(z * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.65e+81], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.7e-208], t$95$1, If[LessEqual[t, 1.12e-104], N[(c * N[(N[(x * y), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.8e-85], t$95$1, If[LessEqual[t, 1.9e+95], N[(a * N[(y5 * N[(y * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.65e81

   1. Initial program 15.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 15.7%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 35.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 43.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 41.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 41.3%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   9. Simplified 41.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]

   if -1.65e81 < t < 7.69999999999999972e-208 or 1.12e-104 < t < 9.80000000000000029e-85

   1. Initial program 30.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.3%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 29.8%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 29.8%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 29.8%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 29.8%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 29.8%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in z around -inf 26.1%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   9. Taylor expanded in c around 0 23.4%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 23.4%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. distribute-rgt-neg-in 23.4%

          \[\leadsto \color{blue}{i \cdot \left(-k \cdot \left(y1 \cdot z\right)\right)} \]

       3. distribute-rgt-neg-in 23.4%

          \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(-y1 \cdot z\right)\right)} \]

       4. distribute-rgt-neg-in 23.4%

          \[\leadsto i \cdot \left(k \cdot \color{blue}{\left(y1 \cdot \left(-z\right)\right)}\right) \]

   11. Simplified 23.4%

       \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y1 \cdot \left(-z\right)\right)\right)} \]

   12. Taylor expanded in i around 0 23.4%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   13. Step-by-step derivation

       1. mul-1-neg 23.4%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. distribute-rgt-neg-in 23.4%

          \[\leadsto \color{blue}{i \cdot \left(-k \cdot \left(y1 \cdot z\right)\right)} \]

       3. *-commutative 23.4%

          \[\leadsto i \cdot \left(-\color{blue}{\left(y1 \cdot z\right) \cdot k}\right) \]

       4. distribute-lft-neg-in 23.4%

          \[\leadsto i \cdot \color{blue}{\left(\left(-y1 \cdot z\right) \cdot k\right)} \]

       5. distribute-rgt-neg-out 23.4%

          \[\leadsto i \cdot \left(\color{blue}{\left(y1 \cdot \left(-z\right)\right)} \cdot k\right) \]

       6. associate-*l* 26.1%

          \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \left(\left(-z\right) \cdot k\right)\right)} \]

       7. distribute-lft-neg-in 26.1%

          \[\leadsto i \cdot \left(y1 \cdot \color{blue}{\left(-z \cdot k\right)}\right) \]

       8. *-commutative 26.1%

          \[\leadsto i \cdot \left(y1 \cdot \left(-\color{blue}{k \cdot z}\right)\right) \]

       9. distribute-rgt-neg-in 26.1%

          \[\leadsto i \cdot \left(y1 \cdot \color{blue}{\left(k \cdot \left(-z\right)\right)}\right) \]

   14. Simplified 26.1%

       \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(k \cdot \left(-z\right)\right)\right)} \]

   if 7.69999999999999972e-208 < t < 1.12e-104

   1. Initial program 28.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.5%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 21.8%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 21.8%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 21.8%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 21.8%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 21.8%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in y around inf 43.7%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 43.7%

         \[\leadsto y \cdot \left(\color{blue}{\left(-1 \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)} - \left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right) \]

      2. neg-mul-1 43.7%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right) \]

      3. mul-1-neg 43.7%

         \[\leadsto y \cdot \left(\left(-k\right) \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(\color{blue}{\left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + c \cdot \left(i \cdot x\right)\right)\right) \]

   10. Simplified 43.7%

       \[\leadsto \color{blue}{y \cdot \left(\left(-k\right) \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(\left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right)} \]

   11. Taylor expanded in x around inf 44.5%

       \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(i \cdot \left(x \cdot y\right)\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg 44.5%

          \[\leadsto \color{blue}{-c \cdot \left(i \cdot \left(x \cdot y\right)\right)} \]

       2. *-commutative 44.5%

          \[\leadsto -\color{blue}{\left(i \cdot \left(x \cdot y\right)\right) \cdot c} \]

       3. distribute-rgt-neg-in 44.5%

          \[\leadsto \color{blue}{\left(i \cdot \left(x \cdot y\right)\right) \cdot \left(-c\right)} \]

       4. *-commutative 44.5%

          \[\leadsto \left(i \cdot \color{blue}{\left(y \cdot x\right)}\right) \cdot \left(-c\right) \]

   13. Simplified 44.5%

       \[\leadsto \color{blue}{\left(i \cdot \left(y \cdot x\right)\right) \cdot \left(-c\right)} \]

   if 9.80000000000000029e-85 < t < 1.9e95

   1. Initial program 38.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 38.5%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 43.2%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 43.2%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 43.2%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 43.2%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 43.2%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 39.6%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around 0 33.7%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y3\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 33.7%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(-y \cdot y3\right)}\right) \]

       2. distribute-lft-neg-out 33.7%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(\left(-y\right) \cdot y3\right)}\right) \]

       3. *-commutative 33.7%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y3 \cdot \left(-y\right)\right)}\right) \]

   11. Simplified 33.7%

       \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y3 \cdot \left(-y\right)\right)}\right) \]

   if 1.9e95 < t

   1. Initial program 13.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 13.5%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 18.9%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 18.9%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 18.9%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 18.9%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 18.9%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 41.2%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf 41.5%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 33.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 7.7 \cdot 10^{-208}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(z \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-104}:\\ \;\;\;\;c \cdot \left(\left(x \cdot y\right) \cdot \left(-i\right)\right)\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-85}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(z \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+95}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 21.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y1 \cdot \left(z \cdot \left(-k\right)\right)\right)\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-206}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-105}:\\ \;\;\;\;y \cdot \left(c \cdot \left(x \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+93}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* y1 (* z (- k))))))
   (if (<= t -1.15e+79)
     (* b (* j (* t y4)))
     (if (<= t 2e-206)
       t_1
       (if (<= t 2.8e-105)
         (* y (* c (* x (- i))))
         (if (<= t 1.1e-82)
           t_1
           (if (<= t 7.2e+93)
             (* a (* y5 (* y (- y3))))
             (* a (* y5 (* t y2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y1 * (z * -k));
	double tmp;
	if (t <= -1.15e+79) {
		tmp = b * (j * (t * y4));
	} else if (t <= 2e-206) {
		tmp = t_1;
	} else if (t <= 2.8e-105) {
		tmp = y * (c * (x * -i));
	} else if (t <= 1.1e-82) {
		tmp = t_1;
	} else if (t <= 7.2e+93) {
		tmp = a * (y5 * (y * -y3));
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (y1 * (z * -k))
    if (t <= (-1.15d+79)) then
        tmp = b * (j * (t * y4))
    else if (t <= 2d-206) then
        tmp = t_1
    else if (t <= 2.8d-105) then
        tmp = y * (c * (x * -i))
    else if (t <= 1.1d-82) then
        tmp = t_1
    else if (t <= 7.2d+93) then
        tmp = a * (y5 * (y * -y3))
    else
        tmp = a * (y5 * (t * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y1 * (z * -k));
	double tmp;
	if (t <= -1.15e+79) {
		tmp = b * (j * (t * y4));
	} else if (t <= 2e-206) {
		tmp = t_1;
	} else if (t <= 2.8e-105) {
		tmp = y * (c * (x * -i));
	} else if (t <= 1.1e-82) {
		tmp = t_1;
	} else if (t <= 7.2e+93) {
		tmp = a * (y5 * (y * -y3));
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (y1 * (z * -k))
	tmp = 0
	if t <= -1.15e+79:
		tmp = b * (j * (t * y4))
	elif t <= 2e-206:
		tmp = t_1
	elif t <= 2.8e-105:
		tmp = y * (c * (x * -i))
	elif t <= 1.1e-82:
		tmp = t_1
	elif t <= 7.2e+93:
		tmp = a * (y5 * (y * -y3))
	else:
		tmp = a * (y5 * (t * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(y1 * Float64(z * Float64(-k))))
	tmp = 0.0
	if (t <= -1.15e+79)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	elseif (t <= 2e-206)
		tmp = t_1;
	elseif (t <= 2.8e-105)
		tmp = Float64(y * Float64(c * Float64(x * Float64(-i))));
	elseif (t <= 1.1e-82)
		tmp = t_1;
	elseif (t <= 7.2e+93)
		tmp = Float64(a * Float64(y5 * Float64(y * Float64(-y3))));
	else
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (y1 * (z * -k));
	tmp = 0.0;
	if (t <= -1.15e+79)
		tmp = b * (j * (t * y4));
	elseif (t <= 2e-206)
		tmp = t_1;
	elseif (t <= 2.8e-105)
		tmp = y * (c * (x * -i));
	elseif (t <= 1.1e-82)
		tmp = t_1;
	elseif (t <= 7.2e+93)
		tmp = a * (y5 * (y * -y3));
	else
		tmp = a * (y5 * (t * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(y1 * N[(z * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+79], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e-206], t$95$1, If[LessEqual[t, 2.8e-105], N[(y * N[(c * N[(x * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e-82], t$95$1, If[LessEqual[t, 7.2e+93], N[(a * N[(y5 * N[(y * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.15e79

   1. Initial program 15.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 15.7%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 35.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 43.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 41.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 41.3%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   9. Simplified 41.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]

   if -1.15e79 < t < 2.00000000000000006e-206 or 2.8e-105 < t < 1.09999999999999993e-82

   1. Initial program 30.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.3%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 29.8%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 29.8%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 29.8%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 29.8%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 29.8%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in z around -inf 26.1%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   9. Taylor expanded in c around 0 23.4%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 23.4%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. distribute-rgt-neg-in 23.4%

          \[\leadsto \color{blue}{i \cdot \left(-k \cdot \left(y1 \cdot z\right)\right)} \]

       3. distribute-rgt-neg-in 23.4%

          \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(-y1 \cdot z\right)\right)} \]

       4. distribute-rgt-neg-in 23.4%

          \[\leadsto i \cdot \left(k \cdot \color{blue}{\left(y1 \cdot \left(-z\right)\right)}\right) \]

   11. Simplified 23.4%

       \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y1 \cdot \left(-z\right)\right)\right)} \]

   12. Taylor expanded in i around 0 23.4%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   13. Step-by-step derivation

       1. mul-1-neg 23.4%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. distribute-rgt-neg-in 23.4%

          \[\leadsto \color{blue}{i \cdot \left(-k \cdot \left(y1 \cdot z\right)\right)} \]

       3. *-commutative 23.4%

          \[\leadsto i \cdot \left(-\color{blue}{\left(y1 \cdot z\right) \cdot k}\right) \]

       4. distribute-lft-neg-in 23.4%

          \[\leadsto i \cdot \color{blue}{\left(\left(-y1 \cdot z\right) \cdot k\right)} \]

       5. distribute-rgt-neg-out 23.4%

          \[\leadsto i \cdot \left(\color{blue}{\left(y1 \cdot \left(-z\right)\right)} \cdot k\right) \]

       6. associate-*l* 26.1%

          \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \left(\left(-z\right) \cdot k\right)\right)} \]

       7. distribute-lft-neg-in 26.1%

          \[\leadsto i \cdot \left(y1 \cdot \color{blue}{\left(-z \cdot k\right)}\right) \]

       8. *-commutative 26.1%

          \[\leadsto i \cdot \left(y1 \cdot \left(-\color{blue}{k \cdot z}\right)\right) \]

       9. distribute-rgt-neg-in 26.1%

          \[\leadsto i \cdot \left(y1 \cdot \color{blue}{\left(k \cdot \left(-z\right)\right)}\right) \]

   14. Simplified 26.1%

       \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(k \cdot \left(-z\right)\right)\right)} \]

   if 2.00000000000000006e-206 < t < 2.8e-105

   1. Initial program 28.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.5%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 21.8%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 21.8%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 21.8%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 21.8%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 21.8%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in y around inf 43.7%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 43.7%

         \[\leadsto y \cdot \left(\color{blue}{\left(-1 \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)} - \left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right) \]

      2. neg-mul-1 43.7%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right) \]

      3. mul-1-neg 43.7%

         \[\leadsto y \cdot \left(\left(-k\right) \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(\color{blue}{\left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + c \cdot \left(i \cdot x\right)\right)\right) \]

   10. Simplified 43.7%

       \[\leadsto \color{blue}{y \cdot \left(\left(-k\right) \cdot \left(b \cdot y4 - i \cdot y5\right) - \left(\left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + c \cdot \left(i \cdot x\right)\right)\right)} \]

   11. Taylor expanded in x around inf 44.3%

       \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot x\right)\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg 44.3%

          \[\leadsto y \cdot \color{blue}{\left(-c \cdot \left(i \cdot x\right)\right)} \]

       2. distribute-rgt-neg-in 44.3%

          \[\leadsto y \cdot \color{blue}{\left(c \cdot \left(-i \cdot x\right)\right)} \]

       3. distribute-rgt-neg-in 44.3%

          \[\leadsto y \cdot \left(c \cdot \color{blue}{\left(i \cdot \left(-x\right)\right)}\right) \]

   13. Simplified 44.3%

       \[\leadsto y \cdot \color{blue}{\left(c \cdot \left(i \cdot \left(-x\right)\right)\right)} \]

   if 1.09999999999999993e-82 < t < 7.1999999999999998e93

   1. Initial program 38.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 38.5%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 43.2%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 43.2%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 43.2%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 43.2%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 43.2%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 39.6%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around 0 33.7%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y3\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 33.7%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(-y \cdot y3\right)}\right) \]

       2. distribute-lft-neg-out 33.7%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(\left(-y\right) \cdot y3\right)}\right) \]

       3. *-commutative 33.7%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y3 \cdot \left(-y\right)\right)}\right) \]

   11. Simplified 33.7%

       \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y3 \cdot \left(-y\right)\right)}\right) \]

   if 7.1999999999999998e93 < t

   1. Initial program 13.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 13.5%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 18.9%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 18.9%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 18.9%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 18.9%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 18.9%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 41.2%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf 41.5%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 33.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-206}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(z \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-105}:\\ \;\;\;\;y \cdot \left(c \cdot \left(x \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-82}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(z \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+93}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 22.0% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+76}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-58}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-97}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+95}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -1.6e+76)
   (* b (* j (* t y4)))
   (if (<= t -1.9e-58)
     (* c (* i (* z t)))
     (if (<= t 1.7e-97)
       (* b (* k (* z y0)))
       (if (<= t 9.6e+95) (* a (* y5 (* y (- y3)))) (* a (* y5 (* t y2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -1.6e+76) {
		tmp = b * (j * (t * y4));
	} else if (t <= -1.9e-58) {
		tmp = c * (i * (z * t));
	} else if (t <= 1.7e-97) {
		tmp = b * (k * (z * y0));
	} else if (t <= 9.6e+95) {
		tmp = a * (y5 * (y * -y3));
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (t <= (-1.6d+76)) then
        tmp = b * (j * (t * y4))
    else if (t <= (-1.9d-58)) then
        tmp = c * (i * (z * t))
    else if (t <= 1.7d-97) then
        tmp = b * (k * (z * y0))
    else if (t <= 9.6d+95) then
        tmp = a * (y5 * (y * -y3))
    else
        tmp = a * (y5 * (t * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -1.6e+76) {
		tmp = b * (j * (t * y4));
	} else if (t <= -1.9e-58) {
		tmp = c * (i * (z * t));
	} else if (t <= 1.7e-97) {
		tmp = b * (k * (z * y0));
	} else if (t <= 9.6e+95) {
		tmp = a * (y5 * (y * -y3));
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if t <= -1.6e+76:
		tmp = b * (j * (t * y4))
	elif t <= -1.9e-58:
		tmp = c * (i * (z * t))
	elif t <= 1.7e-97:
		tmp = b * (k * (z * y0))
	elif t <= 9.6e+95:
		tmp = a * (y5 * (y * -y3))
	else:
		tmp = a * (y5 * (t * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (t <= -1.6e+76)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	elseif (t <= -1.9e-58)
		tmp = Float64(c * Float64(i * Float64(z * t)));
	elseif (t <= 1.7e-97)
		tmp = Float64(b * Float64(k * Float64(z * y0)));
	elseif (t <= 9.6e+95)
		tmp = Float64(a * Float64(y5 * Float64(y * Float64(-y3))));
	else
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (t <= -1.6e+76)
		tmp = b * (j * (t * y4));
	elseif (t <= -1.9e-58)
		tmp = c * (i * (z * t));
	elseif (t <= 1.7e-97)
		tmp = b * (k * (z * y0));
	elseif (t <= 9.6e+95)
		tmp = a * (y5 * (y * -y3));
	else
		tmp = a * (y5 * (t * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[t, -1.6e+76], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.9e-58], N[(c * N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e-97], N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.6e+95], N[(a * N[(y5 * N[(y * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.59999999999999988e76

   1. Initial program 15.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 15.4%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 34.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 42.4%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 40.6%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 40.6%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   9. Simplified 40.6%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]

   if -1.59999999999999988e76 < t < -1.8999999999999999e-58

   1. Initial program 30.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.2%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 30.2%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 30.2%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 30.2%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 30.2%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 30.2%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in z around -inf 31.4%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   9. Taylor expanded in c around inf 25.2%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]

   if -1.8999999999999999e-58 < t < 1.6999999999999999e-97

   1. Initial program 30.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.0%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 40.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 30.1%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 30.1%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 30.1%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 30.1%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 21.4%

      \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 21.4%

          \[\leadsto b \cdot \left(k \cdot \color{blue}{\left(z \cdot y0\right)}\right) \]

   11. Simplified 21.4%

       \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(z \cdot y0\right)\right)} \]

   if 1.6999999999999999e-97 < t < 9.6000000000000002e95

   1. Initial program 38.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 38.9%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 43.5%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 43.5%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 43.5%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 43.5%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 43.5%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 40.1%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around 0 34.4%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y3\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 34.4%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(-y \cdot y3\right)}\right) \]

       2. distribute-lft-neg-out 34.4%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(\left(-y\right) \cdot y3\right)}\right) \]

       3. *-commutative 34.4%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y3 \cdot \left(-y\right)\right)}\right) \]

   11. Simplified 34.4%

       \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y3 \cdot \left(-y\right)\right)}\right) \]

   if 9.6000000000000002e95 < t

   1. Initial program 13.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 13.5%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 18.9%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 18.9%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 18.9%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 18.9%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 18.9%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 41.2%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf 41.5%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 31.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+76}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-58}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-97}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+95}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 28.1% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y3 \cdot \left(c \cdot \left(y \cdot y4\right)\right)\\ \mathbf{if}\;y4 \leq -4 \cdot 10^{+203}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 5.8 \cdot 10^{-90}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 4.6 \cdot 10^{+175}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y3 (* c (* y y4)))))
   (if (<= y4 -4e+203)
     t_1
     (if (<= y4 5.8e-90)
       (* b (* x (- (* y a) (* j y0))))
       (if (<= y4 4.6e+175) (* b (* a (- (* x y) (* z t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y3 * (c * (y * y4));
	double tmp;
	if (y4 <= -4e+203) {
		tmp = t_1;
	} else if (y4 <= 5.8e-90) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y4 <= 4.6e+175) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y3 * (c * (y * y4))
    if (y4 <= (-4d+203)) then
        tmp = t_1
    else if (y4 <= 5.8d-90) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y4 <= 4.6d+175) then
        tmp = b * (a * ((x * y) - (z * t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y3 * (c * (y * y4));
	double tmp;
	if (y4 <= -4e+203) {
		tmp = t_1;
	} else if (y4 <= 5.8e-90) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y4 <= 4.6e+175) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y3 * (c * (y * y4))
	tmp = 0
	if y4 <= -4e+203:
		tmp = t_1
	elif y4 <= 5.8e-90:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y4 <= 4.6e+175:
		tmp = b * (a * ((x * y) - (z * t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y3 * Float64(c * Float64(y * y4)))
	tmp = 0.0
	if (y4 <= -4e+203)
		tmp = t_1;
	elseif (y4 <= 5.8e-90)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y4 <= 4.6e+175)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y3 * (c * (y * y4));
	tmp = 0.0;
	if (y4 <= -4e+203)
		tmp = t_1;
	elseif (y4 <= 5.8e-90)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y4 <= 4.6e+175)
		tmp = b * (a * ((x * y) - (z * t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y3 * N[(c * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -4e+203], t$95$1, If[LessEqual[y4, 5.8e-90], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 4.6e+175], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y4 < -4e203 or 4.5999999999999999e175 < y4

   1. Initial program 10.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 10.8%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 17.1%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 17.1%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 17.1%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 17.1%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 17.1%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in y3 around -inf 42.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   9. Taylor expanded in c around inf 49.3%

      \[\leadsto -1 \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(y \cdot y4\right)\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 49.3%

          \[\leadsto -1 \cdot \left(y3 \cdot \color{blue}{\left(-c \cdot \left(y \cdot y4\right)\right)}\right) \]

       2. *-commutative 49.3%

          \[\leadsto -1 \cdot \left(y3 \cdot \left(-\color{blue}{\left(y \cdot y4\right) \cdot c}\right)\right) \]

       3. distribute-rgt-neg-in 49.3%

          \[\leadsto -1 \cdot \left(y3 \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot \left(-c\right)\right)}\right) \]

   11. Simplified 49.3%

       \[\leadsto -1 \cdot \left(y3 \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot \left(-c\right)\right)}\right) \]

   if -4e203 < y4 < 5.79999999999999967e-90

   1. Initial program 32.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.1%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 42.4%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if 5.79999999999999967e-90 < y4 < 4.5999999999999999e175

   1. Initial program 24.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.0%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 32.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 39.0%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -4 \cdot 10^{+203}:\\ \;\;\;\;y3 \cdot \left(c \cdot \left(y \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 5.8 \cdot 10^{-90}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 4.6 \cdot 10^{+175}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(c \cdot \left(y \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 22.3% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+77}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-117}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(z \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+95}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -5.4e+77)
   (* b (* j (* t y4)))
   (if (<= t 4.8e-117)
     (* i (* y1 (* z (- k))))
     (if (<= t 1.85e+95) (* a (* y5 (* y (- y3)))) (* a (* y5 (* t y2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -5.4e+77) {
		tmp = b * (j * (t * y4));
	} else if (t <= 4.8e-117) {
		tmp = i * (y1 * (z * -k));
	} else if (t <= 1.85e+95) {
		tmp = a * (y5 * (y * -y3));
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (t <= (-5.4d+77)) then
        tmp = b * (j * (t * y4))
    else if (t <= 4.8d-117) then
        tmp = i * (y1 * (z * -k))
    else if (t <= 1.85d+95) then
        tmp = a * (y5 * (y * -y3))
    else
        tmp = a * (y5 * (t * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -5.4e+77) {
		tmp = b * (j * (t * y4));
	} else if (t <= 4.8e-117) {
		tmp = i * (y1 * (z * -k));
	} else if (t <= 1.85e+95) {
		tmp = a * (y5 * (y * -y3));
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if t <= -5.4e+77:
		tmp = b * (j * (t * y4))
	elif t <= 4.8e-117:
		tmp = i * (y1 * (z * -k))
	elif t <= 1.85e+95:
		tmp = a * (y5 * (y * -y3))
	else:
		tmp = a * (y5 * (t * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (t <= -5.4e+77)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	elseif (t <= 4.8e-117)
		tmp = Float64(i * Float64(y1 * Float64(z * Float64(-k))));
	elseif (t <= 1.85e+95)
		tmp = Float64(a * Float64(y5 * Float64(y * Float64(-y3))));
	else
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (t <= -5.4e+77)
		tmp = b * (j * (t * y4));
	elseif (t <= 4.8e-117)
		tmp = i * (y1 * (z * -k));
	elseif (t <= 1.85e+95)
		tmp = a * (y5 * (y * -y3));
	else
		tmp = a * (y5 * (t * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[t, -5.4e+77], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-117], N[(i * N[(y1 * N[(z * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e+95], N[(a * N[(y5 * N[(y * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.3999999999999997e77

   1. Initial program 15.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 15.7%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 35.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 43.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 41.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 41.3%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   9. Simplified 41.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]

   if -5.3999999999999997e77 < t < 4.80000000000000028e-117

   1. Initial program 29.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.6%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 29.1%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 29.1%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 29.1%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 29.1%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 29.1%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in z around -inf 23.1%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   9. Taylor expanded in c around 0 20.5%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 20.5%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. distribute-rgt-neg-in 20.5%

          \[\leadsto \color{blue}{i \cdot \left(-k \cdot \left(y1 \cdot z\right)\right)} \]

       3. distribute-rgt-neg-in 20.5%

          \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(-y1 \cdot z\right)\right)} \]

       4. distribute-rgt-neg-in 20.5%

          \[\leadsto i \cdot \left(k \cdot \color{blue}{\left(y1 \cdot \left(-z\right)\right)}\right) \]

   11. Simplified 20.5%

       \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y1 \cdot \left(-z\right)\right)\right)} \]

   12. Taylor expanded in i around 0 20.5%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   13. Step-by-step derivation

       1. mul-1-neg 20.5%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. distribute-rgt-neg-in 20.5%

          \[\leadsto \color{blue}{i \cdot \left(-k \cdot \left(y1 \cdot z\right)\right)} \]

       3. *-commutative 20.5%

          \[\leadsto i \cdot \left(-\color{blue}{\left(y1 \cdot z\right) \cdot k}\right) \]

       4. distribute-lft-neg-in 20.5%

          \[\leadsto i \cdot \color{blue}{\left(\left(-y1 \cdot z\right) \cdot k\right)} \]

       5. distribute-rgt-neg-out 20.5%

          \[\leadsto i \cdot \left(\color{blue}{\left(y1 \cdot \left(-z\right)\right)} \cdot k\right) \]

       6. associate-*l* 23.8%

          \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \left(\left(-z\right) \cdot k\right)\right)} \]

       7. distribute-lft-neg-in 23.8%

          \[\leadsto i \cdot \left(y1 \cdot \color{blue}{\left(-z \cdot k\right)}\right) \]

       8. *-commutative 23.8%

          \[\leadsto i \cdot \left(y1 \cdot \left(-\color{blue}{k \cdot z}\right)\right) \]

       9. distribute-rgt-neg-in 23.8%

          \[\leadsto i \cdot \left(y1 \cdot \color{blue}{\left(k \cdot \left(-z\right)\right)}\right) \]

   14. Simplified 23.8%

       \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(k \cdot \left(-z\right)\right)\right)} \]

   if 4.80000000000000028e-117 < t < 1.8500000000000001e95

   1. Initial program 38.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 38.3%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 40.5%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 40.5%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 40.5%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 40.5%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 40.5%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 41.3%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around 0 34.4%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y3\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 34.4%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(-y \cdot y3\right)}\right) \]

       2. distribute-lft-neg-out 34.4%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(\left(-y\right) \cdot y3\right)}\right) \]

       3. *-commutative 34.4%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y3 \cdot \left(-y\right)\right)}\right) \]

   11. Simplified 34.4%

       \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y3 \cdot \left(-y\right)\right)}\right) \]

   if 1.8500000000000001e95 < t

   1. Initial program 13.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 13.5%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 18.9%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 18.9%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 18.9%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 18.9%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 18.9%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 41.2%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf 41.5%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+77}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-117}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(z \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+95}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 22.5% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-147}:\\ \;\;\;\;i \cdot \left(k \cdot \left(z \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+97}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -7.4e+79)
   (* b (* j (* t y4)))
   (if (<= t 5.8e-147)
     (* i (* k (* z (- y1))))
     (if (<= t 1.3e+97) (* a (* y5 (* y (- y3)))) (* a (* y5 (* t y2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -7.4e+79) {
		tmp = b * (j * (t * y4));
	} else if (t <= 5.8e-147) {
		tmp = i * (k * (z * -y1));
	} else if (t <= 1.3e+97) {
		tmp = a * (y5 * (y * -y3));
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (t <= (-7.4d+79)) then
        tmp = b * (j * (t * y4))
    else if (t <= 5.8d-147) then
        tmp = i * (k * (z * -y1))
    else if (t <= 1.3d+97) then
        tmp = a * (y5 * (y * -y3))
    else
        tmp = a * (y5 * (t * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -7.4e+79) {
		tmp = b * (j * (t * y4));
	} else if (t <= 5.8e-147) {
		tmp = i * (k * (z * -y1));
	} else if (t <= 1.3e+97) {
		tmp = a * (y5 * (y * -y3));
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if t <= -7.4e+79:
		tmp = b * (j * (t * y4))
	elif t <= 5.8e-147:
		tmp = i * (k * (z * -y1))
	elif t <= 1.3e+97:
		tmp = a * (y5 * (y * -y3))
	else:
		tmp = a * (y5 * (t * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (t <= -7.4e+79)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	elseif (t <= 5.8e-147)
		tmp = Float64(i * Float64(k * Float64(z * Float64(-y1))));
	elseif (t <= 1.3e+97)
		tmp = Float64(a * Float64(y5 * Float64(y * Float64(-y3))));
	else
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (t <= -7.4e+79)
		tmp = b * (j * (t * y4));
	elseif (t <= 5.8e-147)
		tmp = i * (k * (z * -y1));
	elseif (t <= 1.3e+97)
		tmp = a * (y5 * (y * -y3));
	else
		tmp = a * (y5 * (t * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[t, -7.4e+79], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e-147], N[(i * N[(k * N[(z * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+97], N[(a * N[(y5 * N[(y * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.40000000000000019e79

   1. Initial program 15.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 15.7%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 35.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 43.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 41.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 41.3%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   9. Simplified 41.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]

   if -7.40000000000000019e79 < t < 5.8000000000000002e-147

   1. Initial program 30.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.1%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 29.7%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 29.7%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 29.7%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 29.7%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 29.7%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in z around -inf 23.4%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   9. Taylor expanded in c around 0 20.8%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 20.8%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. distribute-rgt-neg-in 20.8%

          \[\leadsto \color{blue}{i \cdot \left(-k \cdot \left(y1 \cdot z\right)\right)} \]

       3. distribute-rgt-neg-in 20.8%

          \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(-y1 \cdot z\right)\right)} \]

       4. distribute-rgt-neg-in 20.8%

          \[\leadsto i \cdot \left(k \cdot \color{blue}{\left(y1 \cdot \left(-z\right)\right)}\right) \]

   11. Simplified 20.8%

       \[\leadsto \color{blue}{i \cdot \left(k \cdot \left(y1 \cdot \left(-z\right)\right)\right)} \]

   if 5.8000000000000002e-147 < t < 1.3e97

   1. Initial program 37.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.0%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 39.1%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 39.1%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 39.1%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 39.1%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 39.1%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 39.9%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around 0 33.3%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y3\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 33.3%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(-y \cdot y3\right)}\right) \]

       2. distribute-lft-neg-out 33.3%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(\left(-y\right) \cdot y3\right)}\right) \]

       3. *-commutative 33.3%

          \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y3 \cdot \left(-y\right)\right)}\right) \]

   11. Simplified 33.3%

       \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(y3 \cdot \left(-y\right)\right)}\right) \]

   if 1.3e97 < t

   1. Initial program 13.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 13.5%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 18.9%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 18.9%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 18.9%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 18.9%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 18.9%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 41.2%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf 41.5%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 30.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-147}:\\ \;\;\;\;i \cdot \left(k \cdot \left(z \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+97}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(y \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 21.3% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -1.15 \cdot 10^{-41}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 1.65 \cdot 10^{-129}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 3.5 \cdot 10^{+163}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -1.15e-41)
   (* a (* y5 (* t y2)))
   (if (<= y2 1.65e-129)
     (* c (* i (* z t)))
     (if (<= y2 3.5e+163) (* b (* k (* y (- y4)))) (* a (* t (* y2 y5)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.15e-41) {
		tmp = a * (y5 * (t * y2));
	} else if (y2 <= 1.65e-129) {
		tmp = c * (i * (z * t));
	} else if (y2 <= 3.5e+163) {
		tmp = b * (k * (y * -y4));
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-1.15d-41)) then
        tmp = a * (y5 * (t * y2))
    else if (y2 <= 1.65d-129) then
        tmp = c * (i * (z * t))
    else if (y2 <= 3.5d+163) then
        tmp = b * (k * (y * -y4))
    else
        tmp = a * (t * (y2 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.15e-41) {
		tmp = a * (y5 * (t * y2));
	} else if (y2 <= 1.65e-129) {
		tmp = c * (i * (z * t));
	} else if (y2 <= 3.5e+163) {
		tmp = b * (k * (y * -y4));
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -1.15e-41:
		tmp = a * (y5 * (t * y2))
	elif y2 <= 1.65e-129:
		tmp = c * (i * (z * t))
	elif y2 <= 3.5e+163:
		tmp = b * (k * (y * -y4))
	else:
		tmp = a * (t * (y2 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -1.15e-41)
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	elseif (y2 <= 1.65e-129)
		tmp = Float64(c * Float64(i * Float64(z * t)));
	elseif (y2 <= 3.5e+163)
		tmp = Float64(b * Float64(k * Float64(y * Float64(-y4))));
	else
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -1.15e-41)
		tmp = a * (y5 * (t * y2));
	elseif (y2 <= 1.65e-129)
		tmp = c * (i * (z * t));
	elseif (y2 <= 3.5e+163)
		tmp = b * (k * (y * -y4));
	else
		tmp = a * (t * (y2 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -1.15e-41], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.65e-129], N[(c * N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.5e+163], N[(b * N[(k * N[(y * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -1.15000000000000005e-41

   1. Initial program 27.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.7%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 22.0%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 22.0%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 22.0%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 22.0%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 22.0%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 30.3%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf 24.4%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]

   if -1.15000000000000005e-41 < y2 < 1.64999999999999994e-129

   1. Initial program 27.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.2%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 32.7%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 32.7%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 32.7%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 32.7%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 32.7%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in z around -inf 37.8%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   9. Taylor expanded in c around inf 26.2%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]

   if 1.64999999999999994e-129 < y2 < 3.5000000000000003e163

   1. Initial program 31.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.2%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 43.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y around -inf 42.2%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 42.2%

         \[\leadsto \color{blue}{-b \cdot \left(y \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)\right)} \]

      2. associate-*r* 33.2%

         \[\leadsto -\color{blue}{\left(b \cdot y\right) \cdot \left(-1 \cdot \left(a \cdot x\right) + k \cdot y4\right)} \]

      3. mul-1-neg 33.2%

         \[\leadsto -\left(b \cdot y\right) \cdot \left(\color{blue}{\left(-a \cdot x\right)} + k \cdot y4\right) \]

   8. Simplified 33.2%

      \[\leadsto \color{blue}{-\left(b \cdot y\right) \cdot \left(\left(-a \cdot x\right) + k \cdot y4\right)} \]

   9. Taylor expanded in a around 0 26.7%

      \[\leadsto -\color{blue}{b \cdot \left(k \cdot \left(y \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 26.7%

          \[\leadsto -b \cdot \color{blue}{\left(\left(y \cdot y4\right) \cdot k\right)} \]

   11. Simplified 26.7%

       \[\leadsto -\color{blue}{b \cdot \left(\left(y \cdot y4\right) \cdot k\right)} \]

   if 3.5000000000000003e163 < y2

   1. Initial program 12.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 12.1%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 12.3%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 12.3%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 12.3%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 12.3%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 12.3%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 41.9%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf 44.5%

      \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 44.5%

          \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   11. Simplified 44.5%

       \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(y5 \cdot y2\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 28.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.15 \cdot 10^{-41}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 1.65 \cdot 10^{-129}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 3.5 \cdot 10^{+163}:\\ \;\;\;\;b \cdot \left(k \cdot \left(y \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 34: 21.1% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -1.15 \cdot 10^{-41}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 1.8 \cdot 10^{-132}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 9.2 \cdot 10^{+153}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -1.15e-41)
   (* a (* y5 (* t y2)))
   (if (<= y2 1.8e-132)
     (* c (* i (* z t)))
     (if (<= y2 9.2e+153) (* i (* j (* x y1))) (* a (* t (* y2 y5)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.15e-41) {
		tmp = a * (y5 * (t * y2));
	} else if (y2 <= 1.8e-132) {
		tmp = c * (i * (z * t));
	} else if (y2 <= 9.2e+153) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-1.15d-41)) then
        tmp = a * (y5 * (t * y2))
    else if (y2 <= 1.8d-132) then
        tmp = c * (i * (z * t))
    else if (y2 <= 9.2d+153) then
        tmp = i * (j * (x * y1))
    else
        tmp = a * (t * (y2 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.15e-41) {
		tmp = a * (y5 * (t * y2));
	} else if (y2 <= 1.8e-132) {
		tmp = c * (i * (z * t));
	} else if (y2 <= 9.2e+153) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -1.15e-41:
		tmp = a * (y5 * (t * y2))
	elif y2 <= 1.8e-132:
		tmp = c * (i * (z * t))
	elif y2 <= 9.2e+153:
		tmp = i * (j * (x * y1))
	else:
		tmp = a * (t * (y2 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -1.15e-41)
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	elseif (y2 <= 1.8e-132)
		tmp = Float64(c * Float64(i * Float64(z * t)));
	elseif (y2 <= 9.2e+153)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	else
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -1.15e-41)
		tmp = a * (y5 * (t * y2));
	elseif (y2 <= 1.8e-132)
		tmp = c * (i * (z * t));
	elseif (y2 <= 9.2e+153)
		tmp = i * (j * (x * y1));
	else
		tmp = a * (t * (y2 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -1.15e-41], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.8e-132], N[(c * N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 9.2e+153], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -1.15000000000000005e-41

   1. Initial program 27.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.7%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 22.0%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 22.0%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 22.0%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 22.0%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 22.0%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 30.3%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf 24.4%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]

   if -1.15000000000000005e-41 < y2 < 1.80000000000000004e-132

   1. Initial program 26.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.4%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 31.9%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 31.9%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 31.9%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 31.9%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 31.9%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in z around -inf 38.2%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   9. Taylor expanded in c around inf 26.4%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]

   if 1.80000000000000004e-132 < y2 < 9.2000000000000005e153

   1. Initial program 33.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.8%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y1 around inf 38.2%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 38.2%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + -1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. mul-1-neg 38.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. unsub-neg 38.2%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      4. *-commutative 38.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right) - a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      5. *-commutative 38.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      6. *-commutative 38.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      7. mul-1-neg 38.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-i \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      8. *-commutative 38.2%

         \[\leadsto y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) \]

   7. Simplified 38.2%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-i \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} \]

   8. Taylor expanded in i around inf 27.2%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 22.5%

         \[\leadsto \color{blue}{\left(i \cdot y1\right) \cdot \left(j \cdot x - k \cdot z\right)} \]

   10. Simplified 22.5%

       \[\leadsto \color{blue}{\left(i \cdot y1\right) \cdot \left(j \cdot x - k \cdot z\right)} \]

   11. Taylor expanded in j around inf 19.1%

       \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]

   if 9.2000000000000005e153 < y2

   1. Initial program 11.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 11.1%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 14.0%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 14.0%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 14.0%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 14.0%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 14.0%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 41.3%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf 41.1%

      \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 41.1%

          \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   11. Simplified 41.1%

       \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(y5 \cdot y2\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 26.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.15 \cdot 10^{-41}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 1.8 \cdot 10^{-132}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;y2 \leq 9.2 \cdot 10^{+153}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 35: 20.8% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;i \leq -2.05 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -2.45 \cdot 10^{-230}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{+162}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* i (* z t)))))
   (if (<= i -2.05e+188)
     t_1
     (if (<= i -2.45e-230)
       (* b (* k (* z y0)))
       (if (<= i 1.05e+162) (* b (* j (* 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 = c * (i * (z * t));
	double tmp;
	if (i <= -2.05e+188) {
		tmp = t_1;
	} else if (i <= -2.45e-230) {
		tmp = b * (k * (z * y0));
	} else if (i <= 1.05e+162) {
		tmp = b * (j * (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 = c * (i * (z * t))
    if (i <= (-2.05d+188)) then
        tmp = t_1
    else if (i <= (-2.45d-230)) then
        tmp = b * (k * (z * y0))
    else if (i <= 1.05d+162) then
        tmp = b * (j * (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 = c * (i * (z * t));
	double tmp;
	if (i <= -2.05e+188) {
		tmp = t_1;
	} else if (i <= -2.45e-230) {
		tmp = b * (k * (z * y0));
	} else if (i <= 1.05e+162) {
		tmp = b * (j * (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 = c * (i * (z * t))
	tmp = 0
	if i <= -2.05e+188:
		tmp = t_1
	elif i <= -2.45e-230:
		tmp = b * (k * (z * y0))
	elif i <= 1.05e+162:
		tmp = b * (j * (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(c * Float64(i * Float64(z * t)))
	tmp = 0.0
	if (i <= -2.05e+188)
		tmp = t_1;
	elseif (i <= -2.45e-230)
		tmp = Float64(b * Float64(k * Float64(z * y0)));
	elseif (i <= 1.05e+162)
		tmp = Float64(b * Float64(j * 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 = c * (i * (z * t));
	tmp = 0.0;
	if (i <= -2.05e+188)
		tmp = t_1;
	elseif (i <= -2.45e-230)
		tmp = b * (k * (z * y0));
	elseif (i <= 1.05e+162)
		tmp = b * (j * (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[(c * N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.05e+188], t$95$1, If[LessEqual[i, -2.45e-230], N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.05e+162], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -2.05e188 or 1.05e162 < i

   1. Initial program 25.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.9%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 31.9%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 31.9%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 31.9%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 31.9%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 31.9%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in z around -inf 38.2%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   9. Taylor expanded in c around inf 37.9%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]

   if -2.05e188 < i < -2.44999999999999996e-230

   1. Initial program 31.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.2%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 36.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 29.3%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 29.3%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 29.3%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 29.3%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 22.6%

      \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 22.6%

          \[\leadsto b \cdot \left(k \cdot \color{blue}{\left(z \cdot y0\right)}\right) \]

   11. Simplified 22.6%

       \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(z \cdot y0\right)\right)} \]

   if -2.44999999999999996e-230 < i < 1.05e162

   1. Initial program 22.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 22.6%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 41.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 34.0%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 23.6%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 23.6%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   9. Simplified 23.6%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 26.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.05 \cdot 10^{+188}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;i \leq -2.45 \cdot 10^{-230}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{+162}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 36: 22.0% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+100}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+92}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -1.6e+100)
   (* b (* j (* t y4)))
   (if (<= t 4.4e+92) (* b (* k (* z y0))) (* a (* y5 (* t y2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -1.6e+100) {
		tmp = b * (j * (t * y4));
	} else if (t <= 4.4e+92) {
		tmp = b * (k * (z * y0));
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (t <= (-1.6d+100)) then
        tmp = b * (j * (t * y4))
    else if (t <= 4.4d+92) then
        tmp = b * (k * (z * y0))
    else
        tmp = a * (y5 * (t * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -1.6e+100) {
		tmp = b * (j * (t * y4));
	} else if (t <= 4.4e+92) {
		tmp = b * (k * (z * y0));
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if t <= -1.6e+100:
		tmp = b * (j * (t * y4))
	elif t <= 4.4e+92:
		tmp = b * (k * (z * y0))
	else:
		tmp = a * (y5 * (t * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (t <= -1.6e+100)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	elseif (t <= 4.4e+92)
		tmp = Float64(b * Float64(k * Float64(z * y0)));
	else
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (t <= -1.6e+100)
		tmp = b * (j * (t * y4));
	elseif (t <= 4.4e+92)
		tmp = b * (k * (z * y0));
	else
		tmp = a * (y5 * (t * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[t, -1.6e+100], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e+92], N[(b * N[(k * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.5999999999999999e100

   1. Initial program 15.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 15.0%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 36.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 47.5%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 45.5%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 45.5%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   9. Simplified 45.5%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]

   if -1.5999999999999999e100 < t < 4.39999999999999984e92

   1. Initial program 32.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.4%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in k around -inf 25.3%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 25.3%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 25.3%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   8. Simplified 25.3%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 17.5%

      \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(y0 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 17.5%

          \[\leadsto b \cdot \left(k \cdot \color{blue}{\left(z \cdot y0\right)}\right) \]

   11. Simplified 17.5%

       \[\leadsto b \cdot \color{blue}{\left(k \cdot \left(z \cdot y0\right)\right)} \]

   if 4.39999999999999984e92 < t

   1. Initial program 13.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 13.2%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 21.1%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 21.1%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 21.1%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 21.1%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 21.1%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 42.8%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf 40.5%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 26.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+100}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+92}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 37: 21.1% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -6.5 \cdot 10^{-42}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 1.95 \cdot 10^{+166}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -6.5e-42)
   (* a (* y5 (* t y2)))
   (if (<= y2 1.95e+166) (* b (* j (* t y4))) (* a (* t (* y2 y5))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -6.5e-42) {
		tmp = a * (y5 * (t * y2));
	} else if (y2 <= 1.95e+166) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-6.5d-42)) then
        tmp = a * (y5 * (t * y2))
    else if (y2 <= 1.95d+166) then
        tmp = b * (j * (t * y4))
    else
        tmp = a * (t * (y2 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -6.5e-42) {
		tmp = a * (y5 * (t * y2));
	} else if (y2 <= 1.95e+166) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -6.5e-42:
		tmp = a * (y5 * (t * y2))
	elif y2 <= 1.95e+166:
		tmp = b * (j * (t * y4))
	else:
		tmp = a * (t * (y2 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -6.5e-42)
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	elseif (y2 <= 1.95e+166)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	else
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -6.5e-42)
		tmp = a * (y5 * (t * y2));
	elseif (y2 <= 1.95e+166)
		tmp = b * (j * (t * y4));
	else
		tmp = a * (t * (y2 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -6.5e-42], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.95e+166], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y2 < -6.4999999999999998e-42

   1. Initial program 27.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.3%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 21.6%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 21.6%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 21.6%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 21.6%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 21.6%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 30.0%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf 24.0%

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]

   if -6.4999999999999998e-42 < y2 < 1.94999999999999996e166

   1. Initial program 28.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.8%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 43.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 30.4%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 18.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 18.1%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   9. Simplified 18.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]

   if 1.94999999999999996e166 < y2

   1. Initial program 12.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 12.5%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 12.7%

      \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 12.7%

         \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      2. *-commutative 12.7%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

      3. *-commutative 12.7%

         \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   7. Simplified 12.7%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   8. Taylor expanded in a around inf 43.2%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in t around inf 45.8%

      \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(y2 \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 45.8%

          \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   11. Simplified 45.8%

       \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(y5 \cdot y2\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 23.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -6.5 \cdot 10^{-42}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 1.95 \cdot 10^{+166}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 38: 16.6% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* y2 (* t y5))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y2 * (t * y5));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * (y2 * (t * y5))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y2 * (t * y5));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (y2 * (t * y5))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(y2 * Float64(t * y5)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (y2 * (t * y5));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y2 * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 26.3%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

3. Simplified 26.3%

   \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
4. Add Preprocessing

5. Taylor expanded in i around -inf 28.6%

   \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
6. Step-by-step derivation

   1. mul-1-neg 28.6%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   2. *-commutative 28.6%

      \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   3. *-commutative 28.6%

      \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

7. Simplified 28.6%

   \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

8. Taylor expanded in a around inf 27.1%

   \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

9. Taylor expanded in t around inf 15.6%

   \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(y2 \cdot y5\right)\right)} \]
10. Step-by-step derivation

    1. *-commutative 15.6%

       \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

11. Simplified 15.6%

    \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(y5 \cdot y2\right)\right)} \]
12. Step-by-step derivation

    1. associate-*r* 15.9%

       \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot y5\right) \cdot y2\right)} \]

13. Applied egg-rr 15.9%

    \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot y5\right) \cdot y2\right)} \]

14. Final simplification 15.9%

    \[\leadsto a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right) \]
15. Add Preprocessing

Alternative 39: 16.7% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* y5 (* t y2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y5 * (t * 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 = a * (y5 * (t * 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 a * (y5 * (t * y2));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (y5 * (t * y2))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(y5 * Float64(t * y2)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (y5 * (t * y2));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 26.3%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

3. Simplified 26.3%

   \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
4. Add Preprocessing

5. Taylor expanded in i around -inf 28.6%

   \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
6. Step-by-step derivation

   1. mul-1-neg 28.6%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   2. *-commutative 28.6%

      \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   3. *-commutative 28.6%

      \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

7. Simplified 28.6%

   \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

8. Taylor expanded in a around inf 27.1%

   \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

9. Taylor expanded in t around inf 15.6%

   \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2\right)}\right) \]
10. Add Preprocessing

Alternative 40: 16.7% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* t (* y2 y5))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (t * (y2 * y5));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * (t * (y2 * y5))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (t * (y2 * y5));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (t * (y2 * y5))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(t * Float64(y2 * y5)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (t * (y2 * y5));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 26.3%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

3. Simplified 26.3%

   \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(\left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right) - \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
4. Add Preprocessing

5. Taylor expanded in i around -inf 28.6%

   \[\leadsto \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]
6. Step-by-step derivation

   1. mul-1-neg 28.6%

      \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   2. *-commutative 28.6%

      \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

   3. *-commutative 28.6%

      \[\leadsto \left(\left(\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

7. Simplified 28.6%

   \[\leadsto \left(\left(\color{blue}{\left(-i \cdot \left(c \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right)\right)} + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) \]

8. Taylor expanded in a around inf 27.1%

   \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

9. Taylor expanded in t around inf 15.6%

   \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(y2 \cdot y5\right)\right)} \]
10. Step-by-step derivation

    1. *-commutative 15.6%

       \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

11. Simplified 15.6%

    \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(y5 \cdot y2\right)\right)} \]

12. Final simplification 15.6%

    \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right) \]
13. Add Preprocessing

Developer target: 28.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot c - y5 \cdot a\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := y2 \cdot t - y3 \cdot y\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := y4 \cdot b - y5 \cdot i\\ t_6 := \left(j \cdot t - k \cdot y\right) \cdot t\_5\\ t_7 := b \cdot a - i \cdot c\\ t_8 := t\_7 \cdot \left(y \cdot x - t \cdot z\right)\\ t_9 := j \cdot x - k \cdot z\\ t_10 := \left(b \cdot y0 - i \cdot y1\right) \cdot t\_9\\ t_11 := t\_9 \cdot \left(y0 \cdot b - i \cdot y1\right)\\ t_12 := y4 \cdot y1 - y5 \cdot y0\\ t_13 := t\_4 \cdot t\_12\\ t_14 := \left(y2 \cdot k - y3 \cdot j\right) \cdot t\_12\\ t_15 := \left(\left(\left(\left(k \cdot y\right) \cdot \left(y5 \cdot i\right) - \left(y \cdot b\right) \cdot \left(y4 \cdot k\right)\right) - \left(y5 \cdot t\right) \cdot \left(i \cdot j\right)\right) - \left(t\_3 \cdot t\_1 - t\_14\right)\right) + \left(t\_8 - \left(t\_11 - \left(y2 \cdot x - y3 \cdot z\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right)\right)\\ t_16 := \left(\left(t\_6 - \left(y3 \cdot y\right) \cdot \left(y5 \cdot a - y4 \cdot c\right)\right) + \left(\left(y5 \cdot a\right) \cdot \left(t \cdot y2\right) + t\_13\right)\right) + \left(t\_2 \cdot \left(c \cdot y0 - a \cdot y1\right) - \left(t\_10 - \left(y \cdot x - z \cdot t\right) \cdot t\_7\right)\right)\\ t_17 := t \cdot y2 - y \cdot y3\\ \mathbf{if}\;y4 < -7.206256231996481 \cdot 10^{+60}:\\ \;\;\;\;\left(t\_8 - \left(t\_11 - t\_6\right)\right) - \left(\frac{t\_3}{\frac{1}{t\_1}} - t\_14\right)\\ \mathbf{elif}\;y4 < -3.364603505246317 \cdot 10^{-66}:\\ \;\;\;\;\left(\left(\left(\left(t \cdot c\right) \cdot \left(i \cdot z\right) - \left(a \cdot t\right) \cdot \left(b \cdot z\right)\right) - \left(y \cdot c\right) \cdot \left(i \cdot x\right)\right) - t\_10\right) + \left(\left(y0 \cdot c - a \cdot y1\right) \cdot t\_2 - \left(t\_17 \cdot \left(y4 \cdot c - a \cdot y5\right) - \left(y1 \cdot y4 - y5 \cdot y0\right) \cdot t\_4\right)\right)\\ \mathbf{elif}\;y4 < -1.2000065055686116 \cdot 10^{-105}:\\ \;\;\;\;t\_16\\ \mathbf{elif}\;y4 < 6.718963124057495 \cdot 10^{-279}:\\ \;\;\;\;t\_15\\ \mathbf{elif}\;y4 < 4.77962681403792 \cdot 10^{-222}:\\ \;\;\;\;t\_16\\ \mathbf{elif}\;y4 < 2.2852241541266835 \cdot 10^{-175}:\\ \;\;\;\;t\_15\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(k \cdot \left(i \cdot \left(z \cdot y1\right)\right) - \left(j \cdot \left(i \cdot \left(x \cdot y1\right)\right) + y0 \cdot \left(k \cdot \left(z \cdot b\right)\right)\right)\right)\right) + \left(z \cdot \left(y3 \cdot \left(a \cdot y1\right)\right) - \left(y2 \cdot \left(x \cdot \left(a \cdot y1\right)\right) + y0 \cdot \left(z \cdot \left(c \cdot y3\right)\right)\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot t\_5\right) - t\_17 \cdot t\_1\right) + t\_13\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y4 c) (* y5 a)))
        (t_2 (- (* x y2) (* z y3)))
        (t_3 (- (* y2 t) (* y3 y)))
        (t_4 (- (* k y2) (* j y3)))
        (t_5 (- (* y4 b) (* y5 i)))
        (t_6 (* (- (* j t) (* k y)) t_5))
        (t_7 (- (* b a) (* i c)))
        (t_8 (* t_7 (- (* y x) (* t z))))
        (t_9 (- (* j x) (* k z)))
        (t_10 (* (- (* b y0) (* i y1)) t_9))
        (t_11 (* t_9 (- (* y0 b) (* i y1))))
        (t_12 (- (* y4 y1) (* y5 y0)))
        (t_13 (* t_4 t_12))
        (t_14 (* (- (* y2 k) (* y3 j)) t_12))
        (t_15
         (+
          (-
           (-
            (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k)))
            (* (* y5 t) (* i j)))
           (- (* t_3 t_1) t_14))
          (- t_8 (- t_11 (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))))
        (t_16
         (+
          (+
           (- t_6 (* (* y3 y) (- (* y5 a) (* y4 c))))
           (+ (* (* y5 a) (* t y2)) t_13))
          (-
           (* t_2 (- (* c y0) (* a y1)))
           (- t_10 (* (- (* y x) (* z t)) t_7)))))
        (t_17 (- (* t y2) (* y y3))))
   (if (< y4 -7.206256231996481e+60)
     (- (- t_8 (- t_11 t_6)) (- (/ t_3 (/ 1.0 t_1)) t_14))
     (if (< y4 -3.364603505246317e-66)
       (+
        (-
         (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x)))
         t_10)
        (-
         (* (- (* y0 c) (* a y1)) t_2)
         (- (* t_17 (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) t_4))))
       (if (< y4 -1.2000065055686116e-105)
         t_16
         (if (< y4 6.718963124057495e-279)
           t_15
           (if (< y4 4.77962681403792e-222)
             t_16
             (if (< y4 2.2852241541266835e-175)
               t_15
               (+
                (-
                 (+
                  (+
                   (-
                    (* (- (* x y) (* z t)) (- (* a b) (* c i)))
                    (-
                     (* k (* i (* z y1)))
                     (+ (* j (* i (* x y1))) (* y0 (* k (* z b))))))
                   (-
                    (* z (* y3 (* a y1)))
                    (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3))))))
                  (* (- (* t j) (* y k)) t_5))
                 (* t_17 t_1))
                t_13)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_17
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (y4 * c) - (y5 * a)
    t_2 = (x * y2) - (z * y3)
    t_3 = (y2 * t) - (y3 * y)
    t_4 = (k * y2) - (j * y3)
    t_5 = (y4 * b) - (y5 * i)
    t_6 = ((j * t) - (k * y)) * t_5
    t_7 = (b * a) - (i * c)
    t_8 = t_7 * ((y * x) - (t * z))
    t_9 = (j * x) - (k * z)
    t_10 = ((b * y0) - (i * y1)) * t_9
    t_11 = t_9 * ((y0 * b) - (i * y1))
    t_12 = (y4 * y1) - (y5 * y0)
    t_13 = t_4 * t_12
    t_14 = ((y2 * k) - (y3 * j)) * t_12
    t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
    t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
    t_17 = (t * y2) - (y * y3)
    if (y4 < (-7.206256231996481d+60)) then
        tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0d0 / t_1)) - t_14)
    else if (y4 < (-3.364603505246317d-66)) then
        tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
    else if (y4 < (-1.2000065055686116d-105)) then
        tmp = t_16
    else if (y4 < 6.718963124057495d-279) then
        tmp = t_15
    else if (y4 < 4.77962681403792d-222) then
        tmp = t_16
    else if (y4 < 2.2852241541266835d-175) then
        tmp = t_15
    else
        tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y4 * c) - (y5 * a)
	t_2 = (x * y2) - (z * y3)
	t_3 = (y2 * t) - (y3 * y)
	t_4 = (k * y2) - (j * y3)
	t_5 = (y4 * b) - (y5 * i)
	t_6 = ((j * t) - (k * y)) * t_5
	t_7 = (b * a) - (i * c)
	t_8 = t_7 * ((y * x) - (t * z))
	t_9 = (j * x) - (k * z)
	t_10 = ((b * y0) - (i * y1)) * t_9
	t_11 = t_9 * ((y0 * b) - (i * y1))
	t_12 = (y4 * y1) - (y5 * y0)
	t_13 = t_4 * t_12
	t_14 = ((y2 * k) - (y3 * j)) * t_12
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
	t_17 = (t * y2) - (y * y3)
	tmp = 0
	if y4 < -7.206256231996481e+60:
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14)
	elif y4 < -3.364603505246317e-66:
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
	elif y4 < -1.2000065055686116e-105:
		tmp = t_16
	elif y4 < 6.718963124057495e-279:
		tmp = t_15
	elif y4 < 4.77962681403792e-222:
		tmp = t_16
	elif y4 < 2.2852241541266835e-175:
		tmp = t_15
	else:
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y4 * c) - Float64(y5 * a))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(Float64(y2 * t) - Float64(y3 * y))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(Float64(y4 * b) - Float64(y5 * i))
	t_6 = Float64(Float64(Float64(j * t) - Float64(k * y)) * t_5)
	t_7 = Float64(Float64(b * a) - Float64(i * c))
	t_8 = Float64(t_7 * Float64(Float64(y * x) - Float64(t * z)))
	t_9 = Float64(Float64(j * x) - Float64(k * z))
	t_10 = Float64(Float64(Float64(b * y0) - Float64(i * y1)) * t_9)
	t_11 = Float64(t_9 * Float64(Float64(y0 * b) - Float64(i * y1)))
	t_12 = Float64(Float64(y4 * y1) - Float64(y5 * y0))
	t_13 = Float64(t_4 * t_12)
	t_14 = Float64(Float64(Float64(y2 * k) - Float64(y3 * j)) * t_12)
	t_15 = Float64(Float64(Float64(Float64(Float64(Float64(k * y) * Float64(y5 * i)) - Float64(Float64(y * b) * Float64(y4 * k))) - Float64(Float64(y5 * t) * Float64(i * j))) - Float64(Float64(t_3 * t_1) - t_14)) + Float64(t_8 - Float64(t_11 - Float64(Float64(Float64(y2 * x) - Float64(y3 * z)) * Float64(Float64(c * y0) - Float64(y1 * a))))))
	t_16 = Float64(Float64(Float64(t_6 - Float64(Float64(y3 * y) * Float64(Float64(y5 * a) - Float64(y4 * c)))) + Float64(Float64(Float64(y5 * a) * Float64(t * y2)) + t_13)) + Float64(Float64(t_2 * Float64(Float64(c * y0) - Float64(a * y1))) - Float64(t_10 - Float64(Float64(Float64(y * x) - Float64(z * t)) * t_7))))
	t_17 = Float64(Float64(t * y2) - Float64(y * y3))
	tmp = 0.0
	if (y4 < -7.206256231996481e+60)
		tmp = Float64(Float64(t_8 - Float64(t_11 - t_6)) - Float64(Float64(t_3 / Float64(1.0 / t_1)) - t_14));
	elseif (y4 < -3.364603505246317e-66)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(t * c) * Float64(i * z)) - Float64(Float64(a * t) * Float64(b * z))) - Float64(Float64(y * c) * Float64(i * x))) - t_10) + Float64(Float64(Float64(Float64(y0 * c) - Float64(a * y1)) * t_2) - Float64(Float64(t_17 * Float64(Float64(y4 * c) - Float64(a * y5))) - Float64(Float64(Float64(y1 * y4) - Float64(y5 * y0)) * t_4))));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * Float64(Float64(a * b) - Float64(c * i))) - Float64(Float64(k * Float64(i * Float64(z * y1))) - Float64(Float64(j * Float64(i * Float64(x * y1))) + Float64(y0 * Float64(k * Float64(z * b)))))) + Float64(Float64(z * Float64(y3 * Float64(a * y1))) - Float64(Float64(y2 * Float64(x * Float64(a * y1))) + Float64(y0 * Float64(z * Float64(c * y3)))))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * t_5)) - Float64(t_17 * t_1)) + t_13);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y4 * c) - (y5 * a);
	t_2 = (x * y2) - (z * y3);
	t_3 = (y2 * t) - (y3 * y);
	t_4 = (k * y2) - (j * y3);
	t_5 = (y4 * b) - (y5 * i);
	t_6 = ((j * t) - (k * y)) * t_5;
	t_7 = (b * a) - (i * c);
	t_8 = t_7 * ((y * x) - (t * z));
	t_9 = (j * x) - (k * z);
	t_10 = ((b * y0) - (i * y1)) * t_9;
	t_11 = t_9 * ((y0 * b) - (i * y1));
	t_12 = (y4 * y1) - (y5 * y0);
	t_13 = t_4 * t_12;
	t_14 = ((y2 * k) - (y3 * j)) * t_12;
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	t_17 = (t * y2) - (y * y3);
	tmp = 0.0;
	if (y4 < -7.206256231996481e+60)
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	elseif (y4 < -3.364603505246317e-66)
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y4 * b), $MachinePrecision] - N[(y5 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$7 * N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * t$95$9), $MachinePrecision]}, Block[{t$95$11 = N[(t$95$9 * N[(N[(y0 * b), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$12 = N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$13 = N[(t$95$4 * t$95$12), $MachinePrecision]}, Block[{t$95$14 = N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * t$95$12), $MachinePrecision]}, Block[{t$95$15 = N[(N[(N[(N[(N[(N[(k * y), $MachinePrecision] * N[(y5 * i), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] * N[(y4 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y5 * t), $MachinePrecision] * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 * t$95$1), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision] + N[(t$95$8 - N[(t$95$11 - N[(N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$16 = N[(N[(N[(t$95$6 - N[(N[(y3 * y), $MachinePrecision] * N[(N[(y5 * a), $MachinePrecision] - N[(y4 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y5 * a), $MachinePrecision] * N[(t * y2), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$10 - N[(N[(N[(y * x), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$17 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, If[Less[y4, -7.206256231996481e+60], N[(N[(t$95$8 - N[(t$95$11 - t$95$6), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 / N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision], If[Less[y4, -3.364603505246317e-66], N[(N[(N[(N[(N[(N[(t * c), $MachinePrecision] * N[(i * z), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * c), $MachinePrecision] * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$10), $MachinePrecision] + N[(N[(N[(N[(y0 * c), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] - N[(N[(t$95$17 * N[(N[(y4 * c), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y1 * y4), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y4, -1.2000065055686116e-105], t$95$16, If[Less[y4, 6.718963124057495e-279], t$95$15, If[Less[y4, 4.77962681403792e-222], t$95$16, If[Less[y4, 2.2852241541266835e-175], t$95$15, N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(k * N[(i * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(k * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(y3 * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y2 * N[(x * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(z * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(t$95$17 * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :name "Linear.Matrix:det44 from linear-1.19.1.3"
  :precision binary64

  :alt
  (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)))))