Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 31.2% → 39.3%

Time: 57.2s

Alternatives: 31

Speedup: 3.1×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 31.2% 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: 39.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(\left(b \cdot \left(x \cdot y - z \cdot t\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ t_2 := z \cdot y3 - x \cdot y2\\ t_3 := i \cdot y5 - b \cdot y4\\ t_4 := j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right) - \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot t\_3\right)\right)\\ t_5 := k \cdot y2 - j \cdot y3\\ t_6 := y4 \cdot \left(\left(y1 \cdot t\_5 - b \cdot \left(y \cdot k - t \cdot j\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;j \leq -2.45 \cdot 10^{+181}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{+58}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right) - \left(y5 \cdot t\_5 + c \cdot t\_2\right)\right)\\ \mathbf{elif}\;j \leq -4.3 \cdot 10^{-32}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -8.6 \cdot 10^{-178}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -3.9 \cdot 10^{-297}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right) + k \cdot t\_3\right)\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{-264}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.65 \cdot 10^{-202}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;j \leq 4.9 \cdot 10^{-139}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;j \leq 9 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(y1 \cdot t\_2\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{+163}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+191}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          a
          (+
           (- (* b (- (* x y) (* z t))) (* y1 (- (* x y2) (* z y3))))
           (* y5 (- (* t y2) (* y y3))))))
        (t_2 (- (* z y3) (* x y2)))
        (t_3 (- (* i y5) (* b y4)))
        (t_4
         (*
          j
          (-
           (* x (- (* i y1) (* b y0)))
           (+ (* y3 (- (* y1 y4) (* y0 y5))) (* t t_3)))))
        (t_5 (- (* k y2) (* j y3)))
        (t_6
         (*
          y4
          (+
           (- (* y1 t_5) (* b (- (* y k) (* t j))))
           (* c (- (* y y3) (* t y2)))))))
   (if (<= j -2.45e+181)
     t_4
     (if (<= j -1.8e+58)
       (* y0 (- (* b (- (* z k) (* x j))) (+ (* y5 t_5) (* c t_2))))
       (if (<= j -4.3e-32)
         (*
          y2
          (+
           (- (* x (- (* c y0) (* a y1))) (* k (- (* y0 y5) (* y1 y4))))
           (* t (- (* a y5) (* c y4)))))
         (if (<= j -8.6e-178)
           t_1
           (if (<= j -3.9e-297)
             (* y (+ (* y3 (- (* c y4) (* a y5))) (* k t_3)))
             (if (<= j 1.85e-264)
               t_1
               (if (<= j 2.65e-202)
                 t_6
                 (if (<= j 4.9e-139)
                   (* y1 (* z (- (* a y3) (* i k))))
                   (if (<= j 9e-57)
                     (* a (* y1 t_2))
                     (if (<= j 1.5e+163)
                       t_6
                       (if (<= j 8.5e+191)
                         (* i (* x (- (* j y1) (* y c))))
                         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 = a * (((b * ((x * y) - (z * t))) - (y1 * ((x * y2) - (z * y3)))) + (y5 * ((t * y2) - (y * y3))));
	double t_2 = (z * y3) - (x * y2);
	double t_3 = (i * y5) - (b * y4);
	double t_4 = j * ((x * ((i * y1) - (b * y0))) - ((y3 * ((y1 * y4) - (y0 * y5))) + (t * t_3)));
	double t_5 = (k * y2) - (j * y3);
	double t_6 = y4 * (((y1 * t_5) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (j <= -2.45e+181) {
		tmp = t_4;
	} else if (j <= -1.8e+58) {
		tmp = y0 * ((b * ((z * k) - (x * j))) - ((y5 * t_5) + (c * t_2)));
	} else if (j <= -4.3e-32) {
		tmp = y2 * (((x * ((c * y0) - (a * y1))) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))));
	} else if (j <= -8.6e-178) {
		tmp = t_1;
	} else if (j <= -3.9e-297) {
		tmp = y * ((y3 * ((c * y4) - (a * y5))) + (k * t_3));
	} else if (j <= 1.85e-264) {
		tmp = t_1;
	} else if (j <= 2.65e-202) {
		tmp = t_6;
	} else if (j <= 4.9e-139) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (j <= 9e-57) {
		tmp = a * (y1 * t_2);
	} else if (j <= 1.5e+163) {
		tmp = t_6;
	} else if (j <= 8.5e+191) {
		tmp = i * (x * ((j * y1) - (y * c)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = a * (((b * ((x * y) - (z * t))) - (y1 * ((x * y2) - (z * y3)))) + (y5 * ((t * y2) - (y * y3))))
    t_2 = (z * y3) - (x * y2)
    t_3 = (i * y5) - (b * y4)
    t_4 = j * ((x * ((i * y1) - (b * y0))) - ((y3 * ((y1 * y4) - (y0 * y5))) + (t * t_3)))
    t_5 = (k * y2) - (j * y3)
    t_6 = y4 * (((y1 * t_5) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))))
    if (j <= (-2.45d+181)) then
        tmp = t_4
    else if (j <= (-1.8d+58)) then
        tmp = y0 * ((b * ((z * k) - (x * j))) - ((y5 * t_5) + (c * t_2)))
    else if (j <= (-4.3d-32)) then
        tmp = y2 * (((x * ((c * y0) - (a * y1))) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))))
    else if (j <= (-8.6d-178)) then
        tmp = t_1
    else if (j <= (-3.9d-297)) then
        tmp = y * ((y3 * ((c * y4) - (a * y5))) + (k * t_3))
    else if (j <= 1.85d-264) then
        tmp = t_1
    else if (j <= 2.65d-202) then
        tmp = t_6
    else if (j <= 4.9d-139) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (j <= 9d-57) then
        tmp = a * (y1 * t_2)
    else if (j <= 1.5d+163) then
        tmp = t_6
    else if (j <= 8.5d+191) then
        tmp = i * (x * ((j * y1) - (y * c)))
    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 = a * (((b * ((x * y) - (z * t))) - (y1 * ((x * y2) - (z * y3)))) + (y5 * ((t * y2) - (y * y3))));
	double t_2 = (z * y3) - (x * y2);
	double t_3 = (i * y5) - (b * y4);
	double t_4 = j * ((x * ((i * y1) - (b * y0))) - ((y3 * ((y1 * y4) - (y0 * y5))) + (t * t_3)));
	double t_5 = (k * y2) - (j * y3);
	double t_6 = y4 * (((y1 * t_5) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (j <= -2.45e+181) {
		tmp = t_4;
	} else if (j <= -1.8e+58) {
		tmp = y0 * ((b * ((z * k) - (x * j))) - ((y5 * t_5) + (c * t_2)));
	} else if (j <= -4.3e-32) {
		tmp = y2 * (((x * ((c * y0) - (a * y1))) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))));
	} else if (j <= -8.6e-178) {
		tmp = t_1;
	} else if (j <= -3.9e-297) {
		tmp = y * ((y3 * ((c * y4) - (a * y5))) + (k * t_3));
	} else if (j <= 1.85e-264) {
		tmp = t_1;
	} else if (j <= 2.65e-202) {
		tmp = t_6;
	} else if (j <= 4.9e-139) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (j <= 9e-57) {
		tmp = a * (y1 * t_2);
	} else if (j <= 1.5e+163) {
		tmp = t_6;
	} else if (j <= 8.5e+191) {
		tmp = i * (x * ((j * y1) - (y * c)));
	} 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 = a * (((b * ((x * y) - (z * t))) - (y1 * ((x * y2) - (z * y3)))) + (y5 * ((t * y2) - (y * y3))))
	t_2 = (z * y3) - (x * y2)
	t_3 = (i * y5) - (b * y4)
	t_4 = j * ((x * ((i * y1) - (b * y0))) - ((y3 * ((y1 * y4) - (y0 * y5))) + (t * t_3)))
	t_5 = (k * y2) - (j * y3)
	t_6 = y4 * (((y1 * t_5) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))))
	tmp = 0
	if j <= -2.45e+181:
		tmp = t_4
	elif j <= -1.8e+58:
		tmp = y0 * ((b * ((z * k) - (x * j))) - ((y5 * t_5) + (c * t_2)))
	elif j <= -4.3e-32:
		tmp = y2 * (((x * ((c * y0) - (a * y1))) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))))
	elif j <= -8.6e-178:
		tmp = t_1
	elif j <= -3.9e-297:
		tmp = y * ((y3 * ((c * y4) - (a * y5))) + (k * t_3))
	elif j <= 1.85e-264:
		tmp = t_1
	elif j <= 2.65e-202:
		tmp = t_6
	elif j <= 4.9e-139:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif j <= 9e-57:
		tmp = a * (y1 * t_2)
	elif j <= 1.5e+163:
		tmp = t_6
	elif j <= 8.5e+191:
		tmp = i * (x * ((j * y1) - (y * c)))
	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(a * Float64(Float64(Float64(b * Float64(Float64(x * y) - Float64(z * t))) - Float64(y1 * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3)))))
	t_2 = Float64(Float64(z * y3) - Float64(x * y2))
	t_3 = Float64(Float64(i * y5) - Float64(b * y4))
	t_4 = Float64(j * Float64(Float64(x * Float64(Float64(i * y1) - Float64(b * y0))) - Float64(Float64(y3 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(t * t_3))))
	t_5 = Float64(Float64(k * y2) - Float64(j * y3))
	t_6 = Float64(y4 * Float64(Float64(Float64(y1 * t_5) - Float64(b * Float64(Float64(y * k) - Float64(t * j)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	tmp = 0.0
	if (j <= -2.45e+181)
		tmp = t_4;
	elseif (j <= -1.8e+58)
		tmp = Float64(y0 * Float64(Float64(b * Float64(Float64(z * k) - Float64(x * j))) - Float64(Float64(y5 * t_5) + Float64(c * t_2))));
	elseif (j <= -4.3e-32)
		tmp = Float64(y2 * Float64(Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) - Float64(k * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (j <= -8.6e-178)
		tmp = t_1;
	elseif (j <= -3.9e-297)
		tmp = Float64(y * Float64(Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(k * t_3)));
	elseif (j <= 1.85e-264)
		tmp = t_1;
	elseif (j <= 2.65e-202)
		tmp = t_6;
	elseif (j <= 4.9e-139)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (j <= 9e-57)
		tmp = Float64(a * Float64(y1 * t_2));
	elseif (j <= 1.5e+163)
		tmp = t_6;
	elseif (j <= 8.5e+191)
		tmp = Float64(i * Float64(x * Float64(Float64(j * y1) - Float64(y * c))));
	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 = a * (((b * ((x * y) - (z * t))) - (y1 * ((x * y2) - (z * y3)))) + (y5 * ((t * y2) - (y * y3))));
	t_2 = (z * y3) - (x * y2);
	t_3 = (i * y5) - (b * y4);
	t_4 = j * ((x * ((i * y1) - (b * y0))) - ((y3 * ((y1 * y4) - (y0 * y5))) + (t * t_3)));
	t_5 = (k * y2) - (j * y3);
	t_6 = y4 * (((y1 * t_5) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))));
	tmp = 0.0;
	if (j <= -2.45e+181)
		tmp = t_4;
	elseif (j <= -1.8e+58)
		tmp = y0 * ((b * ((z * k) - (x * j))) - ((y5 * t_5) + (c * t_2)));
	elseif (j <= -4.3e-32)
		tmp = y2 * (((x * ((c * y0) - (a * y1))) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))));
	elseif (j <= -8.6e-178)
		tmp = t_1;
	elseif (j <= -3.9e-297)
		tmp = y * ((y3 * ((c * y4) - (a * y5))) + (k * t_3));
	elseif (j <= 1.85e-264)
		tmp = t_1;
	elseif (j <= 2.65e-202)
		tmp = t_6;
	elseif (j <= 4.9e-139)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (j <= 9e-57)
		tmp = a * (y1 * t_2);
	elseif (j <= 1.5e+163)
		tmp = t_6;
	elseif (j <= 8.5e+191)
		tmp = i * (x * ((j * y1) - (y * c)));
	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[(a * N[(N[(N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y1 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(j * N[(N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y3 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(y4 * N[(N[(N[(y1 * t$95$5), $MachinePrecision] - N[(b * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.45e+181], t$95$4, If[LessEqual[j, -1.8e+58], N[(y0 * N[(N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y5 * t$95$5), $MachinePrecision] + N[(c * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.3e-32], N[(y2 * N[(N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -8.6e-178], t$95$1, If[LessEqual[j, -3.9e-297], N[(y * N[(N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.85e-264], t$95$1, If[LessEqual[j, 2.65e-202], t$95$6, If[LessEqual[j, 4.9e-139], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9e-57], N[(a * N[(y1 * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.5e+163], t$95$6, If[LessEqual[j, 8.5e+191], N[(i * N[(x * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if j < -2.44999999999999991e181 or 8.4999999999999999e191 < j

   1. Initial program 28.2%

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

   3. Taylor expanded in j around inf 75.4%

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

      1. +-commutative 75.4%

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

      2. mul-1-neg 75.4%

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

      3. unsub-neg 75.4%

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

      4. *-commutative 75.4%

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

   5. Simplified 75.4%

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

   if -2.44999999999999991e181 < j < -1.79999999999999998e58

   1. Initial program 29.7%

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

   3. Taylor expanded in y0 around inf 73.4%

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

      1. +-commutative 73.4%

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

      2. mul-1-neg 73.4%

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

      3. unsub-neg 73.4%

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

      4. *-commutative 73.4%

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

      5. *-commutative 73.4%

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

      6. *-commutative 73.4%

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

      7. *-commutative 73.4%

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

   5. Simplified 73.4%

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

   if -1.79999999999999998e58 < j < -4.2999999999999999e-32

   1. Initial program 38.1%

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

   3. Taylor expanded in y2 around inf 69.8%

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

   if -4.2999999999999999e-32 < j < -8.6e-178 or -3.9000000000000001e-297 < j < 1.84999999999999998e-264

   1. Initial program 52.4%

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

   3. Taylor expanded in a around inf 68.6%

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

      1. +-commutative 68.6%

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

      2. mul-1-neg 68.6%

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

      3. unsub-neg 68.6%

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

      4. *-commutative 68.6%

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

      5. *-commutative 68.6%

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

      6. *-commutative 68.6%

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

      7. mul-1-neg 68.6%

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

      8. *-commutative 68.6%

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

   5. Simplified 68.6%

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

   if -8.6e-178 < j < -3.9000000000000001e-297

   1. Initial program 39.6%

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

   3. Taylor expanded in y1 around inf 56.0%

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

      1. associate-*r* 50.7%

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

      2. *-commutative 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in y around -inf 56.3%

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

   if 1.84999999999999998e-264 < j < 2.65000000000000021e-202 or 8.99999999999999945e-57 < j < 1.50000000000000007e163

   1. Initial program 39.2%

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

   3. Taylor expanded in y4 around inf 55.6%

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

   if 2.65000000000000021e-202 < j < 4.90000000000000031e-139

   1. Initial program 34.4%

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

   3. Taylor expanded in y1 around -inf 67.0%

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

      1. associate-*r* 67.0%

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

      2. neg-mul-1 67.0%

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

      3. +-commutative 67.0%

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

      4. mul-1-neg 67.0%

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

      5. unsub-neg 67.0%

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

      6. *-commutative 67.0%

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

      7. *-commutative 67.0%

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

      8. *-commutative 67.0%

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

      9. *-commutative 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in z around -inf 83.6%

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

   if 4.90000000000000031e-139 < j < 8.99999999999999945e-57

   1. Initial program 33.3%

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

   3. Taylor expanded in y1 around -inf 51.4%

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

      1. associate-*r* 51.4%

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

      2. neg-mul-1 51.4%

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

      3. +-commutative 51.4%

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

      4. mul-1-neg 51.4%

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

      5. unsub-neg 51.4%

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

      6. *-commutative 51.4%

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

      7. *-commutative 51.4%

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

      8. *-commutative 51.4%

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

      9. *-commutative 51.4%

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

   5. Simplified 51.4%

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

   6. Taylor expanded in a around inf 66.9%

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

      1. associate-*r* 66.9%

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

      2. neg-mul-1 66.9%

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

   8. Simplified 66.9%

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

   if 1.50000000000000007e163 < j < 8.4999999999999999e191

   1. Initial program 22.2%

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

   3. Taylor expanded in i around -inf 66.7%

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

   4. Taylor expanded in x around inf 88.9%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 88.9%

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

   6. Simplified 88.9%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(y \cdot c - j \cdot y1\right)\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.45 \cdot 10^{+181}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right) - \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{+58}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right) - \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;j \leq -4.3 \cdot 10^{-32}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -8.6 \cdot 10^{-178}:\\ \;\;\;\;a \cdot \left(\left(b \cdot \left(x \cdot y - z \cdot t\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq -3.9 \cdot 10^{-297}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right) + k \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{-264}:\\ \;\;\;\;a \cdot \left(\left(b \cdot \left(x \cdot y - z \cdot t\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 2.65 \cdot 10^{-202}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot \left(y \cdot k - t \cdot j\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 4.9 \cdot 10^{-139}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;j \leq 9 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{+163}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot \left(y \cdot k - t \cdot j\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+191}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right) - \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 54.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (b * y0) - (i * y1);
	t_2 = (y1 * y4) - (y0 * y5);
	t_3 = (((((b * y4) - (i * y5)) * ((t * j) - (y * k))) - ((((c * y0) - (a * y1)) * ((z * y3) - (x * y2))) + ((t_1 * ((x * j) - (z * k))) + (((x * y) - (z * t)) * ((c * i) - (a * b)))))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (((k * y2) - (j * y3)) * t_2);
	tmp = 0.0;
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = k * (((y2 * t_2) + (y * ((i * y5) - (b * y4)))) + (z * t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $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] * t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, Infinity], t$95$3, N[(k * N[(N[(N[(y2 * t$95$2), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * t$95$1), $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 94.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in k around inf 41.4%

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

      1. +-commutative 41.4%

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

      2. mul-1-neg 41.4%

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

      3. unsub-neg 41.4%

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

      4. *-commutative 41.4%

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

      5. associate-*r* 41.4%

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

      6. neg-mul-1 41.4%

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

   5. Simplified 41.4%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.0%

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

Alternative 3: 41.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot y4 - y0 \cdot y5\\ t_2 := a \cdot \left(\left(b \cdot \left(x \cdot y - z \cdot t\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ t_3 := i \cdot y5 - b \cdot y4\\ t_4 := j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right) - \left(y3 \cdot t\_1 + t \cdot t\_3\right)\right)\\ t_5 := k \cdot y2 - j \cdot y3\\ t_6 := y4 \cdot \left(\left(y1 \cdot t\_5 - b \cdot \left(y \cdot k - t \cdot j\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;j \leq -2.7 \cdot 10^{+181}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;j \leq -2.1 \cdot 10^{+58}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right) - \left(y5 \cdot t\_5 + c \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;j \leq -2.05 \cdot 10^{-13}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-102}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot t\_1 + y \cdot t\_3\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{-264}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 1.62 \cdot 10^{-202}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{-57}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{+163}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+191}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y1 y4) (* y0 y5)))
        (t_2
         (*
          a
          (+
           (- (* b (- (* x y) (* z t))) (* y1 (- (* x y2) (* z y3))))
           (* y5 (- (* t y2) (* y y3))))))
        (t_3 (- (* i y5) (* b y4)))
        (t_4 (* j (- (* x (- (* i y1) (* b y0))) (+ (* y3 t_1) (* t t_3)))))
        (t_5 (- (* k y2) (* j y3)))
        (t_6
         (*
          y4
          (+
           (- (* y1 t_5) (* b (- (* y k) (* t j))))
           (* c (- (* y y3) (* t y2)))))))
   (if (<= j -2.7e+181)
     t_4
     (if (<= j -2.1e+58)
       (*
        y0
        (-
         (* b (- (* z k) (* x j)))
         (+ (* y5 t_5) (* c (- (* z y3) (* x y2))))))
       (if (<= j -2.05e-13)
         (*
          y2
          (+
           (- (* x (- (* c y0) (* a y1))) (* k (- (* y0 y5) (* y1 y4))))
           (* t (- (* a y5) (* c y4)))))
         (if (<= j -6.5e-102)
           (* k (+ (+ (* y2 t_1) (* y t_3)) (* z (- (* b y0) (* i y1)))))
           (if (<= j 4.5e-264)
             t_2
             (if (<= j 1.62e-202)
               t_6
               (if (<= j 1.75e-57)
                 t_2
                 (if (<= j 7.2e+163)
                   t_6
                   (if (<= j 8.5e+191)
                     (* i (* x (- (* j y1) (* y c))))
                     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 = (y1 * y4) - (y0 * y5);
	double t_2 = a * (((b * ((x * y) - (z * t))) - (y1 * ((x * y2) - (z * y3)))) + (y5 * ((t * y2) - (y * y3))));
	double t_3 = (i * y5) - (b * y4);
	double t_4 = j * ((x * ((i * y1) - (b * y0))) - ((y3 * t_1) + (t * t_3)));
	double t_5 = (k * y2) - (j * y3);
	double t_6 = y4 * (((y1 * t_5) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (j <= -2.7e+181) {
		tmp = t_4;
	} else if (j <= -2.1e+58) {
		tmp = y0 * ((b * ((z * k) - (x * j))) - ((y5 * t_5) + (c * ((z * y3) - (x * y2)))));
	} else if (j <= -2.05e-13) {
		tmp = y2 * (((x * ((c * y0) - (a * y1))) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))));
	} else if (j <= -6.5e-102) {
		tmp = k * (((y2 * t_1) + (y * t_3)) + (z * ((b * y0) - (i * y1))));
	} else if (j <= 4.5e-264) {
		tmp = t_2;
	} else if (j <= 1.62e-202) {
		tmp = t_6;
	} else if (j <= 1.75e-57) {
		tmp = t_2;
	} else if (j <= 7.2e+163) {
		tmp = t_6;
	} else if (j <= 8.5e+191) {
		tmp = i * (x * ((j * y1) - (y * c)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = (y1 * y4) - (y0 * y5)
    t_2 = a * (((b * ((x * y) - (z * t))) - (y1 * ((x * y2) - (z * y3)))) + (y5 * ((t * y2) - (y * y3))))
    t_3 = (i * y5) - (b * y4)
    t_4 = j * ((x * ((i * y1) - (b * y0))) - ((y3 * t_1) + (t * t_3)))
    t_5 = (k * y2) - (j * y3)
    t_6 = y4 * (((y1 * t_5) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))))
    if (j <= (-2.7d+181)) then
        tmp = t_4
    else if (j <= (-2.1d+58)) then
        tmp = y0 * ((b * ((z * k) - (x * j))) - ((y5 * t_5) + (c * ((z * y3) - (x * y2)))))
    else if (j <= (-2.05d-13)) then
        tmp = y2 * (((x * ((c * y0) - (a * y1))) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))))
    else if (j <= (-6.5d-102)) then
        tmp = k * (((y2 * t_1) + (y * t_3)) + (z * ((b * y0) - (i * y1))))
    else if (j <= 4.5d-264) then
        tmp = t_2
    else if (j <= 1.62d-202) then
        tmp = t_6
    else if (j <= 1.75d-57) then
        tmp = t_2
    else if (j <= 7.2d+163) then
        tmp = t_6
    else if (j <= 8.5d+191) then
        tmp = i * (x * ((j * y1) - (y * c)))
    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 = (y1 * y4) - (y0 * y5);
	double t_2 = a * (((b * ((x * y) - (z * t))) - (y1 * ((x * y2) - (z * y3)))) + (y5 * ((t * y2) - (y * y3))));
	double t_3 = (i * y5) - (b * y4);
	double t_4 = j * ((x * ((i * y1) - (b * y0))) - ((y3 * t_1) + (t * t_3)));
	double t_5 = (k * y2) - (j * y3);
	double t_6 = y4 * (((y1 * t_5) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (j <= -2.7e+181) {
		tmp = t_4;
	} else if (j <= -2.1e+58) {
		tmp = y0 * ((b * ((z * k) - (x * j))) - ((y5 * t_5) + (c * ((z * y3) - (x * y2)))));
	} else if (j <= -2.05e-13) {
		tmp = y2 * (((x * ((c * y0) - (a * y1))) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))));
	} else if (j <= -6.5e-102) {
		tmp = k * (((y2 * t_1) + (y * t_3)) + (z * ((b * y0) - (i * y1))));
	} else if (j <= 4.5e-264) {
		tmp = t_2;
	} else if (j <= 1.62e-202) {
		tmp = t_6;
	} else if (j <= 1.75e-57) {
		tmp = t_2;
	} else if (j <= 7.2e+163) {
		tmp = t_6;
	} else if (j <= 8.5e+191) {
		tmp = i * (x * ((j * y1) - (y * c)));
	} 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 = (y1 * y4) - (y0 * y5)
	t_2 = a * (((b * ((x * y) - (z * t))) - (y1 * ((x * y2) - (z * y3)))) + (y5 * ((t * y2) - (y * y3))))
	t_3 = (i * y5) - (b * y4)
	t_4 = j * ((x * ((i * y1) - (b * y0))) - ((y3 * t_1) + (t * t_3)))
	t_5 = (k * y2) - (j * y3)
	t_6 = y4 * (((y1 * t_5) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))))
	tmp = 0
	if j <= -2.7e+181:
		tmp = t_4
	elif j <= -2.1e+58:
		tmp = y0 * ((b * ((z * k) - (x * j))) - ((y5 * t_5) + (c * ((z * y3) - (x * y2)))))
	elif j <= -2.05e-13:
		tmp = y2 * (((x * ((c * y0) - (a * y1))) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))))
	elif j <= -6.5e-102:
		tmp = k * (((y2 * t_1) + (y * t_3)) + (z * ((b * y0) - (i * y1))))
	elif j <= 4.5e-264:
		tmp = t_2
	elif j <= 1.62e-202:
		tmp = t_6
	elif j <= 1.75e-57:
		tmp = t_2
	elif j <= 7.2e+163:
		tmp = t_6
	elif j <= 8.5e+191:
		tmp = i * (x * ((j * y1) - (y * c)))
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_2 = Float64(a * Float64(Float64(Float64(b * Float64(Float64(x * y) - Float64(z * t))) - Float64(y1 * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3)))))
	t_3 = Float64(Float64(i * y5) - Float64(b * y4))
	t_4 = Float64(j * Float64(Float64(x * Float64(Float64(i * y1) - Float64(b * y0))) - Float64(Float64(y3 * t_1) + Float64(t * t_3))))
	t_5 = Float64(Float64(k * y2) - Float64(j * y3))
	t_6 = Float64(y4 * Float64(Float64(Float64(y1 * t_5) - Float64(b * Float64(Float64(y * k) - Float64(t * j)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	tmp = 0.0
	if (j <= -2.7e+181)
		tmp = t_4;
	elseif (j <= -2.1e+58)
		tmp = Float64(y0 * Float64(Float64(b * Float64(Float64(z * k) - Float64(x * j))) - Float64(Float64(y5 * t_5) + Float64(c * Float64(Float64(z * y3) - Float64(x * y2))))));
	elseif (j <= -2.05e-13)
		tmp = Float64(y2 * Float64(Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) - Float64(k * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (j <= -6.5e-102)
		tmp = Float64(k * Float64(Float64(Float64(y2 * t_1) + Float64(y * t_3)) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))));
	elseif (j <= 4.5e-264)
		tmp = t_2;
	elseif (j <= 1.62e-202)
		tmp = t_6;
	elseif (j <= 1.75e-57)
		tmp = t_2;
	elseif (j <= 7.2e+163)
		tmp = t_6;
	elseif (j <= 8.5e+191)
		tmp = Float64(i * Float64(x * Float64(Float64(j * y1) - Float64(y * c))));
	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 = (y1 * y4) - (y0 * y5);
	t_2 = a * (((b * ((x * y) - (z * t))) - (y1 * ((x * y2) - (z * y3)))) + (y5 * ((t * y2) - (y * y3))));
	t_3 = (i * y5) - (b * y4);
	t_4 = j * ((x * ((i * y1) - (b * y0))) - ((y3 * t_1) + (t * t_3)));
	t_5 = (k * y2) - (j * y3);
	t_6 = y4 * (((y1 * t_5) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))));
	tmp = 0.0;
	if (j <= -2.7e+181)
		tmp = t_4;
	elseif (j <= -2.1e+58)
		tmp = y0 * ((b * ((z * k) - (x * j))) - ((y5 * t_5) + (c * ((z * y3) - (x * y2)))));
	elseif (j <= -2.05e-13)
		tmp = y2 * (((x * ((c * y0) - (a * y1))) - (k * ((y0 * y5) - (y1 * y4)))) + (t * ((a * y5) - (c * y4))));
	elseif (j <= -6.5e-102)
		tmp = k * (((y2 * t_1) + (y * t_3)) + (z * ((b * y0) - (i * y1))));
	elseif (j <= 4.5e-264)
		tmp = t_2;
	elseif (j <= 1.62e-202)
		tmp = t_6;
	elseif (j <= 1.75e-57)
		tmp = t_2;
	elseif (j <= 7.2e+163)
		tmp = t_6;
	elseif (j <= 8.5e+191)
		tmp = i * (x * ((j * y1) - (y * c)));
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y1 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(j * N[(N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y3 * t$95$1), $MachinePrecision] + N[(t * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(y4 * N[(N[(N[(y1 * t$95$5), $MachinePrecision] - N[(b * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.7e+181], t$95$4, If[LessEqual[j, -2.1e+58], N[(y0 * N[(N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y5 * t$95$5), $MachinePrecision] + N[(c * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.05e-13], N[(y2 * N[(N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6.5e-102], N[(k * N[(N[(N[(y2 * t$95$1), $MachinePrecision] + N[(y * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.5e-264], t$95$2, If[LessEqual[j, 1.62e-202], t$95$6, If[LessEqual[j, 1.75e-57], t$95$2, If[LessEqual[j, 7.2e+163], t$95$6, If[LessEqual[j, 8.5e+191], N[(i * N[(x * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -2.70000000000000007e181 or 8.4999999999999999e191 < j

   1. Initial program 28.2%

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

   3. Taylor expanded in j around inf 75.4%

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

      1. +-commutative 75.4%

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

      2. mul-1-neg 75.4%

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

      3. unsub-neg 75.4%

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

      4. *-commutative 75.4%

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

   5. Simplified 75.4%

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

   if -2.70000000000000007e181 < j < -2.10000000000000012e58

   1. Initial program 29.7%

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

   3. Taylor expanded in y0 around inf 73.4%

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

      1. +-commutative 73.4%

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

      2. mul-1-neg 73.4%

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

      3. unsub-neg 73.4%

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

      4. *-commutative 73.4%

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

      5. *-commutative 73.4%

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

      6. *-commutative 73.4%

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

      7. *-commutative 73.4%

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

   5. Simplified 73.4%

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

   if -2.10000000000000012e58 < j < -2.0500000000000001e-13

   1. Initial program 40.0%

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

   3. Taylor expanded in y2 around inf 68.3%

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

   if -2.0500000000000001e-13 < j < -6.5000000000000003e-102

   1. Initial program 40.8%

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

   3. Taylor expanded in k around inf 70.4%

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

      1. +-commutative 70.4%

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

      2. mul-1-neg 70.4%

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

      3. unsub-neg 70.4%

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

      4. *-commutative 70.4%

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

      5. associate-*r* 70.4%

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

      6. neg-mul-1 70.4%

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

   5. Simplified 70.4%

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

   if -6.5000000000000003e-102 < j < 4.5000000000000001e-264 or 1.6200000000000001e-202 < j < 1.74999999999999996e-57

   1. Initial program 46.0%

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

   3. Taylor expanded in a around inf 60.4%

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

      1. +-commutative 60.4%

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

      2. mul-1-neg 60.4%

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

      3. unsub-neg 60.4%

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

      4. *-commutative 60.4%

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

      5. *-commutative 60.4%

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

      6. *-commutative 60.4%

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

      7. mul-1-neg 60.4%

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

      8. *-commutative 60.4%

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

   5. Simplified 60.4%

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

   if 4.5000000000000001e-264 < j < 1.6200000000000001e-202 or 1.74999999999999996e-57 < j < 7.19999999999999955e163

   1. Initial program 38.6%

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

   3. Taylor expanded in y4 around inf 54.6%

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

   if 7.19999999999999955e163 < j < 8.4999999999999999e191

   1. Initial program 22.2%

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

   3. Taylor expanded in i around -inf 66.7%

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

   4. Taylor expanded in x around inf 88.9%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 88.9%

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

   6. Simplified 88.9%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(y \cdot c - j \cdot y1\right)\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.7 \cdot 10^{+181}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right) - \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \mathbf{elif}\;j \leq -2.1 \cdot 10^{+58}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right) - \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;j \leq -2.05 \cdot 10^{-13}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-102}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{-264}:\\ \;\;\;\;a \cdot \left(\left(b \cdot \left(x \cdot y - z \cdot t\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 1.62 \cdot 10^{-202}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot \left(y \cdot k - t \cdot j\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(\left(b \cdot \left(x \cdot y - z \cdot t\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{+163}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot \left(y \cdot k - t \cdot j\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+191}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right) - \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 43.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ t_2 := y0 \cdot y5 - y1 \cdot y4\\ t_3 := c \cdot y0 - a \cdot y1\\ t_4 := y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\\ t_5 := y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + j \cdot t\_2\right)\right)\\ t_6 := x \cdot y - z \cdot t\\ \mathbf{if}\;y3 \leq -2.2 \cdot 10^{+165}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y3 \leq -9.5 \cdot 10^{+27}:\\ \;\;\;\;a \cdot \left(\left(b \cdot t\_6 - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + t\_4\right)\\ \mathbf{elif}\;y3 \leq -3.3 \cdot 10^{-189}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq 1.65 \cdot 10^{-168}:\\ \;\;\;\;b \cdot \left(\left(a \cdot t\_6 + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq 1.15 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot t\_3 - y \cdot \left(c \cdot i - a \cdot b\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 65000:\\ \;\;\;\;a \cdot \left(t\_4 + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 2.25 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y3 \leq 7.8 \cdot 10^{+127}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t\_3 - k \cdot t\_2\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          k
          (+
           (+ (* y2 (- (* y1 y4) (* y0 y5))) (* y (- (* i y5) (* b y4))))
           (* z (- (* b y0) (* i y1))))))
        (t_2 (- (* y0 y5) (* y1 y4)))
        (t_3 (- (* c y0) (* a y1)))
        (t_4 (* y5 (- (* t y2) (* y y3))))
        (t_5
         (*
          y3
          (+
           (* y (- (* c y4) (* a y5)))
           (+ (* z (- (* a y1) (* c y0))) (* j t_2)))))
        (t_6 (- (* x y) (* z t))))
   (if (<= y3 -2.2e+165)
     t_5
     (if (<= y3 -9.5e+27)
       (* a (+ (- (* b t_6) (* y1 (- (* x y2) (* z y3)))) t_4))
       (if (<= y3 -3.3e-189)
         t_1
         (if (<= y3 1.65e-168)
           (*
            b
            (+
             (+ (* a t_6) (* y4 (- (* t j) (* y k))))
             (* y0 (- (* z k) (* x j)))))
           (if (<= y3 1.15e-83)
             (*
              x
              (+
               (- (* y2 t_3) (* y (- (* c i) (* a b))))
               (* j (- (* i y1) (* b y0)))))
             (if (<= y3 65000.0)
               (* a (+ t_4 (* y1 (- (* z y3) (* x y2)))))
               (if (<= y3 2.25e+77)
                 t_1
                 (if (<= y3 7.8e+127)
                   (*
                    y2
                    (+ (- (* x t_3) (* k t_2)) (* t (- (* a y5) (* c y4)))))
                   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 = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	double t_2 = (y0 * y5) - (y1 * y4);
	double t_3 = (c * y0) - (a * y1);
	double t_4 = y5 * ((t * y2) - (y * y3));
	double t_5 = y3 * ((y * ((c * y4) - (a * y5))) + ((z * ((a * y1) - (c * y0))) + (j * t_2)));
	double t_6 = (x * y) - (z * t);
	double tmp;
	if (y3 <= -2.2e+165) {
		tmp = t_5;
	} else if (y3 <= -9.5e+27) {
		tmp = a * (((b * t_6) - (y1 * ((x * y2) - (z * y3)))) + t_4);
	} else if (y3 <= -3.3e-189) {
		tmp = t_1;
	} else if (y3 <= 1.65e-168) {
		tmp = b * (((a * t_6) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y3 <= 1.15e-83) {
		tmp = x * (((y2 * t_3) - (y * ((c * i) - (a * b)))) + (j * ((i * y1) - (b * y0))));
	} else if (y3 <= 65000.0) {
		tmp = a * (t_4 + (y1 * ((z * y3) - (x * y2))));
	} else if (y3 <= 2.25e+77) {
		tmp = t_1;
	} else if (y3 <= 7.8e+127) {
		tmp = y2 * (((x * t_3) - (k * t_2)) + (t * ((a * y5) - (c * y4))));
	} 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 = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
    t_2 = (y0 * y5) - (y1 * y4)
    t_3 = (c * y0) - (a * y1)
    t_4 = y5 * ((t * y2) - (y * y3))
    t_5 = y3 * ((y * ((c * y4) - (a * y5))) + ((z * ((a * y1) - (c * y0))) + (j * t_2)))
    t_6 = (x * y) - (z * t)
    if (y3 <= (-2.2d+165)) then
        tmp = t_5
    else if (y3 <= (-9.5d+27)) then
        tmp = a * (((b * t_6) - (y1 * ((x * y2) - (z * y3)))) + t_4)
    else if (y3 <= (-3.3d-189)) then
        tmp = t_1
    else if (y3 <= 1.65d-168) then
        tmp = b * (((a * t_6) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    else if (y3 <= 1.15d-83) then
        tmp = x * (((y2 * t_3) - (y * ((c * i) - (a * b)))) + (j * ((i * y1) - (b * y0))))
    else if (y3 <= 65000.0d0) then
        tmp = a * (t_4 + (y1 * ((z * y3) - (x * y2))))
    else if (y3 <= 2.25d+77) then
        tmp = t_1
    else if (y3 <= 7.8d+127) then
        tmp = y2 * (((x * t_3) - (k * t_2)) + (t * ((a * y5) - (c * y4))))
    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 = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	double t_2 = (y0 * y5) - (y1 * y4);
	double t_3 = (c * y0) - (a * y1);
	double t_4 = y5 * ((t * y2) - (y * y3));
	double t_5 = y3 * ((y * ((c * y4) - (a * y5))) + ((z * ((a * y1) - (c * y0))) + (j * t_2)));
	double t_6 = (x * y) - (z * t);
	double tmp;
	if (y3 <= -2.2e+165) {
		tmp = t_5;
	} else if (y3 <= -9.5e+27) {
		tmp = a * (((b * t_6) - (y1 * ((x * y2) - (z * y3)))) + t_4);
	} else if (y3 <= -3.3e-189) {
		tmp = t_1;
	} else if (y3 <= 1.65e-168) {
		tmp = b * (((a * t_6) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y3 <= 1.15e-83) {
		tmp = x * (((y2 * t_3) - (y * ((c * i) - (a * b)))) + (j * ((i * y1) - (b * y0))));
	} else if (y3 <= 65000.0) {
		tmp = a * (t_4 + (y1 * ((z * y3) - (x * y2))));
	} else if (y3 <= 2.25e+77) {
		tmp = t_1;
	} else if (y3 <= 7.8e+127) {
		tmp = y2 * (((x * t_3) - (k * t_2)) + (t * ((a * y5) - (c * y4))));
	} 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 = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))))
	t_2 = (y0 * y5) - (y1 * y4)
	t_3 = (c * y0) - (a * y1)
	t_4 = y5 * ((t * y2) - (y * y3))
	t_5 = y3 * ((y * ((c * y4) - (a * y5))) + ((z * ((a * y1) - (c * y0))) + (j * t_2)))
	t_6 = (x * y) - (z * t)
	tmp = 0
	if y3 <= -2.2e+165:
		tmp = t_5
	elif y3 <= -9.5e+27:
		tmp = a * (((b * t_6) - (y1 * ((x * y2) - (z * y3)))) + t_4)
	elif y3 <= -3.3e-189:
		tmp = t_1
	elif y3 <= 1.65e-168:
		tmp = b * (((a * t_6) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	elif y3 <= 1.15e-83:
		tmp = x * (((y2 * t_3) - (y * ((c * i) - (a * b)))) + (j * ((i * y1) - (b * y0))))
	elif y3 <= 65000.0:
		tmp = a * (t_4 + (y1 * ((z * y3) - (x * y2))))
	elif y3 <= 2.25e+77:
		tmp = t_1
	elif y3 <= 7.8e+127:
		tmp = y2 * (((x * t_3) - (k * t_2)) + (t * ((a * y5) - (c * y4))))
	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(k * Float64(Float64(Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(y * Float64(Float64(i * y5) - Float64(b * y4)))) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))))
	t_2 = Float64(Float64(y0 * y5) - Float64(y1 * y4))
	t_3 = Float64(Float64(c * y0) - Float64(a * y1))
	t_4 = Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3)))
	t_5 = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(z * Float64(Float64(a * y1) - Float64(c * y0))) + Float64(j * t_2))))
	t_6 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (y3 <= -2.2e+165)
		tmp = t_5;
	elseif (y3 <= -9.5e+27)
		tmp = Float64(a * Float64(Float64(Float64(b * t_6) - Float64(y1 * Float64(Float64(x * y2) - Float64(z * y3)))) + t_4));
	elseif (y3 <= -3.3e-189)
		tmp = t_1;
	elseif (y3 <= 1.65e-168)
		tmp = Float64(b * Float64(Float64(Float64(a * t_6) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y3 <= 1.15e-83)
		tmp = Float64(x * Float64(Float64(Float64(y2 * t_3) - Float64(y * Float64(Float64(c * i) - Float64(a * b)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y3 <= 65000.0)
		tmp = Float64(a * Float64(t_4 + Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2)))));
	elseif (y3 <= 2.25e+77)
		tmp = t_1;
	elseif (y3 <= 7.8e+127)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_3) - Float64(k * t_2)) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	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 = k * (((y2 * ((y1 * y4) - (y0 * y5))) + (y * ((i * y5) - (b * y4)))) + (z * ((b * y0) - (i * y1))));
	t_2 = (y0 * y5) - (y1 * y4);
	t_3 = (c * y0) - (a * y1);
	t_4 = y5 * ((t * y2) - (y * y3));
	t_5 = y3 * ((y * ((c * y4) - (a * y5))) + ((z * ((a * y1) - (c * y0))) + (j * t_2)));
	t_6 = (x * y) - (z * t);
	tmp = 0.0;
	if (y3 <= -2.2e+165)
		tmp = t_5;
	elseif (y3 <= -9.5e+27)
		tmp = a * (((b * t_6) - (y1 * ((x * y2) - (z * y3)))) + t_4);
	elseif (y3 <= -3.3e-189)
		tmp = t_1;
	elseif (y3 <= 1.65e-168)
		tmp = b * (((a * t_6) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	elseif (y3 <= 1.15e-83)
		tmp = x * (((y2 * t_3) - (y * ((c * i) - (a * b)))) + (j * ((i * y1) - (b * y0))));
	elseif (y3 <= 65000.0)
		tmp = a * (t_4 + (y1 * ((z * y3) - (x * y2))));
	elseif (y3 <= 2.25e+77)
		tmp = t_1;
	elseif (y3 <= 7.8e+127)
		tmp = y2 * (((x * t_3) - (k * t_2)) + (t * ((a * y5) - (c * y4))));
	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[(k * N[(N[(N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -2.2e+165], t$95$5, If[LessEqual[y3, -9.5e+27], N[(a * N[(N[(N[(b * t$95$6), $MachinePrecision] - N[(y1 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -3.3e-189], t$95$1, If[LessEqual[y3, 1.65e-168], N[(b * N[(N[(N[(a * t$95$6), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.15e-83], N[(x * N[(N[(N[(y2 * t$95$3), $MachinePrecision] - N[(y * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 65000.0], N[(a * N[(t$95$4 + N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.25e+77], t$95$1, If[LessEqual[y3, 7.8e+127], N[(y2 * N[(N[(N[(x * t$95$3), $MachinePrecision] - N[(k * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y3 < -2.1999999999999999e165 or 7.79999999999999962e127 < y3

   1. Initial program 34.5%

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

   3. Taylor expanded in y3 around -inf 68.9%

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

   if -2.1999999999999999e165 < y3 < -9.4999999999999997e27

   1. Initial program 40.7%

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

   3. Taylor expanded in a around inf 60.7%

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

      1. +-commutative 60.7%

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

      2. mul-1-neg 60.7%

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

      3. unsub-neg 60.7%

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

      4. *-commutative 60.7%

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

      5. *-commutative 60.7%

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

      6. *-commutative 60.7%

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

      7. mul-1-neg 60.7%

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

      8. *-commutative 60.7%

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

   5. Simplified 60.7%

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

   if -9.4999999999999997e27 < y3 < -3.3000000000000001e-189 or 65000 < y3 < 2.25000000000000012e77

   1. Initial program 35.1%

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

   3. Taylor expanded in k around inf 59.1%

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

      1. +-commutative 59.1%

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

      2. mul-1-neg 59.1%

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

      3. unsub-neg 59.1%

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

      4. *-commutative 59.1%

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

      5. associate-*r* 59.1%

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

      6. neg-mul-1 59.1%

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

   5. Simplified 59.1%

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

   if -3.3000000000000001e-189 < y3 < 1.6500000000000001e-168

   1. Initial program 44.9%

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

   3. Taylor expanded in b around inf 61.9%

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

   if 1.6500000000000001e-168 < y3 < 1.14999999999999995e-83

   1. Initial program 24.0%

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

   3. Taylor expanded in x around inf 66.7%

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

   if 1.14999999999999995e-83 < y3 < 65000

   1. Initial program 42.9%

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

   3. Taylor expanded in y1 around inf 64.3%

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

      1. associate-*r* 64.3%

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

      2. *-commutative 64.3%

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

   5. Simplified 64.3%

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

   6. Taylor expanded in a around -inf 65.0%

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

      1. mul-1-neg 65.0%

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

   8. Simplified 65.0%

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

   if 2.25000000000000012e77 < y3 < 7.79999999999999962e127

   1. Initial program 27.3%

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

   3. Taylor expanded in y2 around inf 63.9%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -2.2 \cdot 10^{+165}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y3 \leq -9.5 \cdot 10^{+27}:\\ \;\;\;\;a \cdot \left(\left(b \cdot \left(x \cdot y - z \cdot t\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq -3.3 \cdot 10^{-189}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq 1.65 \cdot 10^{-168}:\\ \;\;\;\;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}\;y3 \leq 1.15 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \left(\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - y \cdot \left(c \cdot i - a \cdot b\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 65000:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 2.25 \cdot 10^{+77}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y3 \leq 7.8 \cdot 10^{+127}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) - k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 38.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(i \cdot y5 - b \cdot y4\right)\\ t_2 := j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right) - \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t\_1\right)\right)\\ t_3 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{if}\;j \leq -3.4 \cdot 10^{+169}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.3 \cdot 10^{+134}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -2.6 \cdot 10^{+73}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-264}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq 7.4 \cdot 10^{-144}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(i \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{-40}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq 2.35 \cdot 10^{+151}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(i \cdot \left(x \cdot y1\right) - t\_1\right)\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+191}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (- (* i y5) (* b y4))))
        (t_2
         (*
          j
          (-
           (* x (- (* i y1) (* b y0)))
           (+ (* y3 (- (* y1 y4) (* y0 y5))) t_1))))
        (t_3
         (* a (+ (* y5 (- (* t y2) (* y y3))) (* y1 (- (* z y3) (* x y2)))))))
   (if (<= j -3.4e+169)
     t_2
     (if (<= j -1.3e+134)
       (*
        b
        (+
         (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
         (* y0 (- (* z k) (* x j)))))
       (if (<= j -2.6e+73)
         t_2
         (if (<= j 6e-264)
           t_3
           (if (<= j 7.4e-144)
             (* y1 (* z (* i (- k))))
             (if (<= j 1.05e-40)
               t_3
               (if (<= j 2.35e+151)
                 (*
                  j
                  (+ (* y3 (- (* y0 y5) (* y1 y4))) (- (* i (* x y1)) t_1)))
                 (if (<= j 8.5e+191)
                   (* i (* x (- (* j y1) (* y c))))
                   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 = t * ((i * y5) - (b * y4));
	double t_2 = j * ((x * ((i * y1) - (b * y0))) - ((y3 * ((y1 * y4) - (y0 * y5))) + t_1));
	double t_3 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))));
	double tmp;
	if (j <= -3.4e+169) {
		tmp = t_2;
	} else if (j <= -1.3e+134) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (j <= -2.6e+73) {
		tmp = t_2;
	} else if (j <= 6e-264) {
		tmp = t_3;
	} else if (j <= 7.4e-144) {
		tmp = y1 * (z * (i * -k));
	} else if (j <= 1.05e-40) {
		tmp = t_3;
	} else if (j <= 2.35e+151) {
		tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((i * (x * y1)) - t_1));
	} else if (j <= 8.5e+191) {
		tmp = i * (x * ((j * y1) - (y * c)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * ((i * y5) - (b * y4))
    t_2 = j * ((x * ((i * y1) - (b * y0))) - ((y3 * ((y1 * y4) - (y0 * y5))) + t_1))
    t_3 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))))
    if (j <= (-3.4d+169)) then
        tmp = t_2
    else if (j <= (-1.3d+134)) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    else if (j <= (-2.6d+73)) then
        tmp = t_2
    else if (j <= 6d-264) then
        tmp = t_3
    else if (j <= 7.4d-144) then
        tmp = y1 * (z * (i * -k))
    else if (j <= 1.05d-40) then
        tmp = t_3
    else if (j <= 2.35d+151) then
        tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((i * (x * y1)) - t_1))
    else if (j <= 8.5d+191) then
        tmp = i * (x * ((j * y1) - (y * c)))
    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 = t * ((i * y5) - (b * y4));
	double t_2 = j * ((x * ((i * y1) - (b * y0))) - ((y3 * ((y1 * y4) - (y0 * y5))) + t_1));
	double t_3 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))));
	double tmp;
	if (j <= -3.4e+169) {
		tmp = t_2;
	} else if (j <= -1.3e+134) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (j <= -2.6e+73) {
		tmp = t_2;
	} else if (j <= 6e-264) {
		tmp = t_3;
	} else if (j <= 7.4e-144) {
		tmp = y1 * (z * (i * -k));
	} else if (j <= 1.05e-40) {
		tmp = t_3;
	} else if (j <= 2.35e+151) {
		tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((i * (x * y1)) - t_1));
	} else if (j <= 8.5e+191) {
		tmp = i * (x * ((j * y1) - (y * c)));
	} 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 = t * ((i * y5) - (b * y4))
	t_2 = j * ((x * ((i * y1) - (b * y0))) - ((y3 * ((y1 * y4) - (y0 * y5))) + t_1))
	t_3 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))))
	tmp = 0
	if j <= -3.4e+169:
		tmp = t_2
	elif j <= -1.3e+134:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	elif j <= -2.6e+73:
		tmp = t_2
	elif j <= 6e-264:
		tmp = t_3
	elif j <= 7.4e-144:
		tmp = y1 * (z * (i * -k))
	elif j <= 1.05e-40:
		tmp = t_3
	elif j <= 2.35e+151:
		tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((i * (x * y1)) - t_1))
	elif j <= 8.5e+191:
		tmp = i * (x * ((j * y1) - (y * c)))
	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(t * Float64(Float64(i * y5) - Float64(b * y4)))
	t_2 = Float64(j * Float64(Float64(x * Float64(Float64(i * y1) - Float64(b * y0))) - Float64(Float64(y3 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + t_1)))
	t_3 = Float64(a * Float64(Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2)))))
	tmp = 0.0
	if (j <= -3.4e+169)
		tmp = t_2;
	elseif (j <= -1.3e+134)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (j <= -2.6e+73)
		tmp = t_2;
	elseif (j <= 6e-264)
		tmp = t_3;
	elseif (j <= 7.4e-144)
		tmp = Float64(y1 * Float64(z * Float64(i * Float64(-k))));
	elseif (j <= 1.05e-40)
		tmp = t_3;
	elseif (j <= 2.35e+151)
		tmp = Float64(j * Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(Float64(i * Float64(x * y1)) - t_1)));
	elseif (j <= 8.5e+191)
		tmp = Float64(i * Float64(x * Float64(Float64(j * y1) - Float64(y * c))));
	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 = t * ((i * y5) - (b * y4));
	t_2 = j * ((x * ((i * y1) - (b * y0))) - ((y3 * ((y1 * y4) - (y0 * y5))) + t_1));
	t_3 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))));
	tmp = 0.0;
	if (j <= -3.4e+169)
		tmp = t_2;
	elseif (j <= -1.3e+134)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	elseif (j <= -2.6e+73)
		tmp = t_2;
	elseif (j <= 6e-264)
		tmp = t_3;
	elseif (j <= 7.4e-144)
		tmp = y1 * (z * (i * -k));
	elseif (j <= 1.05e-40)
		tmp = t_3;
	elseif (j <= 2.35e+151)
		tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((i * (x * y1)) - t_1));
	elseif (j <= 8.5e+191)
		tmp = i * (x * ((j * y1) - (y * c)));
	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[(t * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y3 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.4e+169], t$95$2, If[LessEqual[j, -1.3e+134], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.6e+73], t$95$2, If[LessEqual[j, 6e-264], t$95$3, If[LessEqual[j, 7.4e-144], N[(y1 * N[(z * N[(i * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.05e-40], t$95$3, If[LessEqual[j, 2.35e+151], N[(j * N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.5e+191], N[(i * N[(x * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -3.40000000000000028e169 or -1.3000000000000001e134 < j < -2.6000000000000001e73 or 8.4999999999999999e191 < j

   1. Initial program 28.5%

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

   3. Taylor expanded in j around inf 71.7%

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

      1. +-commutative 71.7%

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

      2. mul-1-neg 71.7%

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

      3. unsub-neg 71.7%

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

      4. *-commutative 71.7%

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

   5. Simplified 71.7%

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

   if -3.40000000000000028e169 < j < -1.3000000000000001e134

   1. Initial program 30.8%

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

   3. Taylor expanded in b around inf 62.4%

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

   if -2.6000000000000001e73 < j < 6.0000000000000001e-264 or 7.4000000000000005e-144 < j < 1.05000000000000009e-40

   1. Initial program 42.2%

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

   3. Taylor expanded in y1 around inf 52.1%

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

      1. associate-*r* 52.2%

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

      2. *-commutative 52.2%

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

   5. Simplified 52.2%

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

   6. Taylor expanded in a around -inf 56.7%

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

      1. mul-1-neg 56.7%

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

   8. Simplified 56.7%

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

   if 6.0000000000000001e-264 < j < 7.4000000000000005e-144

   1. Initial program 41.7%

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

   3. Taylor expanded in y1 around -inf 36.4%

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

      1. associate-*r* 36.4%

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

      2. neg-mul-1 36.4%

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

      3. +-commutative 36.4%

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

      4. mul-1-neg 36.4%

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

      5. unsub-neg 36.4%

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

      6. *-commutative 36.4%

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

      7. *-commutative 36.4%

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

      8. *-commutative 36.4%

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

      9. *-commutative 36.4%

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

   5. Simplified 36.4%

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

   6. Taylor expanded in z around -inf 42.5%

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

   7. Taylor expanded in a around 0 42.7%

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

      1. mul-1-neg 42.7%

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

      2. distribute-lft-neg-out 42.7%

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

      3. *-commutative 42.7%

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

   9. Simplified 42.7%

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

   if 1.05000000000000009e-40 < j < 2.34999999999999995e151

   1. Initial program 40.9%

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

   3. Taylor expanded in y1 around inf 46.3%

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

      1. associate-*r* 43.7%

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

      2. *-commutative 43.7%

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

   5. Simplified 43.7%

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

   6. Taylor expanded in j around inf 47.7%

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

   if 2.34999999999999995e151 < j < 8.4999999999999999e191

   1. Initial program 20.0%

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

   3. Taylor expanded in i around -inf 70.0%

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

   4. Taylor expanded in x around inf 80.4%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 80.4%

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

   6. Simplified 80.4%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(y \cdot c - j \cdot y1\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.4 \cdot 10^{+169}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right) - \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \mathbf{elif}\;j \leq -1.3 \cdot 10^{+134}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -2.6 \cdot 10^{+73}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right) - \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-264}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 7.4 \cdot 10^{-144}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(i \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 2.35 \cdot 10^{+151}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(i \cdot \left(x \cdot y1\right) - t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+191}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right) - \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 39.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right) - \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ t_2 := k \cdot y2 - j \cdot y3\\ t_3 := y4 \cdot \left(\left(y1 \cdot t\_2 - b \cdot \left(y \cdot k - t \cdot j\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_4 := z \cdot y3 - x \cdot y2\\ t_5 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot t\_4\right)\\ \mathbf{if}\;j \leq -1.8 \cdot 10^{+181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.5 \cdot 10^{+58}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right) - \left(y5 \cdot t\_2 + c \cdot t\_4\right)\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-264}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;j \leq 3.55 \cdot 10^{-202}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq 1.8 \cdot 10^{-56}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{+164}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+191}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          j
          (-
           (* x (- (* i y1) (* b y0)))
           (+ (* y3 (- (* y1 y4) (* y0 y5))) (* t (- (* i y5) (* b y4)))))))
        (t_2 (- (* k y2) (* j y3)))
        (t_3
         (*
          y4
          (+
           (- (* y1 t_2) (* b (- (* y k) (* t j))))
           (* c (- (* y y3) (* t y2))))))
        (t_4 (- (* z y3) (* x y2)))
        (t_5 (* a (+ (* y5 (- (* t y2) (* y y3))) (* y1 t_4)))))
   (if (<= j -1.8e+181)
     t_1
     (if (<= j -1.5e+58)
       (* y0 (- (* b (- (* z k) (* x j))) (+ (* y5 t_2) (* c t_4))))
       (if (<= j 6e-264)
         t_5
         (if (<= j 3.55e-202)
           t_3
           (if (<= j 1.8e-56)
             t_5
             (if (<= j 1.05e+164)
               t_3
               (if (<= j 8.5e+191)
                 (* i (* x (- (* j y1) (* y c))))
                 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * ((x * ((i * y1) - (b * y0))) - ((y3 * ((y1 * y4) - (y0 * y5))) + (t * ((i * y5) - (b * y4)))));
	double t_2 = (k * y2) - (j * y3);
	double t_3 = y4 * (((y1 * t_2) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))));
	double t_4 = (z * y3) - (x * y2);
	double t_5 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * t_4));
	double tmp;
	if (j <= -1.8e+181) {
		tmp = t_1;
	} else if (j <= -1.5e+58) {
		tmp = y0 * ((b * ((z * k) - (x * j))) - ((y5 * t_2) + (c * t_4)));
	} else if (j <= 6e-264) {
		tmp = t_5;
	} else if (j <= 3.55e-202) {
		tmp = t_3;
	} else if (j <= 1.8e-56) {
		tmp = t_5;
	} else if (j <= 1.05e+164) {
		tmp = t_3;
	} else if (j <= 8.5e+191) {
		tmp = i * (x * ((j * y1) - (y * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = j * ((x * ((i * y1) - (b * y0))) - ((y3 * ((y1 * y4) - (y0 * y5))) + (t * ((i * y5) - (b * y4)))))
    t_2 = (k * y2) - (j * y3)
    t_3 = y4 * (((y1 * t_2) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))))
    t_4 = (z * y3) - (x * y2)
    t_5 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * t_4))
    if (j <= (-1.8d+181)) then
        tmp = t_1
    else if (j <= (-1.5d+58)) then
        tmp = y0 * ((b * ((z * k) - (x * j))) - ((y5 * t_2) + (c * t_4)))
    else if (j <= 6d-264) then
        tmp = t_5
    else if (j <= 3.55d-202) then
        tmp = t_3
    else if (j <= 1.8d-56) then
        tmp = t_5
    else if (j <= 1.05d+164) then
        tmp = t_3
    else if (j <= 8.5d+191) then
        tmp = i * (x * ((j * y1) - (y * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * ((x * ((i * y1) - (b * y0))) - ((y3 * ((y1 * y4) - (y0 * y5))) + (t * ((i * y5) - (b * y4)))));
	double t_2 = (k * y2) - (j * y3);
	double t_3 = y4 * (((y1 * t_2) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))));
	double t_4 = (z * y3) - (x * y2);
	double t_5 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * t_4));
	double tmp;
	if (j <= -1.8e+181) {
		tmp = t_1;
	} else if (j <= -1.5e+58) {
		tmp = y0 * ((b * ((z * k) - (x * j))) - ((y5 * t_2) + (c * t_4)));
	} else if (j <= 6e-264) {
		tmp = t_5;
	} else if (j <= 3.55e-202) {
		tmp = t_3;
	} else if (j <= 1.8e-56) {
		tmp = t_5;
	} else if (j <= 1.05e+164) {
		tmp = t_3;
	} else if (j <= 8.5e+191) {
		tmp = i * (x * ((j * y1) - (y * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * ((x * ((i * y1) - (b * y0))) - ((y3 * ((y1 * y4) - (y0 * y5))) + (t * ((i * y5) - (b * y4)))))
	t_2 = (k * y2) - (j * y3)
	t_3 = y4 * (((y1 * t_2) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))))
	t_4 = (z * y3) - (x * y2)
	t_5 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * t_4))
	tmp = 0
	if j <= -1.8e+181:
		tmp = t_1
	elif j <= -1.5e+58:
		tmp = y0 * ((b * ((z * k) - (x * j))) - ((y5 * t_2) + (c * t_4)))
	elif j <= 6e-264:
		tmp = t_5
	elif j <= 3.55e-202:
		tmp = t_3
	elif j <= 1.8e-56:
		tmp = t_5
	elif j <= 1.05e+164:
		tmp = t_3
	elif j <= 8.5e+191:
		tmp = i * (x * ((j * y1) - (y * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(Float64(x * Float64(Float64(i * y1) - Float64(b * y0))) - Float64(Float64(y3 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(t * Float64(Float64(i * y5) - Float64(b * y4))))))
	t_2 = Float64(Float64(k * y2) - Float64(j * y3))
	t_3 = Float64(y4 * Float64(Float64(Float64(y1 * t_2) - Float64(b * Float64(Float64(y * k) - Float64(t * j)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_4 = Float64(Float64(z * y3) - Float64(x * y2))
	t_5 = Float64(a * Float64(Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y1 * t_4)))
	tmp = 0.0
	if (j <= -1.8e+181)
		tmp = t_1;
	elseif (j <= -1.5e+58)
		tmp = Float64(y0 * Float64(Float64(b * Float64(Float64(z * k) - Float64(x * j))) - Float64(Float64(y5 * t_2) + Float64(c * t_4))));
	elseif (j <= 6e-264)
		tmp = t_5;
	elseif (j <= 3.55e-202)
		tmp = t_3;
	elseif (j <= 1.8e-56)
		tmp = t_5;
	elseif (j <= 1.05e+164)
		tmp = t_3;
	elseif (j <= 8.5e+191)
		tmp = Float64(i * Float64(x * Float64(Float64(j * y1) - Float64(y * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * ((x * ((i * y1) - (b * y0))) - ((y3 * ((y1 * y4) - (y0 * y5))) + (t * ((i * y5) - (b * y4)))));
	t_2 = (k * y2) - (j * y3);
	t_3 = y4 * (((y1 * t_2) - (b * ((y * k) - (t * j)))) + (c * ((y * y3) - (t * y2))));
	t_4 = (z * y3) - (x * y2);
	t_5 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * t_4));
	tmp = 0.0;
	if (j <= -1.8e+181)
		tmp = t_1;
	elseif (j <= -1.5e+58)
		tmp = y0 * ((b * ((z * k) - (x * j))) - ((y5 * t_2) + (c * t_4)));
	elseif (j <= 6e-264)
		tmp = t_5;
	elseif (j <= 3.55e-202)
		tmp = t_3;
	elseif (j <= 1.8e-56)
		tmp = t_5;
	elseif (j <= 1.05e+164)
		tmp = t_3;
	elseif (j <= 8.5e+191)
		tmp = i * (x * ((j * y1) - (y * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y3 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y4 * N[(N[(N[(y1 * t$95$2), $MachinePrecision] - N[(b * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(a * N[(N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.8e+181], t$95$1, If[LessEqual[j, -1.5e+58], N[(y0 * N[(N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y5 * t$95$2), $MachinePrecision] + N[(c * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6e-264], t$95$5, If[LessEqual[j, 3.55e-202], t$95$3, If[LessEqual[j, 1.8e-56], t$95$5, If[LessEqual[j, 1.05e+164], t$95$3, If[LessEqual[j, 8.5e+191], N[(i * N[(x * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.79999999999999992e181 or 8.4999999999999999e191 < j

   1. Initial program 28.2%

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

   3. Taylor expanded in j around inf 75.4%

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

      1. +-commutative 75.4%

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

      2. mul-1-neg 75.4%

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

      3. unsub-neg 75.4%

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

      4. *-commutative 75.4%

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

   5. Simplified 75.4%

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

   if -1.79999999999999992e181 < j < -1.5000000000000001e58

   1. Initial program 29.7%

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

   3. Taylor expanded in y0 around inf 73.4%

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

      1. +-commutative 73.4%

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

      2. mul-1-neg 73.4%

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

      3. unsub-neg 73.4%

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

      4. *-commutative 73.4%

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

      5. *-commutative 73.4%

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

      6. *-commutative 73.4%

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

      7. *-commutative 73.4%

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

   5. Simplified 73.4%

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

   if -1.5000000000000001e58 < j < 6.0000000000000001e-264 or 3.55e-202 < j < 1.79999999999999989e-56

   1. Initial program 43.8%

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

   3. Taylor expanded in y1 around inf 53.2%

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

      1. associate-*r* 52.4%

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

      2. *-commutative 52.4%

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

   5. Simplified 52.4%

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

   6. Taylor expanded in a around -inf 57.1%

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

      1. mul-1-neg 57.1%

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

   8. Simplified 57.1%

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

   if 6.0000000000000001e-264 < j < 3.55e-202 or 1.79999999999999989e-56 < j < 1.04999999999999995e164

   1. Initial program 39.2%

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

   3. Taylor expanded in y4 around inf 55.6%

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

   if 1.04999999999999995e164 < j < 8.4999999999999999e191

   1. Initial program 22.2%

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

   3. Taylor expanded in i around -inf 66.7%

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

   4. Taylor expanded in x around inf 88.9%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 88.9%

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

   6. Simplified 88.9%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(y \cdot c - j \cdot y1\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.8 \cdot 10^{+181}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right) - \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \mathbf{elif}\;j \leq -1.5 \cdot 10^{+58}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right) - \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-264}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 3.55 \cdot 10^{-202}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot \left(y \cdot k - t \cdot j\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.8 \cdot 10^{-56}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{+164}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - b \cdot \left(y \cdot k - t \cdot j\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+191}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right) - \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 37.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(i \cdot y5 - b \cdot y4\right)\\ t_2 := j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right) - \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t\_1\right)\right)\\ t_3 := z \cdot y3 - x \cdot y2\\ t_4 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot t\_3\right)\\ \mathbf{if}\;j \leq -1.8 \cdot 10^{+181}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -2.2 \cdot 10^{+61}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right) - \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot t\_3\right)\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-264}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;j \leq 7.4 \cdot 10^{-144}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(i \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{-40}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;j \leq 4.7 \cdot 10^{+151}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(i \cdot \left(x \cdot y1\right) - t\_1\right)\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+191}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (- (* i y5) (* b y4))))
        (t_2
         (*
          j
          (-
           (* x (- (* i y1) (* b y0)))
           (+ (* y3 (- (* y1 y4) (* y0 y5))) t_1))))
        (t_3 (- (* z y3) (* x y2)))
        (t_4 (* a (+ (* y5 (- (* t y2) (* y y3))) (* y1 t_3)))))
   (if (<= j -1.8e+181)
     t_2
     (if (<= j -2.2e+61)
       (*
        y0
        (-
         (* b (- (* z k) (* x j)))
         (+ (* y5 (- (* k y2) (* j y3))) (* c t_3))))
       (if (<= j 5.8e-264)
         t_4
         (if (<= j 7.4e-144)
           (* y1 (* z (* i (- k))))
           (if (<= j 1.65e-40)
             t_4
             (if (<= j 4.7e+151)
               (* j (+ (* y3 (- (* y0 y5) (* y1 y4))) (- (* i (* x y1)) t_1)))
               (if (<= j 8.5e+191)
                 (* i (* x (- (* j y1) (* y c))))
                 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 = t * ((i * y5) - (b * y4));
	double t_2 = j * ((x * ((i * y1) - (b * y0))) - ((y3 * ((y1 * y4) - (y0 * y5))) + t_1));
	double t_3 = (z * y3) - (x * y2);
	double t_4 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * t_3));
	double tmp;
	if (j <= -1.8e+181) {
		tmp = t_2;
	} else if (j <= -2.2e+61) {
		tmp = y0 * ((b * ((z * k) - (x * j))) - ((y5 * ((k * y2) - (j * y3))) + (c * t_3)));
	} else if (j <= 5.8e-264) {
		tmp = t_4;
	} else if (j <= 7.4e-144) {
		tmp = y1 * (z * (i * -k));
	} else if (j <= 1.65e-40) {
		tmp = t_4;
	} else if (j <= 4.7e+151) {
		tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((i * (x * y1)) - t_1));
	} else if (j <= 8.5e+191) {
		tmp = i * (x * ((j * y1) - (y * c)));
	} 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) :: tmp
    t_1 = t * ((i * y5) - (b * y4))
    t_2 = j * ((x * ((i * y1) - (b * y0))) - ((y3 * ((y1 * y4) - (y0 * y5))) + t_1))
    t_3 = (z * y3) - (x * y2)
    t_4 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * t_3))
    if (j <= (-1.8d+181)) then
        tmp = t_2
    else if (j <= (-2.2d+61)) then
        tmp = y0 * ((b * ((z * k) - (x * j))) - ((y5 * ((k * y2) - (j * y3))) + (c * t_3)))
    else if (j <= 5.8d-264) then
        tmp = t_4
    else if (j <= 7.4d-144) then
        tmp = y1 * (z * (i * -k))
    else if (j <= 1.65d-40) then
        tmp = t_4
    else if (j <= 4.7d+151) then
        tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((i * (x * y1)) - t_1))
    else if (j <= 8.5d+191) then
        tmp = i * (x * ((j * y1) - (y * c)))
    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 = t * ((i * y5) - (b * y4));
	double t_2 = j * ((x * ((i * y1) - (b * y0))) - ((y3 * ((y1 * y4) - (y0 * y5))) + t_1));
	double t_3 = (z * y3) - (x * y2);
	double t_4 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * t_3));
	double tmp;
	if (j <= -1.8e+181) {
		tmp = t_2;
	} else if (j <= -2.2e+61) {
		tmp = y0 * ((b * ((z * k) - (x * j))) - ((y5 * ((k * y2) - (j * y3))) + (c * t_3)));
	} else if (j <= 5.8e-264) {
		tmp = t_4;
	} else if (j <= 7.4e-144) {
		tmp = y1 * (z * (i * -k));
	} else if (j <= 1.65e-40) {
		tmp = t_4;
	} else if (j <= 4.7e+151) {
		tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((i * (x * y1)) - t_1));
	} else if (j <= 8.5e+191) {
		tmp = i * (x * ((j * y1) - (y * c)));
	} 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 = t * ((i * y5) - (b * y4))
	t_2 = j * ((x * ((i * y1) - (b * y0))) - ((y3 * ((y1 * y4) - (y0 * y5))) + t_1))
	t_3 = (z * y3) - (x * y2)
	t_4 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * t_3))
	tmp = 0
	if j <= -1.8e+181:
		tmp = t_2
	elif j <= -2.2e+61:
		tmp = y0 * ((b * ((z * k) - (x * j))) - ((y5 * ((k * y2) - (j * y3))) + (c * t_3)))
	elif j <= 5.8e-264:
		tmp = t_4
	elif j <= 7.4e-144:
		tmp = y1 * (z * (i * -k))
	elif j <= 1.65e-40:
		tmp = t_4
	elif j <= 4.7e+151:
		tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((i * (x * y1)) - t_1))
	elif j <= 8.5e+191:
		tmp = i * (x * ((j * y1) - (y * c)))
	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(t * Float64(Float64(i * y5) - Float64(b * y4)))
	t_2 = Float64(j * Float64(Float64(x * Float64(Float64(i * y1) - Float64(b * y0))) - Float64(Float64(y3 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + t_1)))
	t_3 = Float64(Float64(z * y3) - Float64(x * y2))
	t_4 = Float64(a * Float64(Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y1 * t_3)))
	tmp = 0.0
	if (j <= -1.8e+181)
		tmp = t_2;
	elseif (j <= -2.2e+61)
		tmp = Float64(y0 * Float64(Float64(b * Float64(Float64(z * k) - Float64(x * j))) - Float64(Float64(y5 * Float64(Float64(k * y2) - Float64(j * y3))) + Float64(c * t_3))));
	elseif (j <= 5.8e-264)
		tmp = t_4;
	elseif (j <= 7.4e-144)
		tmp = Float64(y1 * Float64(z * Float64(i * Float64(-k))));
	elseif (j <= 1.65e-40)
		tmp = t_4;
	elseif (j <= 4.7e+151)
		tmp = Float64(j * Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(Float64(i * Float64(x * y1)) - t_1)));
	elseif (j <= 8.5e+191)
		tmp = Float64(i * Float64(x * Float64(Float64(j * y1) - Float64(y * c))));
	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 = t * ((i * y5) - (b * y4));
	t_2 = j * ((x * ((i * y1) - (b * y0))) - ((y3 * ((y1 * y4) - (y0 * y5))) + t_1));
	t_3 = (z * y3) - (x * y2);
	t_4 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * t_3));
	tmp = 0.0;
	if (j <= -1.8e+181)
		tmp = t_2;
	elseif (j <= -2.2e+61)
		tmp = y0 * ((b * ((z * k) - (x * j))) - ((y5 * ((k * y2) - (j * y3))) + (c * t_3)));
	elseif (j <= 5.8e-264)
		tmp = t_4;
	elseif (j <= 7.4e-144)
		tmp = y1 * (z * (i * -k));
	elseif (j <= 1.65e-40)
		tmp = t_4;
	elseif (j <= 4.7e+151)
		tmp = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((i * (x * y1)) - t_1));
	elseif (j <= 8.5e+191)
		tmp = i * (x * ((j * y1) - (y * c)));
	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[(t * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y3 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.8e+181], t$95$2, If[LessEqual[j, -2.2e+61], N[(y0 * N[(N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y5 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.8e-264], t$95$4, If[LessEqual[j, 7.4e-144], N[(y1 * N[(z * N[(i * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.65e-40], t$95$4, If[LessEqual[j, 4.7e+151], N[(j * N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.5e+191], N[(i * N[(x * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -1.79999999999999992e181 or 8.4999999999999999e191 < j

   1. Initial program 28.2%

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

   3. Taylor expanded in j around inf 75.4%

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

      1. +-commutative 75.4%

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

      2. mul-1-neg 75.4%

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

      3. unsub-neg 75.4%

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

      4. *-commutative 75.4%

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

   5. Simplified 75.4%

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

   if -1.79999999999999992e181 < j < -2.2e61

   1. Initial program 29.7%

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

   3. Taylor expanded in y0 around inf 73.4%

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

      1. +-commutative 73.4%

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

      2. mul-1-neg 73.4%

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

      3. unsub-neg 73.4%

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

      4. *-commutative 73.4%

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

      5. *-commutative 73.4%

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

      6. *-commutative 73.4%

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

      7. *-commutative 73.4%

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

   5. Simplified 73.4%

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

   if -2.2e61 < j < 5.7999999999999997e-264 or 7.4000000000000005e-144 < j < 1.64999999999999996e-40

   1. Initial program 43.2%

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

   3. Taylor expanded in y1 around inf 52.8%

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

      1. associate-*r* 52.8%

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

      2. *-commutative 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in a around -inf 57.6%

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

      1. mul-1-neg 57.6%

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

   8. Simplified 57.6%

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

   if 5.7999999999999997e-264 < j < 7.4000000000000005e-144

   1. Initial program 41.7%

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

   3. Taylor expanded in y1 around -inf 36.4%

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

      1. associate-*r* 36.4%

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

      2. neg-mul-1 36.4%

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

      3. +-commutative 36.4%

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

      4. mul-1-neg 36.4%

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

      5. unsub-neg 36.4%

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

      6. *-commutative 36.4%

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

      7. *-commutative 36.4%

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

      8. *-commutative 36.4%

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

      9. *-commutative 36.4%

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

   5. Simplified 36.4%

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

   6. Taylor expanded in z around -inf 42.5%

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

   7. Taylor expanded in a around 0 42.7%

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

      1. mul-1-neg 42.7%

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

      2. distribute-lft-neg-out 42.7%

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

      3. *-commutative 42.7%

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

   9. Simplified 42.7%

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

   if 1.64999999999999996e-40 < j < 4.69999999999999989e151

   1. Initial program 40.9%

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

   3. Taylor expanded in y1 around inf 46.3%

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

      1. associate-*r* 43.7%

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

      2. *-commutative 43.7%

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

   5. Simplified 43.7%

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

   6. Taylor expanded in j around inf 47.7%

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

   if 4.69999999999999989e151 < j < 8.4999999999999999e191

   1. Initial program 20.0%

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

   3. Taylor expanded in i around -inf 70.0%

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

   4. Taylor expanded in x around inf 80.4%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 80.4%

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

   6. Simplified 80.4%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(y \cdot c - j \cdot y1\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.8 \cdot 10^{+181}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right) - \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \mathbf{elif}\;j \leq -2.2 \cdot 10^{+61}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right) - \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right) + c \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-264}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 7.4 \cdot 10^{-144}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(i \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 4.7 \cdot 10^{+151}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(i \cdot \left(x \cdot y1\right) - t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+191}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right) - \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 30.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+77}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot \left(j - \frac{y \cdot k}{t}\right)\right)\right)\\ \mathbf{elif}\;y \leq -9.4 \cdot 10^{-160}:\\ \;\;\;\;\left(k \cdot y4 - x \cdot a\right) \cdot \left(y1 \cdot y2\right)\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-237}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + i \cdot \left(j \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-277}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-297}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-264}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+23}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+174}:\\ \;\;\;\;\left(x \cdot b\right) \cdot \left(y \cdot a - j \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y1 (- (* x i) (* y3 y4))))))
   (if (<= y -1.1e+77)
     (* b (* y4 (* t (- j (/ (* y k) t)))))
     (if (<= y -9.4e-160)
       (* (- (* k y4) (* x a)) (* y1 y2))
       (if (<= y -4.7e-237)
         (* x (+ (* y2 (- (* c y0) (* a y1))) (* i (* j y1))))
         (if (<= y -3.4e-277)
           (* k (* y2 (- (* y1 y4) (* y0 y5))))
           (if (<= y -1.1e-297)
             t_1
             (if (<= y 2.65e-264)
               (* y0 (* y2 (- (* x c) (* k y5))))
               (if (<= y 5.2e-166)
                 t_1
                 (if (<= y 1.06e+23)
                   (* a (* y1 (- (* z y3) (* x y2))))
                   (if (<= y 2.9e+174)
                     (* (* x b) (- (* y a) (* j y0)))
                     (* k (* y (- (* i y5) (* b 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 = j * (y1 * ((x * i) - (y3 * y4)));
	double tmp;
	if (y <= -1.1e+77) {
		tmp = b * (y4 * (t * (j - ((y * k) / t))));
	} else if (y <= -9.4e-160) {
		tmp = ((k * y4) - (x * a)) * (y1 * y2);
	} else if (y <= -4.7e-237) {
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (i * (j * y1)));
	} else if (y <= -3.4e-277) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (y <= -1.1e-297) {
		tmp = t_1;
	} else if (y <= 2.65e-264) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (y <= 5.2e-166) {
		tmp = t_1;
	} else if (y <= 1.06e+23) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y <= 2.9e+174) {
		tmp = (x * b) * ((y * a) - (j * y0));
	} else {
		tmp = k * (y * ((i * y5) - (b * y4)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (y1 * ((x * i) - (y3 * y4)))
    if (y <= (-1.1d+77)) then
        tmp = b * (y4 * (t * (j - ((y * k) / t))))
    else if (y <= (-9.4d-160)) then
        tmp = ((k * y4) - (x * a)) * (y1 * y2)
    else if (y <= (-4.7d-237)) then
        tmp = x * ((y2 * ((c * y0) - (a * y1))) + (i * (j * y1)))
    else if (y <= (-3.4d-277)) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (y <= (-1.1d-297)) then
        tmp = t_1
    else if (y <= 2.65d-264) then
        tmp = y0 * (y2 * ((x * c) - (k * y5)))
    else if (y <= 5.2d-166) then
        tmp = t_1
    else if (y <= 1.06d+23) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (y <= 2.9d+174) then
        tmp = (x * b) * ((y * a) - (j * y0))
    else
        tmp = k * (y * ((i * y5) - (b * 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 = j * (y1 * ((x * i) - (y3 * y4)));
	double tmp;
	if (y <= -1.1e+77) {
		tmp = b * (y4 * (t * (j - ((y * k) / t))));
	} else if (y <= -9.4e-160) {
		tmp = ((k * y4) - (x * a)) * (y1 * y2);
	} else if (y <= -4.7e-237) {
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (i * (j * y1)));
	} else if (y <= -3.4e-277) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (y <= -1.1e-297) {
		tmp = t_1;
	} else if (y <= 2.65e-264) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (y <= 5.2e-166) {
		tmp = t_1;
	} else if (y <= 1.06e+23) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y <= 2.9e+174) {
		tmp = (x * b) * ((y * a) - (j * y0));
	} else {
		tmp = k * (y * ((i * y5) - (b * y4)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (y1 * ((x * i) - (y3 * y4)))
	tmp = 0
	if y <= -1.1e+77:
		tmp = b * (y4 * (t * (j - ((y * k) / t))))
	elif y <= -9.4e-160:
		tmp = ((k * y4) - (x * a)) * (y1 * y2)
	elif y <= -4.7e-237:
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (i * (j * y1)))
	elif y <= -3.4e-277:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif y <= -1.1e-297:
		tmp = t_1
	elif y <= 2.65e-264:
		tmp = y0 * (y2 * ((x * c) - (k * y5)))
	elif y <= 5.2e-166:
		tmp = t_1
	elif y <= 1.06e+23:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif y <= 2.9e+174:
		tmp = (x * b) * ((y * a) - (j * y0))
	else:
		tmp = k * (y * ((i * y5) - (b * 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(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))))
	tmp = 0.0
	if (y <= -1.1e+77)
		tmp = Float64(b * Float64(y4 * Float64(t * Float64(j - Float64(Float64(y * k) / t)))));
	elseif (y <= -9.4e-160)
		tmp = Float64(Float64(Float64(k * y4) - Float64(x * a)) * Float64(y1 * y2));
	elseif (y <= -4.7e-237)
		tmp = Float64(x * Float64(Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(i * Float64(j * y1))));
	elseif (y <= -3.4e-277)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (y <= -1.1e-297)
		tmp = t_1;
	elseif (y <= 2.65e-264)
		tmp = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))));
	elseif (y <= 5.2e-166)
		tmp = t_1;
	elseif (y <= 1.06e+23)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (y <= 2.9e+174)
		tmp = Float64(Float64(x * b) * Float64(Float64(y * a) - Float64(j * y0)));
	else
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * 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 = j * (y1 * ((x * i) - (y3 * y4)));
	tmp = 0.0;
	if (y <= -1.1e+77)
		tmp = b * (y4 * (t * (j - ((y * k) / t))));
	elseif (y <= -9.4e-160)
		tmp = ((k * y4) - (x * a)) * (y1 * y2);
	elseif (y <= -4.7e-237)
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (i * (j * y1)));
	elseif (y <= -3.4e-277)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (y <= -1.1e-297)
		tmp = t_1;
	elseif (y <= 2.65e-264)
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	elseif (y <= 5.2e-166)
		tmp = t_1;
	elseif (y <= 1.06e+23)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (y <= 2.9e+174)
		tmp = (x * b) * ((y * a) - (j * y0));
	else
		tmp = k * (y * ((i * y5) - (b * 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[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.1e+77], N[(b * N[(y4 * N[(t * N[(j - N[(N[(y * k), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.4e-160], N[(N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * N[(y1 * y2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.7e-237], N[(x * N[(N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.4e-277], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.1e-297], t$95$1, If[LessEqual[y, 2.65e-264], N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e-166], t$95$1, If[LessEqual[y, 1.06e+23], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e+174], N[(N[(x * b), $MachinePrecision] * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y < -1.1e77

   1. Initial program 19.5%

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

   3. Taylor expanded in b around inf 27.4%

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

   4. Taylor expanded in y4 around inf 40.0%

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

   5. Taylor expanded in t around inf 51.7%

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

      1. associate-*r/ 51.7%

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

      2. neg-mul-1 51.7%

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

      3. distribute-rgt-neg-in 51.7%

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

   7. Simplified 51.7%

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

   if -1.1e77 < y < -9.3999999999999995e-160

   1. Initial program 46.6%

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

   3. Taylor expanded in y1 around -inf 45.4%

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

      1. associate-*r* 45.4%

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

      2. neg-mul-1 45.4%

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

      3. +-commutative 45.4%

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

      4. mul-1-neg 45.4%

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

      5. unsub-neg 45.4%

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

      6. *-commutative 45.4%

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

      7. *-commutative 45.4%

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

      8. *-commutative 45.4%

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

      9. *-commutative 45.4%

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

   5. Simplified 45.4%

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

   6. Taylor expanded in y2 around -inf 40.4%

      \[\leadsto \color{blue}{y1 \cdot \left(y2 \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(k \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 43.8%

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

      2. distribute-lft-out-- 43.8%

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

   8. Simplified 43.8%

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

   if -9.3999999999999995e-160 < y < -4.6999999999999998e-237

   1. Initial program 46.7%

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

   3. Taylor expanded in y1 around inf 53.3%

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

      1. associate-*r* 53.3%

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

      2. *-commutative 53.3%

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

   5. Simplified 53.3%

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

   6. Taylor expanded in x around inf 60.7%

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

   if -4.6999999999999998e-237 < y < -3.39999999999999982e-277

   1. Initial program 44.4%

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

   3. Taylor expanded in k around inf 58.1%

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

      1. +-commutative 58.1%

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

      2. mul-1-neg 58.1%

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

      3. unsub-neg 58.1%

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

      4. *-commutative 58.1%

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

      5. associate-*r* 58.1%

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

      6. neg-mul-1 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in y2 around inf 56.9%

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

   if -3.39999999999999982e-277 < y < -1.0999999999999999e-297 or 2.6499999999999999e-264 < y < 5.19999999999999979e-166

   1. Initial program 50.4%

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

   3. Taylor expanded in y1 around -inf 47.6%

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

      1. associate-*r* 47.6%

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

      2. neg-mul-1 47.6%

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

      3. +-commutative 47.6%

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

      4. mul-1-neg 47.6%

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

      5. unsub-neg 47.6%

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

      6. *-commutative 47.6%

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

      7. *-commutative 47.6%

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

      8. *-commutative 47.6%

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

      9. *-commutative 47.6%

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

   5. Simplified 47.6%

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

   6. Taylor expanded in j around inf 53.7%

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

      1. +-commutative 53.7%

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

      2. mul-1-neg 53.7%

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

      3. unsub-neg 53.7%

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

   8. Simplified 53.7%

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

   if -1.0999999999999999e-297 < y < 2.6499999999999999e-264

   1. Initial program 0.0%

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

   3. Taylor expanded in y0 around inf 57.1%

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

      1. +-commutative 57.1%

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

      2. mul-1-neg 57.1%

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

      3. unsub-neg 57.1%

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

      4. *-commutative 57.1%

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

      5. *-commutative 57.1%

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

      6. *-commutative 57.1%

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

      7. *-commutative 57.1%

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

   5. Simplified 57.1%

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

   6. Taylor expanded in y2 around inf 72.3%

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

   if 5.19999999999999979e-166 < y < 1.06e23

   1. Initial program 44.0%

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

   3. Taylor expanded in y1 around -inf 43.6%

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

      1. associate-*r* 43.6%

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

      2. neg-mul-1 43.6%

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

      3. +-commutative 43.6%

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

      4. mul-1-neg 43.6%

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

      5. unsub-neg 43.6%

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

      6. *-commutative 43.6%

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

      7. *-commutative 43.6%

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

      8. *-commutative 43.6%

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

      9. *-commutative 43.6%

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

   5. Simplified 43.6%

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

   6. Taylor expanded in a around inf 42.9%

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

      1. associate-*r* 42.9%

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

      2. neg-mul-1 42.9%

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

   8. Simplified 42.9%

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

   if 1.06e23 < y < 2.9e174

   1. Initial program 35.1%

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

   3. Taylor expanded in b around inf 54.3%

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

   4. Taylor expanded in x around inf 52.4%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 52.1%

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

   6. Simplified 52.1%

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

   if 2.9e174 < y

   1. Initial program 19.9%

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

   3. Taylor expanded in k around inf 60.6%

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

      1. +-commutative 60.6%

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

      2. mul-1-neg 60.6%

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

      3. unsub-neg 60.6%

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

      4. *-commutative 60.6%

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

      5. associate-*r* 60.6%

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

      6. neg-mul-1 60.6%

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

   5. Simplified 60.6%

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

   6. Taylor expanded in y around inf 61.0%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+77}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot \left(j - \frac{y \cdot k}{t}\right)\right)\right)\\ \mathbf{elif}\;y \leq -9.4 \cdot 10^{-160}:\\ \;\;\;\;\left(k \cdot y4 - x \cdot a\right) \cdot \left(y1 \cdot y2\right)\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-237}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + i \cdot \left(j \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-277}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-297}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-264}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-166}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+23}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+174}:\\ \;\;\;\;\left(x \cdot b\right) \cdot \left(y \cdot a - j \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ t_2 := j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(i \cdot \left(x \cdot y1\right) - t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \mathbf{if}\;j \leq -4.5 \cdot 10^{+184}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -2.3 \cdot 10^{+61}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-264}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 7.4 \cdot 10^{-144}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(i \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (* a (+ (* y5 (- (* t y2) (* y y3))) (* y1 (- (* z y3) (* x y2))))))
        (t_2
         (*
          j
          (+
           (* y3 (- (* y0 y5) (* y1 y4)))
           (- (* i (* x y1)) (* t (- (* i y5) (* b y4))))))))
   (if (<= j -4.5e+184)
     t_2
     (if (<= j -2.3e+61)
       (*
        c
        (+
         (+ (* y0 (- (* x y2) (* z y3))) (* i (- (* z t) (* x y))))
         (* y4 (- (* y y3) (* t y2)))))
       (if (<= j 6e-264)
         t_1
         (if (<= j 7.4e-144)
           (* y1 (* z (* i (- k))))
           (if (<= j 1.15e-40) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))));
	double t_2 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((i * (x * y1)) - (t * ((i * y5) - (b * y4)))));
	double tmp;
	if (j <= -4.5e+184) {
		tmp = t_2;
	} else if (j <= -2.3e+61) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (j <= 6e-264) {
		tmp = t_1;
	} else if (j <= 7.4e-144) {
		tmp = y1 * (z * (i * -k));
	} else if (j <= 1.15e-40) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))))
    t_2 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((i * (x * y1)) - (t * ((i * y5) - (b * y4)))))
    if (j <= (-4.5d+184)) then
        tmp = t_2
    else if (j <= (-2.3d+61)) then
        tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
    else if (j <= 6d-264) then
        tmp = t_1
    else if (j <= 7.4d-144) then
        tmp = y1 * (z * (i * -k))
    else if (j <= 1.15d-40) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))));
	double t_2 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((i * (x * y1)) - (t * ((i * y5) - (b * y4)))));
	double tmp;
	if (j <= -4.5e+184) {
		tmp = t_2;
	} else if (j <= -2.3e+61) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (j <= 6e-264) {
		tmp = t_1;
	} else if (j <= 7.4e-144) {
		tmp = y1 * (z * (i * -k));
	} else if (j <= 1.15e-40) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))))
	t_2 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((i * (x * y1)) - (t * ((i * y5) - (b * y4)))))
	tmp = 0
	if j <= -4.5e+184:
		tmp = t_2
	elif j <= -2.3e+61:
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))))
	elif j <= 6e-264:
		tmp = t_1
	elif j <= 7.4e-144:
		tmp = y1 * (z * (i * -k))
	elif j <= 1.15e-40:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2)))))
	t_2 = Float64(j * Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(Float64(i * Float64(x * y1)) - Float64(t * Float64(Float64(i * y5) - Float64(b * y4))))))
	tmp = 0.0
	if (j <= -4.5e+184)
		tmp = t_2;
	elseif (j <= -2.3e+61)
		tmp = Float64(c * Float64(Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(i * Float64(Float64(z * t) - Float64(x * y)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (j <= 6e-264)
		tmp = t_1;
	elseif (j <= 7.4e-144)
		tmp = Float64(y1 * Float64(z * Float64(i * Float64(-k))));
	elseif (j <= 1.15e-40)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))));
	t_2 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((i * (x * y1)) - (t * ((i * y5) - (b * y4)))));
	tmp = 0.0;
	if (j <= -4.5e+184)
		tmp = t_2;
	elseif (j <= -2.3e+61)
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (i * ((z * t) - (x * y)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (j <= 6e-264)
		tmp = t_1;
	elseif (j <= 7.4e-144)
		tmp = y1 * (z * (i * -k));
	elseif (j <= 1.15e-40)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4.5e+184], t$95$2, If[LessEqual[j, -2.3e+61], N[(c * N[(N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6e-264], t$95$1, If[LessEqual[j, 7.4e-144], N[(y1 * N[(z * N[(i * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.15e-40], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -4.50000000000000036e184 or 1.15e-40 < j

   1. Initial program 31.6%

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

   3. Taylor expanded in y1 around inf 34.7%

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

      1. associate-*r* 33.7%

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

      2. *-commutative 33.7%

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

   5. Simplified 33.7%

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

   6. Taylor expanded in j around inf 58.1%

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

   if -4.50000000000000036e184 < j < -2.3e61

   1. Initial program 31.6%

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

   3. Taylor expanded in c around inf 50.3%

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

      1. +-commutative 50.3%

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

      2. mul-1-neg 50.3%

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

      3. unsub-neg 50.3%

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

      4. *-commutative 50.3%

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

      5. *-commutative 50.3%

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

      6. *-commutative 50.3%

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

      7. *-commutative 50.3%

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

   5. Simplified 50.3%

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

   if -2.3e61 < j < 6.0000000000000001e-264 or 7.4000000000000005e-144 < j < 1.15e-40

   1. Initial program 43.2%

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

   3. Taylor expanded in y1 around inf 52.8%

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

      1. associate-*r* 52.8%

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

      2. *-commutative 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in a around -inf 57.6%

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

      1. mul-1-neg 57.6%

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

   8. Simplified 57.6%

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

   if 6.0000000000000001e-264 < j < 7.4000000000000005e-144

   1. Initial program 41.7%

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

   3. Taylor expanded in y1 around -inf 36.4%

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

      1. associate-*r* 36.4%

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

      2. neg-mul-1 36.4%

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

      3. +-commutative 36.4%

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

      4. mul-1-neg 36.4%

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

      5. unsub-neg 36.4%

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

      6. *-commutative 36.4%

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

      7. *-commutative 36.4%

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

      8. *-commutative 36.4%

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

      9. *-commutative 36.4%

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

   5. Simplified 36.4%

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

   6. Taylor expanded in z around -inf 42.5%

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

   7. Taylor expanded in a around 0 42.7%

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

      1. mul-1-neg 42.7%

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

      2. distribute-lft-neg-out 42.7%

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

      3. *-commutative 42.7%

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

   9. Simplified 42.7%

      \[\leadsto y1 \cdot \left(z \cdot \color{blue}{\left(k \cdot \left(-i\right)\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.5 \cdot 10^{+184}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(i \cdot \left(x \cdot y1\right) - t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \mathbf{elif}\;j \leq -2.3 \cdot 10^{+61}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t - x \cdot y\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-264}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 7.4 \cdot 10^{-144}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(i \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(i \cdot \left(x \cdot y1\right) - t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 37.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ t_2 := j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(i \cdot \left(x \cdot y1\right) - t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \mathbf{if}\;j \leq -3.5 \cdot 10^{+169}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -5.4 \cdot 10^{+134}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{-264}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 7.4 \cdot 10^{-144}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(i \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-41}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (* a (+ (* y5 (- (* t y2) (* y y3))) (* y1 (- (* z y3) (* x y2))))))
        (t_2
         (*
          j
          (+
           (* y3 (- (* y0 y5) (* y1 y4)))
           (- (* i (* x y1)) (* t (- (* i y5) (* b y4))))))))
   (if (<= j -3.5e+169)
     t_2
     (if (<= j -5.4e+134)
       (*
        b
        (+
         (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
         (* y0 (- (* z k) (* x j)))))
       (if (<= j 3.7e-264)
         t_1
         (if (<= j 7.4e-144)
           (* y1 (* z (* i (- k))))
           (if (<= j 6.2e-41) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))));
	double t_2 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((i * (x * y1)) - (t * ((i * y5) - (b * y4)))));
	double tmp;
	if (j <= -3.5e+169) {
		tmp = t_2;
	} else if (j <= -5.4e+134) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (j <= 3.7e-264) {
		tmp = t_1;
	} else if (j <= 7.4e-144) {
		tmp = y1 * (z * (i * -k));
	} else if (j <= 6.2e-41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))))
    t_2 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((i * (x * y1)) - (t * ((i * y5) - (b * y4)))))
    if (j <= (-3.5d+169)) then
        tmp = t_2
    else if (j <= (-5.4d+134)) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    else if (j <= 3.7d-264) then
        tmp = t_1
    else if (j <= 7.4d-144) then
        tmp = y1 * (z * (i * -k))
    else if (j <= 6.2d-41) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))));
	double t_2 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((i * (x * y1)) - (t * ((i * y5) - (b * y4)))));
	double tmp;
	if (j <= -3.5e+169) {
		tmp = t_2;
	} else if (j <= -5.4e+134) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (j <= 3.7e-264) {
		tmp = t_1;
	} else if (j <= 7.4e-144) {
		tmp = y1 * (z * (i * -k));
	} else if (j <= 6.2e-41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))))
	t_2 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((i * (x * y1)) - (t * ((i * y5) - (b * y4)))))
	tmp = 0
	if j <= -3.5e+169:
		tmp = t_2
	elif j <= -5.4e+134:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	elif j <= 3.7e-264:
		tmp = t_1
	elif j <= 7.4e-144:
		tmp = y1 * (z * (i * -k))
	elif j <= 6.2e-41:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2)))))
	t_2 = Float64(j * Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(Float64(i * Float64(x * y1)) - Float64(t * Float64(Float64(i * y5) - Float64(b * y4))))))
	tmp = 0.0
	if (j <= -3.5e+169)
		tmp = t_2;
	elseif (j <= -5.4e+134)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (j <= 3.7e-264)
		tmp = t_1;
	elseif (j <= 7.4e-144)
		tmp = Float64(y1 * Float64(z * Float64(i * Float64(-k))));
	elseif (j <= 6.2e-41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))));
	t_2 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((i * (x * y1)) - (t * ((i * y5) - (b * y4)))));
	tmp = 0.0;
	if (j <= -3.5e+169)
		tmp = t_2;
	elseif (j <= -5.4e+134)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	elseif (j <= 3.7e-264)
		tmp = t_1;
	elseif (j <= 7.4e-144)
		tmp = y1 * (z * (i * -k));
	elseif (j <= 6.2e-41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.5e+169], t$95$2, If[LessEqual[j, -5.4e+134], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.7e-264], t$95$1, If[LessEqual[j, 7.4e-144], N[(y1 * N[(z * N[(i * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.2e-41], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.50000000000000019e169 or 6.20000000000000001e-41 < j

   1. Initial program 31.4%

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

   3. Taylor expanded in y1 around inf 35.3%

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

      1. associate-*r* 34.3%

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

      2. *-commutative 34.3%

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

   5. Simplified 34.3%

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

   6. Taylor expanded in j around inf 57.8%

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

   if -3.50000000000000019e169 < j < -5.4e134

   1. Initial program 25.0%

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

   3. Taylor expanded in b around inf 67.3%

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

   if -5.4e134 < j < 3.69999999999999996e-264 or 7.4000000000000005e-144 < j < 6.20000000000000001e-41

   1. Initial program 42.0%

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

   3. Taylor expanded in y1 around inf 50.7%

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

      1. associate-*r* 50.7%

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

      2. *-commutative 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in a around -inf 54.1%

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

      1. mul-1-neg 54.1%

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

   8. Simplified 54.1%

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

   if 3.69999999999999996e-264 < j < 7.4000000000000005e-144

   1. Initial program 41.7%

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

   3. Taylor expanded in y1 around -inf 36.4%

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

      1. associate-*r* 36.4%

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

      2. neg-mul-1 36.4%

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

      3. +-commutative 36.4%

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

      4. mul-1-neg 36.4%

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

      5. unsub-neg 36.4%

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

      6. *-commutative 36.4%

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

      7. *-commutative 36.4%

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

      8. *-commutative 36.4%

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

      9. *-commutative 36.4%

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

   5. Simplified 36.4%

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

   6. Taylor expanded in z around -inf 42.5%

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

   7. Taylor expanded in a around 0 42.7%

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

      1. mul-1-neg 42.7%

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

      2. distribute-lft-neg-out 42.7%

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

      3. *-commutative 42.7%

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

   9. Simplified 42.7%

      \[\leadsto y1 \cdot \left(z \cdot \color{blue}{\left(k \cdot \left(-i\right)\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.5 \cdot 10^{+169}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(i \cdot \left(x \cdot y1\right) - t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \mathbf{elif}\;j \leq -5.4 \cdot 10^{+134}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{-264}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 7.4 \cdot 10^{-144}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(i \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-41}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(i \cdot \left(x \cdot y1\right) - t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(i \cdot \left(x \cdot y1\right) - t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ t_2 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{if}\;j \leq -7.6 \cdot 10^{+183}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + i \cdot \left(j \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 5.7 \cdot 10^{-264}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 7.4 \cdot 10^{-144}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(i \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-43}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          j
          (+
           (* y3 (- (* y0 y5) (* y1 y4)))
           (- (* i (* x y1)) (* t (- (* i y5) (* b y4)))))))
        (t_2
         (* a (+ (* y5 (- (* t y2) (* y y3))) (* y1 (- (* z y3) (* x y2)))))))
   (if (<= j -7.6e+183)
     t_1
     (if (<= j -1.1e+62)
       (* x (+ (* y2 (- (* c y0) (* a y1))) (* i (* j y1))))
       (if (<= j 5.7e-264)
         t_2
         (if (<= j 7.4e-144)
           (* y1 (* z (* i (- k))))
           (if (<= j 2.3e-43) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((i * (x * y1)) - (t * ((i * y5) - (b * y4)))));
	double t_2 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))));
	double tmp;
	if (j <= -7.6e+183) {
		tmp = t_1;
	} else if (j <= -1.1e+62) {
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (i * (j * y1)));
	} else if (j <= 5.7e-264) {
		tmp = t_2;
	} else if (j <= 7.4e-144) {
		tmp = y1 * (z * (i * -k));
	} else if (j <= 2.3e-43) {
		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 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((i * (x * y1)) - (t * ((i * y5) - (b * y4)))))
    t_2 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))))
    if (j <= (-7.6d+183)) then
        tmp = t_1
    else if (j <= (-1.1d+62)) then
        tmp = x * ((y2 * ((c * y0) - (a * y1))) + (i * (j * y1)))
    else if (j <= 5.7d-264) then
        tmp = t_2
    else if (j <= 7.4d-144) then
        tmp = y1 * (z * (i * -k))
    else if (j <= 2.3d-43) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((i * (x * y1)) - (t * ((i * y5) - (b * y4)))));
	double t_2 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))));
	double tmp;
	if (j <= -7.6e+183) {
		tmp = t_1;
	} else if (j <= -1.1e+62) {
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (i * (j * y1)));
	} else if (j <= 5.7e-264) {
		tmp = t_2;
	} else if (j <= 7.4e-144) {
		tmp = y1 * (z * (i * -k));
	} else if (j <= 2.3e-43) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((i * (x * y1)) - (t * ((i * y5) - (b * y4)))))
	t_2 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))))
	tmp = 0
	if j <= -7.6e+183:
		tmp = t_1
	elif j <= -1.1e+62:
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (i * (j * y1)))
	elif j <= 5.7e-264:
		tmp = t_2
	elif j <= 7.4e-144:
		tmp = y1 * (z * (i * -k))
	elif j <= 2.3e-43:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(Float64(i * Float64(x * y1)) - Float64(t * Float64(Float64(i * y5) - Float64(b * y4))))))
	t_2 = Float64(a * Float64(Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2)))))
	tmp = 0.0
	if (j <= -7.6e+183)
		tmp = t_1;
	elseif (j <= -1.1e+62)
		tmp = Float64(x * Float64(Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(i * Float64(j * y1))));
	elseif (j <= 5.7e-264)
		tmp = t_2;
	elseif (j <= 7.4e-144)
		tmp = Float64(y1 * Float64(z * Float64(i * Float64(-k))));
	elseif (j <= 2.3e-43)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((i * (x * y1)) - (t * ((i * y5) - (b * y4)))));
	t_2 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))));
	tmp = 0.0;
	if (j <= -7.6e+183)
		tmp = t_1;
	elseif (j <= -1.1e+62)
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (i * (j * y1)));
	elseif (j <= 5.7e-264)
		tmp = t_2;
	elseif (j <= 7.4e-144)
		tmp = y1 * (z * (i * -k));
	elseif (j <= 2.3e-43)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7.6e+183], t$95$1, If[LessEqual[j, -1.1e+62], N[(x * N[(N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.7e-264], t$95$2, If[LessEqual[j, 7.4e-144], N[(y1 * N[(z * N[(i * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.3e-43], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -7.60000000000000002e183 or 2.2999999999999999e-43 < j

   1. Initial program 31.6%

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

   3. Taylor expanded in y1 around inf 34.7%

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

      1. associate-*r* 33.7%

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

      2. *-commutative 33.7%

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

   5. Simplified 33.7%

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

   6. Taylor expanded in j around inf 58.1%

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

   if -7.60000000000000002e183 < j < -1.10000000000000007e62

   1. Initial program 29.7%

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

   3. Taylor expanded in y1 around inf 29.9%

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

      1. associate-*r* 29.9%

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

      2. *-commutative 29.9%

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

   5. Simplified 29.9%

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

   6. Taylor expanded in x around inf 49.5%

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

   if -1.10000000000000007e62 < j < 5.7000000000000004e-264 or 7.4000000000000005e-144 < j < 2.2999999999999999e-43

   1. Initial program 43.8%

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

   3. Taylor expanded in y1 around inf 53.3%

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

      1. associate-*r* 53.3%

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

      2. *-commutative 53.3%

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

   5. Simplified 53.3%

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

   6. Taylor expanded in a around -inf 57.0%

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

      1. mul-1-neg 57.0%

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

   8. Simplified 57.0%

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

   if 5.7000000000000004e-264 < j < 7.4000000000000005e-144

   1. Initial program 41.7%

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

   3. Taylor expanded in y1 around -inf 36.4%

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

      1. associate-*r* 36.4%

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

      2. neg-mul-1 36.4%

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

      3. +-commutative 36.4%

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

      4. mul-1-neg 36.4%

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

      5. unsub-neg 36.4%

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

      6. *-commutative 36.4%

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

      7. *-commutative 36.4%

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

      8. *-commutative 36.4%

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

      9. *-commutative 36.4%

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

   5. Simplified 36.4%

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

   6. Taylor expanded in z around -inf 42.5%

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

   7. Taylor expanded in a around 0 42.7%

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

      1. mul-1-neg 42.7%

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

      2. distribute-lft-neg-out 42.7%

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

      3. *-commutative 42.7%

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

   9. Simplified 42.7%

      \[\leadsto y1 \cdot \left(z \cdot \color{blue}{\left(k \cdot \left(-i\right)\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.6 \cdot 10^{+183}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(i \cdot \left(x \cdot y1\right) - t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + i \cdot \left(j \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 5.7 \cdot 10^{-264}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 7.4 \cdot 10^{-144}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(i \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-43}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(i \cdot \left(x \cdot y1\right) - t \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 33.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{if}\;j \leq -2.8 \cdot 10^{+206}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -2 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + i \cdot \left(j \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-264}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 7.4 \cdot 10^{-144}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(i \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 4.6 \cdot 10^{+145}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right) + k \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (* a (+ (* y5 (- (* t y2) (* y y3))) (* y1 (- (* z y3) (* x y2)))))))
   (if (<= j -2.8e+206)
     (* t (* j (- (* b y4) (* i y5))))
     (if (<= j -2e+62)
       (* x (+ (* y2 (- (* c y0) (* a y1))) (* i (* j y1))))
       (if (<= j 5.8e-264)
         t_1
         (if (<= j 7.4e-144)
           (* y1 (* z (* i (- k))))
           (if (<= j 3.2e-60)
             t_1
             (if (<= j 4.6e+145)
               (*
                y
                (+ (* y3 (- (* c y4) (* a y5))) (* k (- (* i y5) (* b y4)))))
               (* i (* x (- (* j y1) (* y c))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))));
	double tmp;
	if (j <= -2.8e+206) {
		tmp = t * (j * ((b * y4) - (i * y5)));
	} else if (j <= -2e+62) {
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (i * (j * y1)));
	} else if (j <= 5.8e-264) {
		tmp = t_1;
	} else if (j <= 7.4e-144) {
		tmp = y1 * (z * (i * -k));
	} else if (j <= 3.2e-60) {
		tmp = t_1;
	} else if (j <= 4.6e+145) {
		tmp = y * ((y3 * ((c * y4) - (a * y5))) + (k * ((i * y5) - (b * y4))));
	} else {
		tmp = i * (x * ((j * y1) - (y * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))))
    if (j <= (-2.8d+206)) then
        tmp = t * (j * ((b * y4) - (i * y5)))
    else if (j <= (-2d+62)) then
        tmp = x * ((y2 * ((c * y0) - (a * y1))) + (i * (j * y1)))
    else if (j <= 5.8d-264) then
        tmp = t_1
    else if (j <= 7.4d-144) then
        tmp = y1 * (z * (i * -k))
    else if (j <= 3.2d-60) then
        tmp = t_1
    else if (j <= 4.6d+145) then
        tmp = y * ((y3 * ((c * y4) - (a * y5))) + (k * ((i * y5) - (b * y4))))
    else
        tmp = i * (x * ((j * y1) - (y * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))));
	double tmp;
	if (j <= -2.8e+206) {
		tmp = t * (j * ((b * y4) - (i * y5)));
	} else if (j <= -2e+62) {
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (i * (j * y1)));
	} else if (j <= 5.8e-264) {
		tmp = t_1;
	} else if (j <= 7.4e-144) {
		tmp = y1 * (z * (i * -k));
	} else if (j <= 3.2e-60) {
		tmp = t_1;
	} else if (j <= 4.6e+145) {
		tmp = y * ((y3 * ((c * y4) - (a * y5))) + (k * ((i * y5) - (b * y4))));
	} else {
		tmp = i * (x * ((j * y1) - (y * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))))
	tmp = 0
	if j <= -2.8e+206:
		tmp = t * (j * ((b * y4) - (i * y5)))
	elif j <= -2e+62:
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (i * (j * y1)))
	elif j <= 5.8e-264:
		tmp = t_1
	elif j <= 7.4e-144:
		tmp = y1 * (z * (i * -k))
	elif j <= 3.2e-60:
		tmp = t_1
	elif j <= 4.6e+145:
		tmp = y * ((y3 * ((c * y4) - (a * y5))) + (k * ((i * y5) - (b * y4))))
	else:
		tmp = i * (x * ((j * y1) - (y * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2)))))
	tmp = 0.0
	if (j <= -2.8e+206)
		tmp = Float64(t * Float64(j * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (j <= -2e+62)
		tmp = Float64(x * Float64(Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(i * Float64(j * y1))));
	elseif (j <= 5.8e-264)
		tmp = t_1;
	elseif (j <= 7.4e-144)
		tmp = Float64(y1 * Float64(z * Float64(i * Float64(-k))));
	elseif (j <= 3.2e-60)
		tmp = t_1;
	elseif (j <= 4.6e+145)
		tmp = Float64(y * Float64(Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(k * Float64(Float64(i * y5) - Float64(b * y4)))));
	else
		tmp = Float64(i * Float64(x * Float64(Float64(j * y1) - Float64(y * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))));
	tmp = 0.0;
	if (j <= -2.8e+206)
		tmp = t * (j * ((b * y4) - (i * y5)));
	elseif (j <= -2e+62)
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (i * (j * y1)));
	elseif (j <= 5.8e-264)
		tmp = t_1;
	elseif (j <= 7.4e-144)
		tmp = y1 * (z * (i * -k));
	elseif (j <= 3.2e-60)
		tmp = t_1;
	elseif (j <= 4.6e+145)
		tmp = y * ((y3 * ((c * y4) - (a * y5))) + (k * ((i * y5) - (b * y4))));
	else
		tmp = i * (x * ((j * y1) - (y * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.8e+206], N[(t * N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2e+62], N[(x * N[(N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.8e-264], t$95$1, If[LessEqual[j, 7.4e-144], N[(y1 * N[(z * N[(i * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.2e-60], t$95$1, If[LessEqual[j, 4.6e+145], N[(y * N[(N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(x * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -2.7999999999999998e206

   1. Initial program 16.7%

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

   3. Taylor expanded in t around inf 62.7%

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

   4. Taylor expanded in j around inf 71.3%

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

   if -2.7999999999999998e206 < j < -2.00000000000000007e62

   1. Initial program 26.8%

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

   3. Taylor expanded in y1 around inf 27.0%

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

      1. associate-*r* 27.0%

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

      2. *-commutative 27.0%

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

   5. Simplified 27.0%

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

   6. Taylor expanded in x around inf 49.6%

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

   if -2.00000000000000007e62 < j < 5.7999999999999997e-264 or 7.4000000000000005e-144 < j < 3.2000000000000001e-60

   1. Initial program 44.5%

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

   3. Taylor expanded in y1 around inf 54.4%

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

      1. associate-*r* 54.5%

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

      2. *-commutative 54.5%

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

   5. Simplified 54.5%

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

   6. Taylor expanded in a around -inf 58.4%

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

      1. mul-1-neg 58.4%

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

   8. Simplified 58.4%

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

   if 5.7999999999999997e-264 < j < 7.4000000000000005e-144

   1. Initial program 41.7%

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

   3. Taylor expanded in y1 around -inf 36.4%

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

      1. associate-*r* 36.4%

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

      2. neg-mul-1 36.4%

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

      3. +-commutative 36.4%

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

      4. mul-1-neg 36.4%

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

      5. unsub-neg 36.4%

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

      6. *-commutative 36.4%

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

      7. *-commutative 36.4%

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

      8. *-commutative 36.4%

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

      9. *-commutative 36.4%

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

   5. Simplified 36.4%

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

   6. Taylor expanded in z around -inf 42.5%

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

   7. Taylor expanded in a around 0 42.7%

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

      1. mul-1-neg 42.7%

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

      2. distribute-lft-neg-out 42.7%

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

      3. *-commutative 42.7%

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

   9. Simplified 42.7%

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

   if 3.2000000000000001e-60 < j < 4.6e145

   1. Initial program 36.5%

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

   3. Taylor expanded in y1 around inf 41.6%

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

      1. associate-*r* 39.2%

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

      2. *-commutative 39.2%

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

   5. Simplified 39.2%

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

   6. Taylor expanded in y around -inf 44.5%

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

   if 4.6e145 < j

   1. Initial program 38.8%

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

   3. Taylor expanded in i around -inf 39.3%

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

   4. Taylor expanded in x around inf 50.5%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 50.5%

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

   6. Simplified 50.5%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(y \cdot c - j \cdot y1\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.8 \cdot 10^{+206}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -2 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + i \cdot \left(j \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-264}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 7.4 \cdot 10^{-144}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(i \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{-60}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 4.6 \cdot 10^{+145}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right) + k \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 30.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+76}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot \left(j - \frac{y \cdot k}{t}\right)\right)\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-159}:\\ \;\;\;\;\left(k \cdot y4 - x \cdot a\right) \cdot \left(y1 \cdot y2\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-196}:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-213}:\\ \;\;\;\;\left(k \cdot y1\right) \cdot \left(y2 \cdot y4 - z \cdot i\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-166}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+22}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+176}:\\ \;\;\;\;\left(x \cdot b\right) \cdot \left(y \cdot a - j \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -5.5e+76)
   (* b (* y4 (* t (- j (/ (* y k) t)))))
   (if (<= y -3e-159)
     (* (- (* k y4) (* x a)) (* y1 y2))
     (if (<= y -2.9e-196)
       (* i (* t (- (* z c) (* j y5))))
       (if (<= y -1.3e-213)
         (* (* k y1) (- (* y2 y4) (* z i)))
         (if (<= y 5.8e-166)
           (* j (* y1 (- (* x i) (* y3 y4))))
           (if (<= y 1.8e+22)
             (* a (* y1 (- (* z y3) (* x y2))))
             (if (<= y 1.45e+176)
               (* (* x b) (- (* y a) (* j y0)))
               (* k (* y (- (* i y5) (* b y4))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -5.5e+76) {
		tmp = b * (y4 * (t * (j - ((y * k) / t))));
	} else if (y <= -3e-159) {
		tmp = ((k * y4) - (x * a)) * (y1 * y2);
	} else if (y <= -2.9e-196) {
		tmp = i * (t * ((z * c) - (j * y5)));
	} else if (y <= -1.3e-213) {
		tmp = (k * y1) * ((y2 * y4) - (z * i));
	} else if (y <= 5.8e-166) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (y <= 1.8e+22) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y <= 1.45e+176) {
		tmp = (x * b) * ((y * a) - (j * y0));
	} else {
		tmp = k * (y * ((i * y5) - (b * y4)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y <= (-5.5d+76)) then
        tmp = b * (y4 * (t * (j - ((y * k) / t))))
    else if (y <= (-3d-159)) then
        tmp = ((k * y4) - (x * a)) * (y1 * y2)
    else if (y <= (-2.9d-196)) then
        tmp = i * (t * ((z * c) - (j * y5)))
    else if (y <= (-1.3d-213)) then
        tmp = (k * y1) * ((y2 * y4) - (z * i))
    else if (y <= 5.8d-166) then
        tmp = j * (y1 * ((x * i) - (y3 * y4)))
    else if (y <= 1.8d+22) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (y <= 1.45d+176) then
        tmp = (x * b) * ((y * a) - (j * y0))
    else
        tmp = k * (y * ((i * y5) - (b * y4)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -5.5e+76) {
		tmp = b * (y4 * (t * (j - ((y * k) / t))));
	} else if (y <= -3e-159) {
		tmp = ((k * y4) - (x * a)) * (y1 * y2);
	} else if (y <= -2.9e-196) {
		tmp = i * (t * ((z * c) - (j * y5)));
	} else if (y <= -1.3e-213) {
		tmp = (k * y1) * ((y2 * y4) - (z * i));
	} else if (y <= 5.8e-166) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (y <= 1.8e+22) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y <= 1.45e+176) {
		tmp = (x * b) * ((y * a) - (j * y0));
	} else {
		tmp = k * (y * ((i * y5) - (b * y4)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y <= -5.5e+76:
		tmp = b * (y4 * (t * (j - ((y * k) / t))))
	elif y <= -3e-159:
		tmp = ((k * y4) - (x * a)) * (y1 * y2)
	elif y <= -2.9e-196:
		tmp = i * (t * ((z * c) - (j * y5)))
	elif y <= -1.3e-213:
		tmp = (k * y1) * ((y2 * y4) - (z * i))
	elif y <= 5.8e-166:
		tmp = j * (y1 * ((x * i) - (y3 * y4)))
	elif y <= 1.8e+22:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif y <= 1.45e+176:
		tmp = (x * b) * ((y * a) - (j * y0))
	else:
		tmp = k * (y * ((i * y5) - (b * y4)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y <= -5.5e+76)
		tmp = Float64(b * Float64(y4 * Float64(t * Float64(j - Float64(Float64(y * k) / t)))));
	elseif (y <= -3e-159)
		tmp = Float64(Float64(Float64(k * y4) - Float64(x * a)) * Float64(y1 * y2));
	elseif (y <= -2.9e-196)
		tmp = Float64(i * Float64(t * Float64(Float64(z * c) - Float64(j * y5))));
	elseif (y <= -1.3e-213)
		tmp = Float64(Float64(k * y1) * Float64(Float64(y2 * y4) - Float64(z * i)));
	elseif (y <= 5.8e-166)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (y <= 1.8e+22)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (y <= 1.45e+176)
		tmp = Float64(Float64(x * b) * Float64(Float64(y * a) - Float64(j * y0)));
	else
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y <= -5.5e+76)
		tmp = b * (y4 * (t * (j - ((y * k) / t))));
	elseif (y <= -3e-159)
		tmp = ((k * y4) - (x * a)) * (y1 * y2);
	elseif (y <= -2.9e-196)
		tmp = i * (t * ((z * c) - (j * y5)));
	elseif (y <= -1.3e-213)
		tmp = (k * y1) * ((y2 * y4) - (z * i));
	elseif (y <= 5.8e-166)
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	elseif (y <= 1.8e+22)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (y <= 1.45e+176)
		tmp = (x * b) * ((y * a) - (j * y0));
	else
		tmp = k * (y * ((i * y5) - (b * y4)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y, -5.5e+76], N[(b * N[(y4 * N[(t * N[(j - N[(N[(y * k), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3e-159], N[(N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * N[(y1 * y2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.9e-196], N[(i * N[(t * N[(N[(z * c), $MachinePrecision] - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.3e-213], N[(N[(k * y1), $MachinePrecision] * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e-166], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+22], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e+176], N[(N[(x * b), $MachinePrecision] * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y < -5.5000000000000001e76

   1. Initial program 19.5%

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

   3. Taylor expanded in b around inf 27.4%

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

   4. Taylor expanded in y4 around inf 40.0%

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

   5. Taylor expanded in t around inf 51.7%

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

      1. associate-*r/ 51.7%

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

      2. neg-mul-1 51.7%

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

      3. distribute-rgt-neg-in 51.7%

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

   7. Simplified 51.7%

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

   if -5.5000000000000001e76 < y < -3.00000000000000009e-159

   1. Initial program 46.6%

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

   3. Taylor expanded in y1 around -inf 45.4%

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

      1. associate-*r* 45.4%

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

      2. neg-mul-1 45.4%

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

      3. +-commutative 45.4%

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

      4. mul-1-neg 45.4%

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

      5. unsub-neg 45.4%

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

      6. *-commutative 45.4%

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

      7. *-commutative 45.4%

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

      8. *-commutative 45.4%

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

      9. *-commutative 45.4%

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

   5. Simplified 45.4%

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

   6. Taylor expanded in y2 around -inf 40.4%

      \[\leadsto \color{blue}{y1 \cdot \left(y2 \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(k \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 43.8%

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

      2. distribute-lft-out-- 43.8%

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

   8. Simplified 43.8%

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

   if -3.00000000000000009e-159 < y < -2.89999999999999987e-196

   1. Initial program 66.7%

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

   3. Taylor expanded in t around inf 45.3%

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

   4. Taylor expanded in i around inf 57.0%

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

      1. +-commutative 57.0%

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

      2. mul-1-neg 57.0%

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

      3. sub-neg 57.0%

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

   6. Simplified 57.0%

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

   if -2.89999999999999987e-196 < y < -1.3000000000000001e-213

   1. Initial program 33.3%

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

   3. Taylor expanded in k around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-*r* 100.0%

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

      6. neg-mul-1 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y1 around inf 100.0%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4 - i \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 100.0%

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

   8. Simplified 100.0%

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

   if -1.3000000000000001e-213 < y < 5.8e-166

   1. Initial program 39.9%

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

   3. Taylor expanded in y1 around -inf 42.3%

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

      1. associate-*r* 42.3%

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

      2. neg-mul-1 42.3%

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

      3. +-commutative 42.3%

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

      4. mul-1-neg 42.3%

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

      5. unsub-neg 42.3%

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

      6. *-commutative 42.3%

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

      7. *-commutative 42.3%

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

      8. *-commutative 42.3%

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

      9. *-commutative 42.3%

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

   5. Simplified 42.3%

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

   6. Taylor expanded in j around inf 44.5%

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

      1. +-commutative 44.5%

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

      2. mul-1-neg 44.5%

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

      3. unsub-neg 44.5%

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

   8. Simplified 44.5%

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

   if 5.8e-166 < y < 1.8e22

   1. Initial program 44.0%

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

   3. Taylor expanded in y1 around -inf 43.6%

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

      1. associate-*r* 43.6%

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

      2. neg-mul-1 43.6%

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

      3. +-commutative 43.6%

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

      4. mul-1-neg 43.6%

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

      5. unsub-neg 43.6%

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

      6. *-commutative 43.6%

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

      7. *-commutative 43.6%

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

      8. *-commutative 43.6%

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

      9. *-commutative 43.6%

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

   5. Simplified 43.6%

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

   6. Taylor expanded in a around inf 42.9%

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

      1. associate-*r* 42.9%

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

      2. neg-mul-1 42.9%

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

   8. Simplified 42.9%

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

   if 1.8e22 < y < 1.4500000000000001e176

   1. Initial program 35.1%

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

   3. Taylor expanded in b around inf 54.3%

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

   4. Taylor expanded in x around inf 52.4%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 52.1%

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

   6. Simplified 52.1%

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

   if 1.4500000000000001e176 < y

   1. Initial program 19.9%

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

   3. Taylor expanded in k around inf 60.6%

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

      1. +-commutative 60.6%

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

      2. mul-1-neg 60.6%

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

      3. unsub-neg 60.6%

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

      4. *-commutative 60.6%

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

      5. associate-*r* 60.6%

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

      6. neg-mul-1 60.6%

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

   5. Simplified 60.6%

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

   6. Taylor expanded in y around inf 61.0%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+76}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot \left(j - \frac{y \cdot k}{t}\right)\right)\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-159}:\\ \;\;\;\;\left(k \cdot y4 - x \cdot a\right) \cdot \left(y1 \cdot y2\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-196}:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-213}:\\ \;\;\;\;\left(k \cdot y1\right) \cdot \left(y2 \cdot y4 - z \cdot i\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-166}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+22}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+176}:\\ \;\;\;\;\left(x \cdot b\right) \cdot \left(y \cdot a - j \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 31.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{+220}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.05 \cdot 10^{-71}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -6.9 \cdot 10^{-230}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-285}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-249}:\\ \;\;\;\;\left(t \cdot c\right) \cdot \left(z \cdot i - y2 \cdot y4\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-141}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-55}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (* a (- (* y2 y5) (* z b))))))
   (if (<= a -3.4e+220)
     t_1
     (if (<= a -3.05e-71)
       (* a (* y1 (- (* z y3) (* x y2))))
       (if (<= a -6.9e-230)
         (* y0 (* y3 (- (* j y5) (* z c))))
         (if (<= a 6.6e-285)
           (* j (* y1 (- (* x i) (* y3 y4))))
           (if (<= a 4.3e-249)
             (* (* t c) (- (* z i) (* y2 y4)))
             (if (<= a 6e-141)
               (* y0 (* y2 (- (* x c) (* k y5))))
               (if (<= a 2.4e-55)
                 (* k (* y (- (* i y5) (* b 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 = t * (a * ((y2 * y5) - (z * b)));
	double tmp;
	if (a <= -3.4e+220) {
		tmp = t_1;
	} else if (a <= -3.05e-71) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (a <= -6.9e-230) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (a <= 6.6e-285) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (a <= 4.3e-249) {
		tmp = (t * c) * ((z * i) - (y2 * y4));
	} else if (a <= 6e-141) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (a <= 2.4e-55) {
		tmp = k * (y * ((i * y5) - (b * 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 = t * (a * ((y2 * y5) - (z * b)))
    if (a <= (-3.4d+220)) then
        tmp = t_1
    else if (a <= (-3.05d-71)) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (a <= (-6.9d-230)) then
        tmp = y0 * (y3 * ((j * y5) - (z * c)))
    else if (a <= 6.6d-285) then
        tmp = j * (y1 * ((x * i) - (y3 * y4)))
    else if (a <= 4.3d-249) then
        tmp = (t * c) * ((z * i) - (y2 * y4))
    else if (a <= 6d-141) then
        tmp = y0 * (y2 * ((x * c) - (k * y5)))
    else if (a <= 2.4d-55) then
        tmp = k * (y * ((i * y5) - (b * 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 = t * (a * ((y2 * y5) - (z * b)));
	double tmp;
	if (a <= -3.4e+220) {
		tmp = t_1;
	} else if (a <= -3.05e-71) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (a <= -6.9e-230) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (a <= 6.6e-285) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (a <= 4.3e-249) {
		tmp = (t * c) * ((z * i) - (y2 * y4));
	} else if (a <= 6e-141) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (a <= 2.4e-55) {
		tmp = k * (y * ((i * y5) - (b * 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 = t * (a * ((y2 * y5) - (z * b)))
	tmp = 0
	if a <= -3.4e+220:
		tmp = t_1
	elif a <= -3.05e-71:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif a <= -6.9e-230:
		tmp = y0 * (y3 * ((j * y5) - (z * c)))
	elif a <= 6.6e-285:
		tmp = j * (y1 * ((x * i) - (y3 * y4)))
	elif a <= 4.3e-249:
		tmp = (t * c) * ((z * i) - (y2 * y4))
	elif a <= 6e-141:
		tmp = y0 * (y2 * ((x * c) - (k * y5)))
	elif a <= 2.4e-55:
		tmp = k * (y * ((i * y5) - (b * 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(t * Float64(a * Float64(Float64(y2 * y5) - Float64(z * b))))
	tmp = 0.0
	if (a <= -3.4e+220)
		tmp = t_1;
	elseif (a <= -3.05e-71)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (a <= -6.9e-230)
		tmp = Float64(y0 * Float64(y3 * Float64(Float64(j * y5) - Float64(z * c))));
	elseif (a <= 6.6e-285)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (a <= 4.3e-249)
		tmp = Float64(Float64(t * c) * Float64(Float64(z * i) - Float64(y2 * y4)));
	elseif (a <= 6e-141)
		tmp = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))));
	elseif (a <= 2.4e-55)
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * 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 = t * (a * ((y2 * y5) - (z * b)));
	tmp = 0.0;
	if (a <= -3.4e+220)
		tmp = t_1;
	elseif (a <= -3.05e-71)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (a <= -6.9e-230)
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	elseif (a <= 6.6e-285)
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	elseif (a <= 4.3e-249)
		tmp = (t * c) * ((z * i) - (y2 * y4));
	elseif (a <= 6e-141)
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	elseif (a <= 2.4e-55)
		tmp = k * (y * ((i * y5) - (b * 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[(t * N[(a * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.4e+220], t$95$1, If[LessEqual[a, -3.05e-71], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.9e-230], N[(y0 * N[(y3 * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.6e-285], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.3e-249], N[(N[(t * c), $MachinePrecision] * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e-141], N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e-55], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -3.4e220 or 2.39999999999999991e-55 < a

   1. Initial program 25.0%

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

   3. Taylor expanded in t around inf 40.2%

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

   4. Taylor expanded in a around inf 48.8%

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

      1. cancel-sign-sub-inv 48.8%

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

      2. metadata-eval 48.8%

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

      3. *-lft-identity 48.8%

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

      4. +-commutative 48.8%

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

      5. mul-1-neg 48.8%

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

      6. sub-neg 48.8%

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

   6. Simplified 48.8%

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

   if -3.4e220 < a < -3.0499999999999999e-71

   1. Initial program 45.7%

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

   3. Taylor expanded in y1 around -inf 52.6%

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

      1. associate-*r* 52.6%

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

      2. neg-mul-1 52.6%

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

      3. +-commutative 52.6%

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

      4. mul-1-neg 52.6%

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

      5. unsub-neg 52.6%

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

      6. *-commutative 52.6%

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

      7. *-commutative 52.6%

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

      8. *-commutative 52.6%

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

      9. *-commutative 52.6%

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

   5. Simplified 52.6%

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

   6. Taylor expanded in a around inf 43.4%

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

      1. associate-*r* 43.4%

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

      2. neg-mul-1 43.4%

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

   8. Simplified 43.4%

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

   if -3.0499999999999999e-71 < a < -6.9000000000000002e-230

   1. Initial program 45.2%

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

   3. Taylor expanded in y0 around inf 55.9%

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

      1. +-commutative 55.9%

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

      2. mul-1-neg 55.9%

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

      3. unsub-neg 55.9%

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

      4. *-commutative 55.9%

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

      5. *-commutative 55.9%

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

      6. *-commutative 55.9%

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

      7. *-commutative 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in y3 around inf 41.8%

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

      1. cancel-sign-sub-inv 41.8%

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

      2. metadata-eval 41.8%

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

      3. *-lft-identity 41.8%

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

      4. +-commutative 41.8%

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

      5. mul-1-neg 41.8%

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

      6. unsub-neg 41.8%

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

   8. Simplified 41.8%

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

   if -6.9000000000000002e-230 < a < 6.5999999999999997e-285

   1. Initial program 37.0%

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

   3. Taylor expanded in y1 around -inf 48.0%

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

      1. associate-*r* 48.0%

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

      2. neg-mul-1 48.0%

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

      3. +-commutative 48.0%

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

      4. mul-1-neg 48.0%

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

      5. unsub-neg 48.0%

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

      6. *-commutative 48.0%

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

      7. *-commutative 48.0%

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

      8. *-commutative 48.0%

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

      9. *-commutative 48.0%

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

   5. Simplified 48.0%

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

   6. Taylor expanded in j around inf 48.8%

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

      1. +-commutative 48.8%

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

      2. mul-1-neg 48.8%

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

      3. unsub-neg 48.8%

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

   8. Simplified 48.8%

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

   if 6.5999999999999997e-285 < a < 4.3000000000000002e-249

   1. Initial program 56.9%

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

   3. Taylor expanded in t around inf 37.2%

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

   4. Taylor expanded in c around inf 66.0%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 66.0%

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

   6. Simplified 66.0%

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

   if 4.3000000000000002e-249 < a < 5.99999999999999967e-141

   1. Initial program 57.7%

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

   3. Taylor expanded in y0 around inf 50.8%

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

      1. +-commutative 50.8%

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

      2. mul-1-neg 50.8%

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

      3. unsub-neg 50.8%

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

      4. *-commutative 50.8%

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

      5. *-commutative 50.8%

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

      6. *-commutative 50.8%

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

      7. *-commutative 50.8%

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

   5. Simplified 50.8%

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

   6. Taylor expanded in y2 around inf 40.3%

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

   if 5.99999999999999967e-141 < a < 2.39999999999999991e-55

   1. Initial program 22.7%

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

   3. Taylor expanded in k around inf 50.2%

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

      1. +-commutative 50.2%

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

      2. mul-1-neg 50.2%

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

      3. unsub-neg 50.2%

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

      4. *-commutative 50.2%

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

      5. associate-*r* 50.2%

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

      6. neg-mul-1 50.2%

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

   5. Simplified 50.2%

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

   6. Taylor expanded in y around inf 54.9%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+220}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -3.05 \cdot 10^{-71}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -6.9 \cdot 10^{-230}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-285}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-249}:\\ \;\;\;\;\left(t \cdot c\right) \cdot \left(z \cdot i - y2 \cdot y4\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-141}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-55}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 32.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ t_2 := t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{if}\;a \leq -1.6 \cdot 10^{+148}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-229}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-234}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-145}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-142}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 10^{-56}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y1 (- (* x i) (* y3 y4)))))
        (t_2 (* t (* a (- (* y2 y5) (* z b))))))
   (if (<= a -1.6e+148)
     t_2
     (if (<= a -3.2e-41)
       t_1
       (if (<= a -1.25e-229)
         (* y0 (* y3 (- (* j y5) (* z c))))
         (if (<= a 7.6e-234)
           t_1
           (if (<= a 5.2e-145)
             (* y0 (* y2 (- (* x c) (* k y5))))
             (if (<= a 3e-142)
               (* k (* y1 (* y2 y4)))
               (if (<= a 1e-56) (* k (* y (- (* i y5) (* b y4)))) 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 = j * (y1 * ((x * i) - (y3 * y4)));
	double t_2 = t * (a * ((y2 * y5) - (z * b)));
	double tmp;
	if (a <= -1.6e+148) {
		tmp = t_2;
	} else if (a <= -3.2e-41) {
		tmp = t_1;
	} else if (a <= -1.25e-229) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (a <= 7.6e-234) {
		tmp = t_1;
	} else if (a <= 5.2e-145) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (a <= 3e-142) {
		tmp = k * (y1 * (y2 * y4));
	} else if (a <= 1e-56) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} 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 = j * (y1 * ((x * i) - (y3 * y4)))
    t_2 = t * (a * ((y2 * y5) - (z * b)))
    if (a <= (-1.6d+148)) then
        tmp = t_2
    else if (a <= (-3.2d-41)) then
        tmp = t_1
    else if (a <= (-1.25d-229)) then
        tmp = y0 * (y3 * ((j * y5) - (z * c)))
    else if (a <= 7.6d-234) then
        tmp = t_1
    else if (a <= 5.2d-145) then
        tmp = y0 * (y2 * ((x * c) - (k * y5)))
    else if (a <= 3d-142) then
        tmp = k * (y1 * (y2 * y4))
    else if (a <= 1d-56) then
        tmp = k * (y * ((i * y5) - (b * y4)))
    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 = j * (y1 * ((x * i) - (y3 * y4)));
	double t_2 = t * (a * ((y2 * y5) - (z * b)));
	double tmp;
	if (a <= -1.6e+148) {
		tmp = t_2;
	} else if (a <= -3.2e-41) {
		tmp = t_1;
	} else if (a <= -1.25e-229) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (a <= 7.6e-234) {
		tmp = t_1;
	} else if (a <= 5.2e-145) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (a <= 3e-142) {
		tmp = k * (y1 * (y2 * y4));
	} else if (a <= 1e-56) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} 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 = j * (y1 * ((x * i) - (y3 * y4)))
	t_2 = t * (a * ((y2 * y5) - (z * b)))
	tmp = 0
	if a <= -1.6e+148:
		tmp = t_2
	elif a <= -3.2e-41:
		tmp = t_1
	elif a <= -1.25e-229:
		tmp = y0 * (y3 * ((j * y5) - (z * c)))
	elif a <= 7.6e-234:
		tmp = t_1
	elif a <= 5.2e-145:
		tmp = y0 * (y2 * ((x * c) - (k * y5)))
	elif a <= 3e-142:
		tmp = k * (y1 * (y2 * y4))
	elif a <= 1e-56:
		tmp = k * (y * ((i * y5) - (b * y4)))
	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(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))))
	t_2 = Float64(t * Float64(a * Float64(Float64(y2 * y5) - Float64(z * b))))
	tmp = 0.0
	if (a <= -1.6e+148)
		tmp = t_2;
	elseif (a <= -3.2e-41)
		tmp = t_1;
	elseif (a <= -1.25e-229)
		tmp = Float64(y0 * Float64(y3 * Float64(Float64(j * y5) - Float64(z * c))));
	elseif (a <= 7.6e-234)
		tmp = t_1;
	elseif (a <= 5.2e-145)
		tmp = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))));
	elseif (a <= 3e-142)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (a <= 1e-56)
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))));
	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 = j * (y1 * ((x * i) - (y3 * y4)));
	t_2 = t * (a * ((y2 * y5) - (z * b)));
	tmp = 0.0;
	if (a <= -1.6e+148)
		tmp = t_2;
	elseif (a <= -3.2e-41)
		tmp = t_1;
	elseif (a <= -1.25e-229)
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	elseif (a <= 7.6e-234)
		tmp = t_1;
	elseif (a <= 5.2e-145)
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	elseif (a <= 3e-142)
		tmp = k * (y1 * (y2 * y4));
	elseif (a <= 1e-56)
		tmp = k * (y * ((i * y5) - (b * y4)));
	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[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(a * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.6e+148], t$95$2, If[LessEqual[a, -3.2e-41], t$95$1, If[LessEqual[a, -1.25e-229], N[(y0 * N[(y3 * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.6e-234], t$95$1, If[LessEqual[a, 5.2e-145], N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3e-142], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e-56], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.6e148 or 1e-56 < a

   1. Initial program 26.0%

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

   3. Taylor expanded in t around inf 40.9%

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

   4. Taylor expanded in a around inf 49.9%

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

      1. cancel-sign-sub-inv 49.9%

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

      2. metadata-eval 49.9%

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

      3. *-lft-identity 49.9%

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

      4. +-commutative 49.9%

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

      5. mul-1-neg 49.9%

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

      6. sub-neg 49.9%

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

   6. Simplified 49.9%

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

   if -1.6e148 < a < -3.20000000000000012e-41 or -1.25000000000000004e-229 < a < 7.59999999999999968e-234

   1. Initial program 45.9%

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

   3. Taylor expanded in y1 around -inf 49.0%

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

      1. associate-*r* 49.0%

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

      2. neg-mul-1 49.0%

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

      3. +-commutative 49.0%

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

      4. mul-1-neg 49.0%

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

      5. unsub-neg 49.0%

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

      6. *-commutative 49.0%

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

      7. *-commutative 49.0%

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

      8. *-commutative 49.0%

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

      9. *-commutative 49.0%

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

   5. Simplified 49.0%

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

   6. Taylor expanded in j around inf 41.2%

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

      1. +-commutative 41.2%

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

      2. mul-1-neg 41.2%

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

      3. unsub-neg 41.2%

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

   8. Simplified 41.2%

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

   if -3.20000000000000012e-41 < a < -1.25000000000000004e-229

   1. Initial program 46.0%

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

   3. Taylor expanded in y0 around inf 52.2%

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

      1. +-commutative 52.2%

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

      2. mul-1-neg 52.2%

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

      3. unsub-neg 52.2%

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

      4. *-commutative 52.2%

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

      5. *-commutative 52.2%

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

      6. *-commutative 52.2%

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

      7. *-commutative 52.2%

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

   5. Simplified 52.2%

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

   6. Taylor expanded in y3 around inf 40.4%

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

      1. cancel-sign-sub-inv 40.4%

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

      2. metadata-eval 40.4%

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

      3. *-lft-identity 40.4%

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

      4. +-commutative 40.4%

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

      5. mul-1-neg 40.4%

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

      6. unsub-neg 40.4%

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

   8. Simplified 40.4%

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

   if 7.59999999999999968e-234 < a < 5.1999999999999999e-145

   1. Initial program 54.5%

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

   3. Taylor expanded in y0 around inf 50.9%

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

      1. +-commutative 50.9%

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

      2. mul-1-neg 50.9%

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

      3. unsub-neg 50.9%

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

      4. *-commutative 50.9%

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

      5. *-commutative 50.9%

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

      6. *-commutative 50.9%

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

      7. *-commutative 50.9%

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

   5. Simplified 50.9%

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

   6. Taylor expanded in y2 around inf 43.0%

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

   if 5.1999999999999999e-145 < a < 3.0000000000000001e-142

   1. Initial program 100.0%

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

   3. Taylor expanded in y1 around -inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

      3. +-commutative 100.0%

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

      4. mul-1-neg 100.0%

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

      5. unsub-neg 100.0%

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

      6. *-commutative 100.0%

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

      7. *-commutative 100.0%

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

      8. *-commutative 100.0%

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

      9. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y4 around -inf 100.0%

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

      1. associate-*r* 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in k around inf 100.0%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 100.0%

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

   11. Simplified 100.0%

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

   if 3.0000000000000001e-142 < a < 1e-56

   1. Initial program 22.7%

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

   3. Taylor expanded in k around inf 50.2%

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

      1. +-commutative 50.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 50.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 50.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 50.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 50.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 50.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 50.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y around inf 54.9%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+148}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-41}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-229}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-234}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-145}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-142}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 10^{-56}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 31.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ t_2 := t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{+153}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-234}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-233}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-145}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-145}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-54}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y1 (- (* x i) (* y3 y4)))))
        (t_2 (* t (* a (- (* y2 y5) (* z b))))))
   (if (<= a -2.8e+153)
     t_2
     (if (<= a -6.8e-18)
       t_1
       (if (<= a -1.15e-234)
         (* t (* j (- (* b y4) (* i y5))))
         (if (<= a 3.6e-233)
           t_1
           (if (<= a 5.8e-145)
             (* y0 (* y2 (- (* x c) (* k y5))))
             (if (<= a 8.6e-145)
               (* k (* y1 (* y2 y4)))
               (if (<= a 1.55e-54)
                 (* k (* y (- (* i y5) (* b y4))))
                 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 = j * (y1 * ((x * i) - (y3 * y4)));
	double t_2 = t * (a * ((y2 * y5) - (z * b)));
	double tmp;
	if (a <= -2.8e+153) {
		tmp = t_2;
	} else if (a <= -6.8e-18) {
		tmp = t_1;
	} else if (a <= -1.15e-234) {
		tmp = t * (j * ((b * y4) - (i * y5)));
	} else if (a <= 3.6e-233) {
		tmp = t_1;
	} else if (a <= 5.8e-145) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (a <= 8.6e-145) {
		tmp = k * (y1 * (y2 * y4));
	} else if (a <= 1.55e-54) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} 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 = j * (y1 * ((x * i) - (y3 * y4)))
    t_2 = t * (a * ((y2 * y5) - (z * b)))
    if (a <= (-2.8d+153)) then
        tmp = t_2
    else if (a <= (-6.8d-18)) then
        tmp = t_1
    else if (a <= (-1.15d-234)) then
        tmp = t * (j * ((b * y4) - (i * y5)))
    else if (a <= 3.6d-233) then
        tmp = t_1
    else if (a <= 5.8d-145) then
        tmp = y0 * (y2 * ((x * c) - (k * y5)))
    else if (a <= 8.6d-145) then
        tmp = k * (y1 * (y2 * y4))
    else if (a <= 1.55d-54) then
        tmp = k * (y * ((i * y5) - (b * y4)))
    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 = j * (y1 * ((x * i) - (y3 * y4)));
	double t_2 = t * (a * ((y2 * y5) - (z * b)));
	double tmp;
	if (a <= -2.8e+153) {
		tmp = t_2;
	} else if (a <= -6.8e-18) {
		tmp = t_1;
	} else if (a <= -1.15e-234) {
		tmp = t * (j * ((b * y4) - (i * y5)));
	} else if (a <= 3.6e-233) {
		tmp = t_1;
	} else if (a <= 5.8e-145) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (a <= 8.6e-145) {
		tmp = k * (y1 * (y2 * y4));
	} else if (a <= 1.55e-54) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} 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 = j * (y1 * ((x * i) - (y3 * y4)))
	t_2 = t * (a * ((y2 * y5) - (z * b)))
	tmp = 0
	if a <= -2.8e+153:
		tmp = t_2
	elif a <= -6.8e-18:
		tmp = t_1
	elif a <= -1.15e-234:
		tmp = t * (j * ((b * y4) - (i * y5)))
	elif a <= 3.6e-233:
		tmp = t_1
	elif a <= 5.8e-145:
		tmp = y0 * (y2 * ((x * c) - (k * y5)))
	elif a <= 8.6e-145:
		tmp = k * (y1 * (y2 * y4))
	elif a <= 1.55e-54:
		tmp = k * (y * ((i * y5) - (b * y4)))
	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(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))))
	t_2 = Float64(t * Float64(a * Float64(Float64(y2 * y5) - Float64(z * b))))
	tmp = 0.0
	if (a <= -2.8e+153)
		tmp = t_2;
	elseif (a <= -6.8e-18)
		tmp = t_1;
	elseif (a <= -1.15e-234)
		tmp = Float64(t * Float64(j * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (a <= 3.6e-233)
		tmp = t_1;
	elseif (a <= 5.8e-145)
		tmp = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))));
	elseif (a <= 8.6e-145)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (a <= 1.55e-54)
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))));
	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 = j * (y1 * ((x * i) - (y3 * y4)));
	t_2 = t * (a * ((y2 * y5) - (z * b)));
	tmp = 0.0;
	if (a <= -2.8e+153)
		tmp = t_2;
	elseif (a <= -6.8e-18)
		tmp = t_1;
	elseif (a <= -1.15e-234)
		tmp = t * (j * ((b * y4) - (i * y5)));
	elseif (a <= 3.6e-233)
		tmp = t_1;
	elseif (a <= 5.8e-145)
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	elseif (a <= 8.6e-145)
		tmp = k * (y1 * (y2 * y4));
	elseif (a <= 1.55e-54)
		tmp = k * (y * ((i * y5) - (b * y4)));
	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[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(a * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.8e+153], t$95$2, If[LessEqual[a, -6.8e-18], t$95$1, If[LessEqual[a, -1.15e-234], N[(t * N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.6e-233], t$95$1, If[LessEqual[a, 5.8e-145], N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.6e-145], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e-54], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -2.79999999999999985e153 or 1.55000000000000002e-54 < a

   1. Initial program 26.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 40.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 49.9%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(b \cdot z\right) - -1 \cdot \left(y2 \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. cancel-sign-sub-inv 49.9%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right) + \left(--1\right) \cdot \left(y2 \cdot y5\right)\right)}\right) \]

      2. metadata-eval 49.9%

         \[\leadsto t \cdot \left(a \cdot \left(-1 \cdot \left(b \cdot z\right) + \color{blue}{1} \cdot \left(y2 \cdot y5\right)\right)\right) \]

      3. *-lft-identity 49.9%

         \[\leadsto t \cdot \left(a \cdot \left(-1 \cdot \left(b \cdot z\right) + \color{blue}{y2 \cdot y5}\right)\right) \]

      4. +-commutative 49.9%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      5. mul-1-neg 49.9%

         \[\leadsto t \cdot \left(a \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      6. sub-neg 49.9%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \]

   6. Simplified 49.9%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

   if -2.79999999999999985e153 < a < -6.80000000000000002e-18 or -1.14999999999999995e-234 < a < 3.60000000000000007e-233

   1. Initial program 49.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 48.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 48.2%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 48.2%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 48.2%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 48.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 48.2%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 48.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 48.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 48.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 48.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 48.2%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in j around inf 42.5%

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 42.5%

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 42.5%

         \[\leadsto j \cdot \left(y1 \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 42.5%

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

   8. Simplified 42.5%

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(i \cdot x - y3 \cdot y4\right)\right)} \]

   if -6.80000000000000002e-18 < a < -1.14999999999999995e-234

   1. Initial program 39.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 29.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 37.9%

      \[\leadsto t \cdot \color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   if 3.60000000000000007e-233 < a < 5.79999999999999968e-145

   1. Initial program 54.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 50.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.9%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 50.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 50.9%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 50.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 50.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 50.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 50.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 50.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y2 around inf 43.0%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(c \cdot x - k \cdot y5\right)\right)} \]

   if 5.79999999999999968e-145 < a < 8.5999999999999998e-145

   1. Initial program 100.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 100.0%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 100.0%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 100.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 100.0%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 100.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 100.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 100.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 100.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around -inf 100.0%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(y1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} \]

   8. Simplified 100.0%

      \[\leadsto \color{blue}{\left(y1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} \]

   9. Taylor expanded in k around inf 100.0%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 100.0%

          \[\leadsto k \cdot \left(y1 \cdot \color{blue}{\left(y4 \cdot y2\right)}\right) \]

   11. Simplified 100.0%

       \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y4 \cdot y2\right)\right)} \]

   if 8.5999999999999998e-145 < a < 1.55000000000000002e-54

   1. Initial program 22.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 50.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 50.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 50.2%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 50.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 50.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 50.2%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 50.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y around inf 54.9%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+153}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-18}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-234}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-233}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-145}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-145}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-54}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 33.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.12 \cdot 10^{+206}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -6.2 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + i \cdot \left(j \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 9.6 \cdot 10^{-265}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{-81}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;j \leq 1.08 \cdot 10^{-38}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -1.12e+206)
   (* t (* j (- (* b y4) (* i y5))))
   (if (<= j -6.2e+61)
     (* x (+ (* y2 (- (* c y0) (* a y1))) (* i (* j y1))))
     (if (<= j 9.6e-265)
       (* a (+ (* y5 (- (* t y2) (* y y3))) (* y1 (- (* z y3) (* x y2)))))
       (if (<= j 6.5e-81)
         (* y1 (* z (- (* a y3) (* i k))))
         (if (<= j 1.08e-38)
           (* c (+ (* y0 (- (* x y2) (* z y3))) (* y4 (- (* y y3) (* t y2)))))
           (* i (* x (- (* j y1) (* y c))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.12e+206) {
		tmp = t * (j * ((b * y4) - (i * y5)));
	} else if (j <= -6.2e+61) {
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (i * (j * y1)));
	} else if (j <= 9.6e-265) {
		tmp = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))));
	} else if (j <= 6.5e-81) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (j <= 1.08e-38) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	} else {
		tmp = i * (x * ((j * y1) - (y * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (j <= (-1.12d+206)) then
        tmp = t * (j * ((b * y4) - (i * y5)))
    else if (j <= (-6.2d+61)) then
        tmp = x * ((y2 * ((c * y0) - (a * y1))) + (i * (j * y1)))
    else if (j <= 9.6d-265) then
        tmp = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))))
    else if (j <= 6.5d-81) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (j <= 1.08d-38) then
        tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))))
    else
        tmp = i * (x * ((j * y1) - (y * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.12e+206) {
		tmp = t * (j * ((b * y4) - (i * y5)));
	} else if (j <= -6.2e+61) {
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (i * (j * y1)));
	} else if (j <= 9.6e-265) {
		tmp = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))));
	} else if (j <= 6.5e-81) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (j <= 1.08e-38) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	} else {
		tmp = i * (x * ((j * y1) - (y * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if j <= -1.12e+206:
		tmp = t * (j * ((b * y4) - (i * y5)))
	elif j <= -6.2e+61:
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (i * (j * y1)))
	elif j <= 9.6e-265:
		tmp = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))))
	elif j <= 6.5e-81:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif j <= 1.08e-38:
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))))
	else:
		tmp = i * (x * ((j * y1) - (y * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -1.12e+206)
		tmp = Float64(t * Float64(j * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (j <= -6.2e+61)
		tmp = Float64(x * Float64(Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(i * Float64(j * y1))));
	elseif (j <= 9.6e-265)
		tmp = Float64(a * Float64(Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2)))));
	elseif (j <= 6.5e-81)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (j <= 1.08e-38)
		tmp = Float64(c * Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	else
		tmp = Float64(i * Float64(x * Float64(Float64(j * y1) - Float64(y * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (j <= -1.12e+206)
		tmp = t * (j * ((b * y4) - (i * y5)));
	elseif (j <= -6.2e+61)
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (i * (j * y1)));
	elseif (j <= 9.6e-265)
		tmp = a * ((y5 * ((t * y2) - (y * y3))) + (y1 * ((z * y3) - (x * y2))));
	elseif (j <= 6.5e-81)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (j <= 1.08e-38)
		tmp = c * ((y0 * ((x * y2) - (z * y3))) + (y4 * ((y * y3) - (t * y2))));
	else
		tmp = i * (x * ((j * y1) - (y * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -1.12e+206], N[(t * N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6.2e+61], N[(x * N[(N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9.6e-265], N[(a * N[(N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.5e-81], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.08e-38], N[(c * N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(x * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -1.11999999999999997e206

   1. Initial program 16.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 62.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 71.3%

      \[\leadsto t \cdot \color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   if -1.11999999999999997e206 < j < -6.1999999999999998e61

   1. Initial program 26.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 27.0%

      \[\leadsto \left(\left(\left(\color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. associate-*r* 27.0%

         \[\leadsto \left(\left(\left(\color{blue}{\left(i \cdot y1\right) \cdot \left(j \cdot x - k \cdot z\right)} + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. *-commutative 27.0%

         \[\leadsto \left(\left(\left(\left(i \cdot y1\right) \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 27.0%

      \[\leadsto \left(\left(\left(\color{blue}{\left(i \cdot y1\right) \cdot \left(j \cdot x - z \cdot k\right)} + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in x around inf 49.6%

      \[\leadsto \color{blue}{x \cdot \left(i \cdot \left(j \cdot y1\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   if -6.1999999999999998e61 < j < 9.5999999999999999e-265

   1. Initial program 46.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 55.2%

      \[\leadsto \left(\left(\left(\color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. associate-*r* 55.2%

         \[\leadsto \left(\left(\left(\color{blue}{\left(i \cdot y1\right) \cdot \left(j \cdot x - k \cdot z\right)} + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. *-commutative 55.2%

         \[\leadsto \left(\left(\left(\left(i \cdot y1\right) \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 55.2%

      \[\leadsto \left(\left(\left(\color{blue}{\left(i \cdot y1\right) \cdot \left(j \cdot x - z \cdot k\right)} + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in a around -inf 54.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 54.9%

         \[\leadsto \color{blue}{-a \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   8. Simplified 54.9%

      \[\leadsto \color{blue}{-a \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if 9.5999999999999999e-265 < j < 6.5000000000000002e-81

   1. Initial program 41.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 49.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 49.3%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 49.3%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 49.3%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 49.3%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 49.3%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 49.3%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 49.3%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 49.3%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 49.3%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 49.3%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in z around -inf 52.7%

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]

   if 6.5000000000000002e-81 < j < 1.08e-38

   1. Initial program 37.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 37.5%

      \[\leadsto \left(\left(\left(\color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. associate-*r* 37.5%

         \[\leadsto \left(\left(\left(\color{blue}{\left(i \cdot y1\right) \cdot \left(j \cdot x - k \cdot z\right)} + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. *-commutative 37.5%

         \[\leadsto \left(\left(\left(\left(i \cdot y1\right) \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 37.5%

      \[\leadsto \left(\left(\left(\color{blue}{\left(i \cdot y1\right) \cdot \left(j \cdot x - z \cdot k\right)} + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in c around inf 62.8%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if 1.08e-38 < j

   1. Initial program 36.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf 39.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   4. Taylor expanded in x around inf 41.9%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right)\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 41.9%

         \[\leadsto -1 \cdot \left(i \cdot \left(x \cdot \left(\color{blue}{y \cdot c} - j \cdot y1\right)\right)\right) \]

   6. Simplified 41.9%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(x \cdot \left(y \cdot c - j \cdot y1\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.12 \cdot 10^{+206}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -6.2 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + i \cdot \left(j \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq 9.6 \cdot 10^{-265}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{-81}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;j \leq 1.08 \cdot 10^{-38}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 23.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -9.2 \cdot 10^{+65}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -1.2 \cdot 10^{-262}:\\ \;\;\;\;\left(y1 \cdot y2\right) \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y4 \leq 3.8 \cdot 10^{-193}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 4.6 \cdot 10^{-97}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq 1.55 \cdot 10^{+61} \lor \neg \left(y4 \leq 5.5 \cdot 10^{+124}\right):\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -9.2e+65)
   (* j (* y1 (* y3 (- y4))))
   (if (<= y4 -1.2e-262)
     (* (* y1 y2) (* x (- a)))
     (if (<= y4 3.8e-193)
       (* y0 (* y2 (* k (- y5))))
       (if (<= y4 4.6e-97)
         (* y0 (* y2 (* x c)))
         (if (or (<= y4 1.55e+61) (not (<= y4 5.5e+124)))
           (* b (* y4 (- (* t j) (* y k))))
           (* y1 (* z (* 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 tmp;
	if (y4 <= -9.2e+65) {
		tmp = j * (y1 * (y3 * -y4));
	} else if (y4 <= -1.2e-262) {
		tmp = (y1 * y2) * (x * -a);
	} else if (y4 <= 3.8e-193) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (y4 <= 4.6e-97) {
		tmp = y0 * (y2 * (x * c));
	} else if ((y4 <= 1.55e+61) || !(y4 <= 5.5e+124)) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else {
		tmp = y1 * (z * (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) :: tmp
    if (y4 <= (-9.2d+65)) then
        tmp = j * (y1 * (y3 * -y4))
    else if (y4 <= (-1.2d-262)) then
        tmp = (y1 * y2) * (x * -a)
    else if (y4 <= 3.8d-193) then
        tmp = y0 * (y2 * (k * -y5))
    else if (y4 <= 4.6d-97) then
        tmp = y0 * (y2 * (x * c))
    else if ((y4 <= 1.55d+61) .or. (.not. (y4 <= 5.5d+124))) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else
        tmp = y1 * (z * (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 tmp;
	if (y4 <= -9.2e+65) {
		tmp = j * (y1 * (y3 * -y4));
	} else if (y4 <= -1.2e-262) {
		tmp = (y1 * y2) * (x * -a);
	} else if (y4 <= 3.8e-193) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (y4 <= 4.6e-97) {
		tmp = y0 * (y2 * (x * c));
	} else if ((y4 <= 1.55e+61) || !(y4 <= 5.5e+124)) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else {
		tmp = y1 * (z * (a * y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y4 <= -9.2e+65:
		tmp = j * (y1 * (y3 * -y4))
	elif y4 <= -1.2e-262:
		tmp = (y1 * y2) * (x * -a)
	elif y4 <= 3.8e-193:
		tmp = y0 * (y2 * (k * -y5))
	elif y4 <= 4.6e-97:
		tmp = y0 * (y2 * (x * c))
	elif (y4 <= 1.55e+61) or not (y4 <= 5.5e+124):
		tmp = b * (y4 * ((t * j) - (y * k)))
	else:
		tmp = y1 * (z * (a * y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -9.2e+65)
		tmp = Float64(j * Float64(y1 * Float64(y3 * Float64(-y4))));
	elseif (y4 <= -1.2e-262)
		tmp = Float64(Float64(y1 * y2) * Float64(x * Float64(-a)));
	elseif (y4 <= 3.8e-193)
		tmp = Float64(y0 * Float64(y2 * Float64(k * Float64(-y5))));
	elseif (y4 <= 4.6e-97)
		tmp = Float64(y0 * Float64(y2 * Float64(x * c)));
	elseif ((y4 <= 1.55e+61) || !(y4 <= 5.5e+124))
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	else
		tmp = Float64(y1 * Float64(z * 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)
	tmp = 0.0;
	if (y4 <= -9.2e+65)
		tmp = j * (y1 * (y3 * -y4));
	elseif (y4 <= -1.2e-262)
		tmp = (y1 * y2) * (x * -a);
	elseif (y4 <= 3.8e-193)
		tmp = y0 * (y2 * (k * -y5));
	elseif (y4 <= 4.6e-97)
		tmp = y0 * (y2 * (x * c));
	elseif ((y4 <= 1.55e+61) || ~((y4 <= 5.5e+124)))
		tmp = b * (y4 * ((t * j) - (y * k)));
	else
		tmp = y1 * (z * (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_] := If[LessEqual[y4, -9.2e+65], N[(j * N[(y1 * N[(y3 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.2e-262], N[(N[(y1 * y2), $MachinePrecision] * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 3.8e-193], N[(y0 * N[(y2 * N[(k * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 4.6e-97], N[(y0 * N[(y2 * N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y4, 1.55e+61], N[Not[LessEqual[y4, 5.5e+124]], $MachinePrecision]], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(z * N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y4 < -9.2e65

   1. Initial program 27.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 42.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 42.2%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 42.2%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 42.2%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around -inf 42.4%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 44.7%

         \[\leadsto \color{blue}{\left(y1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} \]

   8. Simplified 44.7%

      \[\leadsto \color{blue}{\left(y1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} \]

   9. Taylor expanded in k around 0 44.4%

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 44.4%

          \[\leadsto \color{blue}{-j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)} \]

       2. *-commutative 44.4%

          \[\leadsto -j \cdot \left(y1 \cdot \color{blue}{\left(y4 \cdot y3\right)}\right) \]

   11. Simplified 44.4%

       \[\leadsto \color{blue}{-j \cdot \left(y1 \cdot \left(y4 \cdot y3\right)\right)} \]

   if -9.2e65 < y4 < -1.2e-262

   1. Initial program 43.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 46.3%

      \[\leadsto \left(\left(\left(\color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. associate-*r* 43.9%

         \[\leadsto \left(\left(\left(\color{blue}{\left(i \cdot y1\right) \cdot \left(j \cdot x - k \cdot z\right)} + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. *-commutative 43.9%

         \[\leadsto \left(\left(\left(\left(i \cdot y1\right) \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 43.9%

      \[\leadsto \left(\left(\left(\color{blue}{\left(i \cdot y1\right) \cdot \left(j \cdot x - z \cdot k\right)} + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in a around -inf 45.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 45.7%

         \[\leadsto \color{blue}{-a \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   8. Simplified 45.7%

      \[\leadsto \color{blue}{-a \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in x around inf 24.6%

      \[\leadsto -\color{blue}{a \cdot \left(x \cdot \left(y1 \cdot y2\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 25.7%

          \[\leadsto -\color{blue}{\left(a \cdot x\right) \cdot \left(y1 \cdot y2\right)} \]

       2. *-commutative 25.7%

          \[\leadsto -\left(a \cdot x\right) \cdot \color{blue}{\left(y2 \cdot y1\right)} \]

   11. Simplified 25.7%

       \[\leadsto -\color{blue}{\left(a \cdot x\right) \cdot \left(y2 \cdot y1\right)} \]

   if -1.2e-262 < y4 < 3.80000000000000004e-193

   1. Initial program 41.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 56.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 56.0%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 56.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 56.0%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 56.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 56.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 56.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 56.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 56.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y2 around inf 48.0%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(c \cdot x - k \cdot y5\right)\right)} \]

   7. Taylor expanded in c around 0 42.9%

      \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(-1 \cdot \left(k \cdot y5\right)\right)}\right) \]
   8. Step-by-step derivation

      1. neg-mul-1 42.9%

         \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(-k \cdot y5\right)}\right) \]

      2. distribute-rgt-neg-in 42.9%

         \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot \left(-y5\right)\right)}\right) \]

   9. Simplified 42.9%

      \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot \left(-y5\right)\right)}\right) \]

   if 3.80000000000000004e-193 < y4 < 4.59999999999999988e-97

   1. Initial program 31.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 37.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 37.8%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 37.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 37.8%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 37.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 37.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 37.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 37.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 37.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y2 around inf 33.8%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(c \cdot x - k \cdot y5\right)\right)} \]

   7. Taylor expanded in c around inf 33.3%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 33.7%

         \[\leadsto y0 \cdot \color{blue}{\left(\left(c \cdot x\right) \cdot y2\right)} \]

   9. Simplified 33.7%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(c \cdot x\right) \cdot y2\right)} \]

   if 4.59999999999999988e-97 < y4 < 1.55e61 or 5.49999999999999977e124 < y4

   1. Initial program 33.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 45.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 43.2%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if 1.55e61 < y4 < 5.49999999999999977e124

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 42.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 42.3%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 42.3%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 42.3%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 42.3%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 42.3%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 42.3%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 42.3%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 42.3%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 42.3%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 42.3%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in z around -inf 43.2%

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]

   7. Taylor expanded in a around inf 43.0%

      \[\leadsto y1 \cdot \left(z \cdot \color{blue}{\left(a \cdot y3\right)}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -9.2 \cdot 10^{+65}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -1.2 \cdot 10^{-262}:\\ \;\;\;\;\left(y1 \cdot y2\right) \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y4 \leq 3.8 \cdot 10^{-193}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 4.6 \cdot 10^{-97}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{elif}\;y4 \leq 1.55 \cdot 10^{+61} \lor \neg \left(y4 \leq 5.5 \cdot 10^{+124}\right):\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 31.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ t_2 := t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{if}\;a \leq -1.85 \cdot 10^{+150}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{-244}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{-54}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y1 (- (* x i) (* y3 y4)))))
        (t_2 (* t (* a (- (* y2 y5) (* z b))))))
   (if (<= a -1.85e+150)
     t_2
     (if (<= a -6.5e-18)
       t_1
       (if (<= a -9.8e-244)
         (* t (* j (- (* b y4) (* i y5))))
         (if (<= a 1.3e-216)
           t_1
           (if (<= a 7.4e-54) (* k (* y (- (* i y5) (* b y4)))) 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 = j * (y1 * ((x * i) - (y3 * y4)));
	double t_2 = t * (a * ((y2 * y5) - (z * b)));
	double tmp;
	if (a <= -1.85e+150) {
		tmp = t_2;
	} else if (a <= -6.5e-18) {
		tmp = t_1;
	} else if (a <= -9.8e-244) {
		tmp = t * (j * ((b * y4) - (i * y5)));
	} else if (a <= 1.3e-216) {
		tmp = t_1;
	} else if (a <= 7.4e-54) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} 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 = j * (y1 * ((x * i) - (y3 * y4)))
    t_2 = t * (a * ((y2 * y5) - (z * b)))
    if (a <= (-1.85d+150)) then
        tmp = t_2
    else if (a <= (-6.5d-18)) then
        tmp = t_1
    else if (a <= (-9.8d-244)) then
        tmp = t * (j * ((b * y4) - (i * y5)))
    else if (a <= 1.3d-216) then
        tmp = t_1
    else if (a <= 7.4d-54) then
        tmp = k * (y * ((i * y5) - (b * y4)))
    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 = j * (y1 * ((x * i) - (y3 * y4)));
	double t_2 = t * (a * ((y2 * y5) - (z * b)));
	double tmp;
	if (a <= -1.85e+150) {
		tmp = t_2;
	} else if (a <= -6.5e-18) {
		tmp = t_1;
	} else if (a <= -9.8e-244) {
		tmp = t * (j * ((b * y4) - (i * y5)));
	} else if (a <= 1.3e-216) {
		tmp = t_1;
	} else if (a <= 7.4e-54) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} 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 = j * (y1 * ((x * i) - (y3 * y4)))
	t_2 = t * (a * ((y2 * y5) - (z * b)))
	tmp = 0
	if a <= -1.85e+150:
		tmp = t_2
	elif a <= -6.5e-18:
		tmp = t_1
	elif a <= -9.8e-244:
		tmp = t * (j * ((b * y4) - (i * y5)))
	elif a <= 1.3e-216:
		tmp = t_1
	elif a <= 7.4e-54:
		tmp = k * (y * ((i * y5) - (b * y4)))
	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(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))))
	t_2 = Float64(t * Float64(a * Float64(Float64(y2 * y5) - Float64(z * b))))
	tmp = 0.0
	if (a <= -1.85e+150)
		tmp = t_2;
	elseif (a <= -6.5e-18)
		tmp = t_1;
	elseif (a <= -9.8e-244)
		tmp = Float64(t * Float64(j * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (a <= 1.3e-216)
		tmp = t_1;
	elseif (a <= 7.4e-54)
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))));
	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 = j * (y1 * ((x * i) - (y3 * y4)));
	t_2 = t * (a * ((y2 * y5) - (z * b)));
	tmp = 0.0;
	if (a <= -1.85e+150)
		tmp = t_2;
	elseif (a <= -6.5e-18)
		tmp = t_1;
	elseif (a <= -9.8e-244)
		tmp = t * (j * ((b * y4) - (i * y5)));
	elseif (a <= 1.3e-216)
		tmp = t_1;
	elseif (a <= 7.4e-54)
		tmp = k * (y * ((i * y5) - (b * y4)));
	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[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(a * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.85e+150], t$95$2, If[LessEqual[a, -6.5e-18], t$95$1, If[LessEqual[a, -9.8e-244], N[(t * N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e-216], t$95$1, If[LessEqual[a, 7.4e-54], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.84999999999999994e150 or 7.4000000000000006e-54 < a

   1. Initial program 26.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 40.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 49.9%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(b \cdot z\right) - -1 \cdot \left(y2 \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. cancel-sign-sub-inv 49.9%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right) + \left(--1\right) \cdot \left(y2 \cdot y5\right)\right)}\right) \]

      2. metadata-eval 49.9%

         \[\leadsto t \cdot \left(a \cdot \left(-1 \cdot \left(b \cdot z\right) + \color{blue}{1} \cdot \left(y2 \cdot y5\right)\right)\right) \]

      3. *-lft-identity 49.9%

         \[\leadsto t \cdot \left(a \cdot \left(-1 \cdot \left(b \cdot z\right) + \color{blue}{y2 \cdot y5}\right)\right) \]

      4. +-commutative 49.9%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      5. mul-1-neg 49.9%

         \[\leadsto t \cdot \left(a \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      6. sub-neg 49.9%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \]

   6. Simplified 49.9%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

   if -1.84999999999999994e150 < a < -6.50000000000000008e-18 or -9.80000000000000029e-244 < a < 1.2999999999999999e-216

   1. Initial program 50.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 47.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 47.7%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 47.7%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 47.7%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 47.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 47.7%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 47.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 47.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 47.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 47.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 47.7%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in j around inf 41.1%

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 41.1%

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 41.1%

         \[\leadsto j \cdot \left(y1 \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 41.1%

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

   8. Simplified 41.1%

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(i \cdot x - y3 \cdot y4\right)\right)} \]

   if -6.50000000000000008e-18 < a < -9.80000000000000029e-244

   1. Initial program 39.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 29.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 37.9%

      \[\leadsto t \cdot \color{blue}{\left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   if 1.2999999999999999e-216 < a < 7.4000000000000006e-54

   1. Initial program 37.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 53.3%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 53.3%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 53.3%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 53.3%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 53.3%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 53.3%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 53.3%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 53.3%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y around inf 43.6%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{+150}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-18}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{-244}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-216}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{-54}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 32.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ t_2 := t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{+154}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-231}:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-218}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-58}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y1 (- (* x i) (* y3 y4)))))
        (t_2 (* t (* a (- (* y2 y5) (* z b))))))
   (if (<= a -2.2e+154)
     t_2
     (if (<= a -4.4e-51)
       t_1
       (if (<= a -6.5e-231)
         (* i (* t (- (* z c) (* j y5))))
         (if (<= a 7.6e-218)
           t_1
           (if (<= a 6.5e-58) (* k (* y (- (* i y5) (* b y4)))) 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 = j * (y1 * ((x * i) - (y3 * y4)));
	double t_2 = t * (a * ((y2 * y5) - (z * b)));
	double tmp;
	if (a <= -2.2e+154) {
		tmp = t_2;
	} else if (a <= -4.4e-51) {
		tmp = t_1;
	} else if (a <= -6.5e-231) {
		tmp = i * (t * ((z * c) - (j * y5)));
	} else if (a <= 7.6e-218) {
		tmp = t_1;
	} else if (a <= 6.5e-58) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} 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 = j * (y1 * ((x * i) - (y3 * y4)))
    t_2 = t * (a * ((y2 * y5) - (z * b)))
    if (a <= (-2.2d+154)) then
        tmp = t_2
    else if (a <= (-4.4d-51)) then
        tmp = t_1
    else if (a <= (-6.5d-231)) then
        tmp = i * (t * ((z * c) - (j * y5)))
    else if (a <= 7.6d-218) then
        tmp = t_1
    else if (a <= 6.5d-58) then
        tmp = k * (y * ((i * y5) - (b * y4)))
    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 = j * (y1 * ((x * i) - (y3 * y4)));
	double t_2 = t * (a * ((y2 * y5) - (z * b)));
	double tmp;
	if (a <= -2.2e+154) {
		tmp = t_2;
	} else if (a <= -4.4e-51) {
		tmp = t_1;
	} else if (a <= -6.5e-231) {
		tmp = i * (t * ((z * c) - (j * y5)));
	} else if (a <= 7.6e-218) {
		tmp = t_1;
	} else if (a <= 6.5e-58) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} 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 = j * (y1 * ((x * i) - (y3 * y4)))
	t_2 = t * (a * ((y2 * y5) - (z * b)))
	tmp = 0
	if a <= -2.2e+154:
		tmp = t_2
	elif a <= -4.4e-51:
		tmp = t_1
	elif a <= -6.5e-231:
		tmp = i * (t * ((z * c) - (j * y5)))
	elif a <= 7.6e-218:
		tmp = t_1
	elif a <= 6.5e-58:
		tmp = k * (y * ((i * y5) - (b * y4)))
	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(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))))
	t_2 = Float64(t * Float64(a * Float64(Float64(y2 * y5) - Float64(z * b))))
	tmp = 0.0
	if (a <= -2.2e+154)
		tmp = t_2;
	elseif (a <= -4.4e-51)
		tmp = t_1;
	elseif (a <= -6.5e-231)
		tmp = Float64(i * Float64(t * Float64(Float64(z * c) - Float64(j * y5))));
	elseif (a <= 7.6e-218)
		tmp = t_1;
	elseif (a <= 6.5e-58)
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))));
	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 = j * (y1 * ((x * i) - (y3 * y4)));
	t_2 = t * (a * ((y2 * y5) - (z * b)));
	tmp = 0.0;
	if (a <= -2.2e+154)
		tmp = t_2;
	elseif (a <= -4.4e-51)
		tmp = t_1;
	elseif (a <= -6.5e-231)
		tmp = i * (t * ((z * c) - (j * y5)));
	elseif (a <= 7.6e-218)
		tmp = t_1;
	elseif (a <= 6.5e-58)
		tmp = k * (y * ((i * y5) - (b * y4)));
	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[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(a * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.2e+154], t$95$2, If[LessEqual[a, -4.4e-51], t$95$1, If[LessEqual[a, -6.5e-231], N[(i * N[(t * N[(N[(z * c), $MachinePrecision] - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.6e-218], t$95$1, If[LessEqual[a, 6.5e-58], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.2000000000000001e154 or 6.49999999999999964e-58 < a

   1. Initial program 26.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 40.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 49.9%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(b \cdot z\right) - -1 \cdot \left(y2 \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. cancel-sign-sub-inv 49.9%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right) + \left(--1\right) \cdot \left(y2 \cdot y5\right)\right)}\right) \]

      2. metadata-eval 49.9%

         \[\leadsto t \cdot \left(a \cdot \left(-1 \cdot \left(b \cdot z\right) + \color{blue}{1} \cdot \left(y2 \cdot y5\right)\right)\right) \]

      3. *-lft-identity 49.9%

         \[\leadsto t \cdot \left(a \cdot \left(-1 \cdot \left(b \cdot z\right) + \color{blue}{y2 \cdot y5}\right)\right) \]

      4. +-commutative 49.9%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{\left(y2 \cdot y5 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      5. mul-1-neg 49.9%

         \[\leadsto t \cdot \left(a \cdot \left(y2 \cdot y5 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      6. sub-neg 49.9%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{\left(y2 \cdot y5 - b \cdot z\right)}\right) \]

   6. Simplified 49.9%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]

   if -2.2000000000000001e154 < a < -4.4e-51 or -6.5000000000000004e-231 < a < 7.5999999999999997e-218

   1. Initial program 46.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 49.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 49.1%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 49.1%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 49.1%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 49.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 49.1%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 49.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 49.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 49.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 49.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 49.1%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in j around inf 39.3%

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 39.3%

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 39.3%

         \[\leadsto j \cdot \left(y1 \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 39.3%

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

   8. Simplified 39.3%

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(i \cdot x - y3 \cdot y4\right)\right)} \]

   if -4.4e-51 < a < -6.5000000000000004e-231

   1. Initial program 47.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 32.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in i around inf 35.4%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 35.4%

         \[\leadsto i \cdot \left(t \cdot \color{blue}{\left(c \cdot z + -1 \cdot \left(j \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 35.4%

         \[\leadsto i \cdot \left(t \cdot \left(c \cdot z + \color{blue}{\left(-j \cdot y5\right)}\right)\right) \]

      3. sub-neg 35.4%

         \[\leadsto i \cdot \left(t \cdot \color{blue}{\left(c \cdot z - j \cdot y5\right)}\right) \]

   6. Simplified 35.4%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \left(c \cdot z - j \cdot y5\right)\right)} \]

   if 7.5999999999999997e-218 < a < 6.49999999999999964e-58

   1. Initial program 37.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 53.3%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 53.3%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 53.3%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 53.3%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 53.3%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 53.3%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 53.3%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 53.3%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y around inf 43.6%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+154}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-51}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-231}:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-218}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-58}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.5% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -1.95:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -7 \cdot 10^{-254}:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 3.1 \cdot 10^{-291}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.3 \cdot 10^{+108}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 1.26 \cdot 10^{+219}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -1.95)
   (* k (* y2 (- (* y1 y4) (* y0 y5))))
   (if (<= y2 -7e-254)
     (* i (* t (- (* z c) (* j y5))))
     (if (<= y2 3.1e-291)
       (* j (* y1 (* y3 (- y4))))
       (if (<= y2 1.3e+108)
         (* j (* y1 (- (* x i) (* y3 y4))))
         (if (<= y2 1.26e+219)
           (* c (* x (* y0 y2)))
           (* k (* y1 (* y2 y4)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.95) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (y2 <= -7e-254) {
		tmp = i * (t * ((z * c) - (j * y5)));
	} else if (y2 <= 3.1e-291) {
		tmp = j * (y1 * (y3 * -y4));
	} else if (y2 <= 1.3e+108) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (y2 <= 1.26e+219) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = k * (y1 * (y2 * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-1.95d0)) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (y2 <= (-7d-254)) then
        tmp = i * (t * ((z * c) - (j * y5)))
    else if (y2 <= 3.1d-291) then
        tmp = j * (y1 * (y3 * -y4))
    else if (y2 <= 1.3d+108) then
        tmp = j * (y1 * ((x * i) - (y3 * y4)))
    else if (y2 <= 1.26d+219) then
        tmp = c * (x * (y0 * y2))
    else
        tmp = k * (y1 * (y2 * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.95) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (y2 <= -7e-254) {
		tmp = i * (t * ((z * c) - (j * y5)));
	} else if (y2 <= 3.1e-291) {
		tmp = j * (y1 * (y3 * -y4));
	} else if (y2 <= 1.3e+108) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (y2 <= 1.26e+219) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = k * (y1 * (y2 * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -1.95:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif y2 <= -7e-254:
		tmp = i * (t * ((z * c) - (j * y5)))
	elif y2 <= 3.1e-291:
		tmp = j * (y1 * (y3 * -y4))
	elif y2 <= 1.3e+108:
		tmp = j * (y1 * ((x * i) - (y3 * y4)))
	elif y2 <= 1.26e+219:
		tmp = c * (x * (y0 * y2))
	else:
		tmp = k * (y1 * (y2 * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -1.95)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (y2 <= -7e-254)
		tmp = Float64(i * Float64(t * Float64(Float64(z * c) - Float64(j * y5))));
	elseif (y2 <= 3.1e-291)
		tmp = Float64(j * Float64(y1 * Float64(y3 * Float64(-y4))));
	elseif (y2 <= 1.3e+108)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (y2 <= 1.26e+219)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	else
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -1.95)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (y2 <= -7e-254)
		tmp = i * (t * ((z * c) - (j * y5)));
	elseif (y2 <= 3.1e-291)
		tmp = j * (y1 * (y3 * -y4));
	elseif (y2 <= 1.3e+108)
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	elseif (y2 <= 1.26e+219)
		tmp = c * (x * (y0 * y2));
	else
		tmp = k * (y1 * (y2 * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -1.95], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -7e-254], N[(i * N[(t * N[(N[(z * c), $MachinePrecision] - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.1e-291], N[(j * N[(y1 * N[(y3 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.3e+108], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.26e+219], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y2 < -1.94999999999999996

   1. Initial program 26.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 52.8%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 52.8%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 52.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 52.8%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 52.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 52.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 52.8%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 52.8%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y2 around inf 42.3%

      \[\leadsto \color{blue}{k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   if -1.94999999999999996 < y2 < -7.00000000000000014e-254

   1. Initial program 51.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 41.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in i around inf 34.5%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 34.5%

         \[\leadsto i \cdot \left(t \cdot \color{blue}{\left(c \cdot z + -1 \cdot \left(j \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 34.5%

         \[\leadsto i \cdot \left(t \cdot \left(c \cdot z + \color{blue}{\left(-j \cdot y5\right)}\right)\right) \]

      3. sub-neg 34.5%

         \[\leadsto i \cdot \left(t \cdot \color{blue}{\left(c \cdot z - j \cdot y5\right)}\right) \]

   6. Simplified 34.5%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \left(c \cdot z - j \cdot y5\right)\right)} \]

   if -7.00000000000000014e-254 < y2 < 3.10000000000000011e-291

   1. Initial program 33.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 38.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 38.9%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 38.9%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 38.9%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 38.9%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 38.9%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 38.9%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 38.9%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 38.9%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 38.9%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 38.9%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around -inf 39.6%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 34.8%

         \[\leadsto \color{blue}{\left(y1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} \]

   8. Simplified 34.8%

      \[\leadsto \color{blue}{\left(y1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} \]

   9. Taylor expanded in k around 0 44.2%

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 44.2%

          \[\leadsto \color{blue}{-j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)} \]

       2. *-commutative 44.2%

          \[\leadsto -j \cdot \left(y1 \cdot \color{blue}{\left(y4 \cdot y3\right)}\right) \]

   11. Simplified 44.2%

       \[\leadsto \color{blue}{-j \cdot \left(y1 \cdot \left(y4 \cdot y3\right)\right)} \]

   if 3.10000000000000011e-291 < y2 < 1.3000000000000001e108

   1. Initial program 42.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 42.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 42.8%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 42.8%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 42.8%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 42.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 42.8%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 42.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 42.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 42.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 42.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 42.8%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in j around inf 36.6%

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 36.6%

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 36.6%

         \[\leadsto j \cdot \left(y1 \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 36.6%

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

   8. Simplified 36.6%

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(i \cdot x - y3 \cdot y4\right)\right)} \]

   if 1.3000000000000001e108 < y2 < 1.2599999999999999e219

   1. Initial program 24.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 50.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.5%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 50.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 50.5%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 50.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 50.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 50.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 50.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 50.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y2 around inf 55.4%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(c \cdot x - k \cdot y5\right)\right)} \]

   7. Taylor expanded in c around inf 47.5%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if 1.2599999999999999e219 < y2

   1. Initial program 28.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 50.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 50.8%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 50.8%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 50.8%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 50.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 50.8%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 50.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 50.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 50.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 50.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 50.8%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around -inf 50.7%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 50.7%

         \[\leadsto \color{blue}{\left(y1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} \]

   8. Simplified 50.7%

      \[\leadsto \color{blue}{\left(y1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} \]

   9. Taylor expanded in k around inf 64.4%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 64.4%

          \[\leadsto k \cdot \left(y1 \cdot \color{blue}{\left(y4 \cdot y2\right)}\right) \]

   11. Simplified 64.4%

       \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y4 \cdot y2\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.95:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq -7 \cdot 10^{-254}:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 3.1 \cdot 10^{-291}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.3 \cdot 10^{+108}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 1.26 \cdot 10^{+219}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 31.4% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ t_2 := k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{if}\;y \leq -1.06 \cdot 10^{+64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.04 \cdot 10^{-255}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-168}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 10^{+165}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* t (- (* z c) (* j y5)))))
        (t_2 (* k (* y (- (* i y5) (* b y4))))))
   (if (<= y -1.06e+64)
     t_2
     (if (<= y 1.04e-255)
       t_1
       (if (<= y 4e-168)
         (* j (* y1 (- (* x i) (* y3 y4))))
         (if (<= y 1e+165) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (t * ((z * c) - (j * y5)));
	double t_2 = k * (y * ((i * y5) - (b * y4)));
	double tmp;
	if (y <= -1.06e+64) {
		tmp = t_2;
	} else if (y <= 1.04e-255) {
		tmp = t_1;
	} else if (y <= 4e-168) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (y <= 1e+165) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * (t * ((z * c) - (j * y5)))
    t_2 = k * (y * ((i * y5) - (b * y4)))
    if (y <= (-1.06d+64)) then
        tmp = t_2
    else if (y <= 1.04d-255) then
        tmp = t_1
    else if (y <= 4d-168) then
        tmp = j * (y1 * ((x * i) - (y3 * y4)))
    else if (y <= 1d+165) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (t * ((z * c) - (j * y5)));
	double t_2 = k * (y * ((i * y5) - (b * y4)));
	double tmp;
	if (y <= -1.06e+64) {
		tmp = t_2;
	} else if (y <= 1.04e-255) {
		tmp = t_1;
	} else if (y <= 4e-168) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (y <= 1e+165) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (t * ((z * c) - (j * y5)))
	t_2 = k * (y * ((i * y5) - (b * y4)))
	tmp = 0
	if y <= -1.06e+64:
		tmp = t_2
	elif y <= 1.04e-255:
		tmp = t_1
	elif y <= 4e-168:
		tmp = j * (y1 * ((x * i) - (y3 * y4)))
	elif y <= 1e+165:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(t * Float64(Float64(z * c) - Float64(j * y5))))
	t_2 = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))))
	tmp = 0.0
	if (y <= -1.06e+64)
		tmp = t_2;
	elseif (y <= 1.04e-255)
		tmp = t_1;
	elseif (y <= 4e-168)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (y <= 1e+165)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (t * ((z * c) - (j * y5)));
	t_2 = k * (y * ((i * y5) - (b * y4)));
	tmp = 0.0;
	if (y <= -1.06e+64)
		tmp = t_2;
	elseif (y <= 1.04e-255)
		tmp = t_1;
	elseif (y <= 4e-168)
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	elseif (y <= 1e+165)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(t * N[(N[(z * c), $MachinePrecision] - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.06e+64], t$95$2, If[LessEqual[y, 1.04e-255], t$95$1, If[LessEqual[y, 4e-168], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+165], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.06e64 or 9.99999999999999899e164 < y

   1. Initial program 21.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf 48.0%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 48.0%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + -1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      2. mul-1-neg 48.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \color{blue}{\left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      3. unsub-neg 48.0%

         \[\leadsto k \cdot \left(\color{blue}{\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      4. *-commutative 48.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \]

      5. associate-*r* 48.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

      6. neg-mul-1 48.0%

         \[\leadsto k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \color{blue}{\left(-z\right)} \cdot \left(b \cdot y0 - i \cdot y1\right)\right) \]

   5. Simplified 48.0%

      \[\leadsto \color{blue}{k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - \left(b \cdot y4 - i \cdot y5\right) \cdot y\right) - \left(-z\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y around inf 50.8%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)} \]

   if -1.06e64 < y < 1.04e-255 or 4.0000000000000002e-168 < y < 9.99999999999999899e164

   1. Initial program 42.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 36.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in i around inf 32.0%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 32.0%

         \[\leadsto i \cdot \left(t \cdot \color{blue}{\left(c \cdot z + -1 \cdot \left(j \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 32.0%

         \[\leadsto i \cdot \left(t \cdot \left(c \cdot z + \color{blue}{\left(-j \cdot y5\right)}\right)\right) \]

      3. sub-neg 32.0%

         \[\leadsto i \cdot \left(t \cdot \color{blue}{\left(c \cdot z - j \cdot y5\right)}\right) \]

   6. Simplified 32.0%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \left(c \cdot z - j \cdot y5\right)\right)} \]

   if 1.04e-255 < y < 4.0000000000000002e-168

   1. Initial program 46.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 46.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 46.8%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 46.8%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 46.8%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 46.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 46.8%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 46.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 46.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 46.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 46.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 46.8%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in j around inf 58.2%

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 58.2%

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 58.2%

         \[\leadsto j \cdot \left(y1 \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 58.2%

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

   8. Simplified 58.2%

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(i \cdot x - y3 \cdot y4\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+64}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.04 \cdot 10^{-255}:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-168}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 10^{+165}:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 30.2% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{if}\;y4 \leq -4.2 \cdot 10^{+158}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 8 \cdot 10^{-255}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 3.7 \cdot 10^{-193}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 0.02:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* t (- (* z c) (* j y5))))))
   (if (<= y4 -4.2e+158)
     (* j (* y1 (- (* x i) (* y3 y4))))
     (if (<= y4 8e-255)
       t_1
       (if (<= y4 3.7e-193)
         (* y0 (* y2 (* k (- y5))))
         (if (<= y4 0.02) t_1 (* b (* y4 (- (* t j) (* y k))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (t * ((z * c) - (j * y5)));
	double tmp;
	if (y4 <= -4.2e+158) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (y4 <= 8e-255) {
		tmp = t_1;
	} else if (y4 <= 3.7e-193) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (y4 <= 0.02) {
		tmp = t_1;
	} else {
		tmp = b * (y4 * ((t * j) - (y * k)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (t * ((z * c) - (j * y5)))
    if (y4 <= (-4.2d+158)) then
        tmp = j * (y1 * ((x * i) - (y3 * y4)))
    else if (y4 <= 8d-255) then
        tmp = t_1
    else if (y4 <= 3.7d-193) then
        tmp = y0 * (y2 * (k * -y5))
    else if (y4 <= 0.02d0) then
        tmp = t_1
    else
        tmp = b * (y4 * ((t * j) - (y * k)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (t * ((z * c) - (j * y5)));
	double tmp;
	if (y4 <= -4.2e+158) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (y4 <= 8e-255) {
		tmp = t_1;
	} else if (y4 <= 3.7e-193) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (y4 <= 0.02) {
		tmp = t_1;
	} else {
		tmp = b * (y4 * ((t * j) - (y * k)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (t * ((z * c) - (j * y5)))
	tmp = 0
	if y4 <= -4.2e+158:
		tmp = j * (y1 * ((x * i) - (y3 * y4)))
	elif y4 <= 8e-255:
		tmp = t_1
	elif y4 <= 3.7e-193:
		tmp = y0 * (y2 * (k * -y5))
	elif y4 <= 0.02:
		tmp = t_1
	else:
		tmp = b * (y4 * ((t * j) - (y * k)))
	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(t * Float64(Float64(z * c) - Float64(j * y5))))
	tmp = 0.0
	if (y4 <= -4.2e+158)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (y4 <= 8e-255)
		tmp = t_1;
	elseif (y4 <= 3.7e-193)
		tmp = Float64(y0 * Float64(y2 * Float64(k * Float64(-y5))));
	elseif (y4 <= 0.02)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (t * ((z * c) - (j * y5)));
	tmp = 0.0;
	if (y4 <= -4.2e+158)
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	elseif (y4 <= 8e-255)
		tmp = t_1;
	elseif (y4 <= 3.7e-193)
		tmp = y0 * (y2 * (k * -y5));
	elseif (y4 <= 0.02)
		tmp = t_1;
	else
		tmp = b * (y4 * ((t * j) - (y * k)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(t * N[(N[(z * c), $MachinePrecision] - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -4.2e+158], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 8e-255], t$95$1, If[LessEqual[y4, 3.7e-193], N[(y0 * N[(y2 * N[(k * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 0.02], t$95$1, N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y4 < -4.1999999999999998e158

   1. Initial program 32.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 33.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 33.1%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 33.1%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 33.1%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 33.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 33.1%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 33.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 33.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 33.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 33.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 33.1%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in j around inf 56.4%

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 56.4%

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 56.4%

         \[\leadsto j \cdot \left(y1 \cdot \left(i \cdot x + \color{blue}{\left(-y3 \cdot y4\right)}\right)\right) \]

      3. unsub-neg 56.4%

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x - y3 \cdot y4\right)}\right) \]

   8. Simplified 56.4%

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(i \cdot x - y3 \cdot y4\right)\right)} \]

   if -4.1999999999999998e158 < y4 < 8.0000000000000001e-255 or 3.7000000000000002e-193 < y4 < 0.0200000000000000004

   1. Initial program 37.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 39.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in i around inf 34.0%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 34.0%

         \[\leadsto i \cdot \left(t \cdot \color{blue}{\left(c \cdot z + -1 \cdot \left(j \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 34.0%

         \[\leadsto i \cdot \left(t \cdot \left(c \cdot z + \color{blue}{\left(-j \cdot y5\right)}\right)\right) \]

      3. sub-neg 34.0%

         \[\leadsto i \cdot \left(t \cdot \color{blue}{\left(c \cdot z - j \cdot y5\right)}\right) \]

   6. Simplified 34.0%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \left(c \cdot z - j \cdot y5\right)\right)} \]

   if 8.0000000000000001e-255 < y4 < 3.7000000000000002e-193

   1. Initial program 50.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 56.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 56.8%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 56.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 56.8%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 56.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 56.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 56.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 56.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 56.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y2 around inf 50.6%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(c \cdot x - k \cdot y5\right)\right)} \]

   7. Taylor expanded in c around 0 56.9%

      \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(-1 \cdot \left(k \cdot y5\right)\right)}\right) \]
   8. Step-by-step derivation

      1. neg-mul-1 56.9%

         \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(-k \cdot y5\right)}\right) \]

      2. distribute-rgt-neg-in 56.9%

         \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot \left(-y5\right)\right)}\right) \]

   9. Simplified 56.9%

      \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot \left(-y5\right)\right)}\right) \]

   if 0.0200000000000000004 < y4

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 41.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 40.5%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -4.2 \cdot 10^{+158}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 8 \cdot 10^{-255}:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 3.7 \cdot 10^{-193}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 0.02:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.7% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{if}\;y4 \leq -2.2 \cdot 10^{+158}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 3.1 \cdot 10^{-254}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 4.4 \cdot 10^{-193}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 0.0142:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* t (- (* z c) (* j y5))))))
   (if (<= y4 -2.2e+158)
     (* j (* y1 (* y3 (- y4))))
     (if (<= y4 3.1e-254)
       t_1
       (if (<= y4 4.4e-193)
         (* y0 (* y2 (* k (- y5))))
         (if (<= y4 0.0142) t_1 (* b (* y4 (- (* t j) (* y k))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (t * ((z * c) - (j * y5)));
	double tmp;
	if (y4 <= -2.2e+158) {
		tmp = j * (y1 * (y3 * -y4));
	} else if (y4 <= 3.1e-254) {
		tmp = t_1;
	} else if (y4 <= 4.4e-193) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (y4 <= 0.0142) {
		tmp = t_1;
	} else {
		tmp = b * (y4 * ((t * j) - (y * k)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (t * ((z * c) - (j * y5)))
    if (y4 <= (-2.2d+158)) then
        tmp = j * (y1 * (y3 * -y4))
    else if (y4 <= 3.1d-254) then
        tmp = t_1
    else if (y4 <= 4.4d-193) then
        tmp = y0 * (y2 * (k * -y5))
    else if (y4 <= 0.0142d0) then
        tmp = t_1
    else
        tmp = b * (y4 * ((t * j) - (y * k)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (t * ((z * c) - (j * y5)));
	double tmp;
	if (y4 <= -2.2e+158) {
		tmp = j * (y1 * (y3 * -y4));
	} else if (y4 <= 3.1e-254) {
		tmp = t_1;
	} else if (y4 <= 4.4e-193) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (y4 <= 0.0142) {
		tmp = t_1;
	} else {
		tmp = b * (y4 * ((t * j) - (y * k)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (t * ((z * c) - (j * y5)))
	tmp = 0
	if y4 <= -2.2e+158:
		tmp = j * (y1 * (y3 * -y4))
	elif y4 <= 3.1e-254:
		tmp = t_1
	elif y4 <= 4.4e-193:
		tmp = y0 * (y2 * (k * -y5))
	elif y4 <= 0.0142:
		tmp = t_1
	else:
		tmp = b * (y4 * ((t * j) - (y * k)))
	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(t * Float64(Float64(z * c) - Float64(j * y5))))
	tmp = 0.0
	if (y4 <= -2.2e+158)
		tmp = Float64(j * Float64(y1 * Float64(y3 * Float64(-y4))));
	elseif (y4 <= 3.1e-254)
		tmp = t_1;
	elseif (y4 <= 4.4e-193)
		tmp = Float64(y0 * Float64(y2 * Float64(k * Float64(-y5))));
	elseif (y4 <= 0.0142)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (t * ((z * c) - (j * y5)));
	tmp = 0.0;
	if (y4 <= -2.2e+158)
		tmp = j * (y1 * (y3 * -y4));
	elseif (y4 <= 3.1e-254)
		tmp = t_1;
	elseif (y4 <= 4.4e-193)
		tmp = y0 * (y2 * (k * -y5));
	elseif (y4 <= 0.0142)
		tmp = t_1;
	else
		tmp = b * (y4 * ((t * j) - (y * k)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(t * N[(N[(z * c), $MachinePrecision] - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -2.2e+158], N[(j * N[(y1 * N[(y3 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 3.1e-254], t$95$1, If[LessEqual[y4, 4.4e-193], N[(y0 * N[(y2 * N[(k * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 0.0142], t$95$1, N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y4 < -2.2000000000000001e158

   1. Initial program 32.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 33.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 33.1%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 33.1%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 33.1%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 33.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 33.1%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 33.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 33.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 33.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 33.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 33.1%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around -inf 45.2%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 49.0%

         \[\leadsto \color{blue}{\left(y1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} \]

   8. Simplified 49.0%

      \[\leadsto \color{blue}{\left(y1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} \]

   9. Taylor expanded in k around 0 52.4%

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 52.4%

          \[\leadsto \color{blue}{-j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)} \]

       2. *-commutative 52.4%

          \[\leadsto -j \cdot \left(y1 \cdot \color{blue}{\left(y4 \cdot y3\right)}\right) \]

   11. Simplified 52.4%

       \[\leadsto \color{blue}{-j \cdot \left(y1 \cdot \left(y4 \cdot y3\right)\right)} \]

   if -2.2000000000000001e158 < y4 < 3.09999999999999988e-254 or 4.39999999999999953e-193 < y4 < 0.014200000000000001

   1. Initial program 37.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 39.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in i around inf 34.0%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 34.0%

         \[\leadsto i \cdot \left(t \cdot \color{blue}{\left(c \cdot z + -1 \cdot \left(j \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 34.0%

         \[\leadsto i \cdot \left(t \cdot \left(c \cdot z + \color{blue}{\left(-j \cdot y5\right)}\right)\right) \]

      3. sub-neg 34.0%

         \[\leadsto i \cdot \left(t \cdot \color{blue}{\left(c \cdot z - j \cdot y5\right)}\right) \]

   6. Simplified 34.0%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \left(c \cdot z - j \cdot y5\right)\right)} \]

   if 3.09999999999999988e-254 < y4 < 4.39999999999999953e-193

   1. Initial program 50.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 56.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 56.8%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 56.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 56.8%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 56.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 56.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 56.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 56.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 56.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y2 around inf 50.6%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(c \cdot x - k \cdot y5\right)\right)} \]

   7. Taylor expanded in c around 0 56.9%

      \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(-1 \cdot \left(k \cdot y5\right)\right)}\right) \]
   8. Step-by-step derivation

      1. neg-mul-1 56.9%

         \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(-k \cdot y5\right)}\right) \]

      2. distribute-rgt-neg-in 56.9%

         \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot \left(-y5\right)\right)}\right) \]

   9. Simplified 56.9%

      \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot \left(-y5\right)\right)}\right) \]

   if 0.014200000000000001 < y4

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 41.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 40.5%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -2.2 \cdot 10^{+158}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 3.1 \cdot 10^{-254}:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 4.4 \cdot 10^{-193}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 0.0142:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 21.6% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -1 \cdot 10^{+67}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -1.5 \cdot 10^{-261}:\\ \;\;\;\;\left(y1 \cdot y2\right) \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y4 \leq 2.02 \cdot 10^{-168}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 1.9 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \left(-x \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -1e+67)
   (* j (* y1 (* y3 (- y4))))
   (if (<= y4 -1.5e-261)
     (* (* y1 y2) (* x (- a)))
     (if (<= y4 2.02e-168)
       (* y0 (* y2 (* k (- y5))))
       (if (<= y4 1.9e-35) (* a (- (* x (* y1 y2)))) (* b (* j (* t y4))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1e+67) {
		tmp = j * (y1 * (y3 * -y4));
	} else if (y4 <= -1.5e-261) {
		tmp = (y1 * y2) * (x * -a);
	} else if (y4 <= 2.02e-168) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (y4 <= 1.9e-35) {
		tmp = a * -(x * (y1 * y2));
	} else {
		tmp = b * (j * (t * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y4 <= (-1d+67)) then
        tmp = j * (y1 * (y3 * -y4))
    else if (y4 <= (-1.5d-261)) then
        tmp = (y1 * y2) * (x * -a)
    else if (y4 <= 2.02d-168) then
        tmp = y0 * (y2 * (k * -y5))
    else if (y4 <= 1.9d-35) then
        tmp = a * -(x * (y1 * y2))
    else
        tmp = b * (j * (t * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1e+67) {
		tmp = j * (y1 * (y3 * -y4));
	} else if (y4 <= -1.5e-261) {
		tmp = (y1 * y2) * (x * -a);
	} else if (y4 <= 2.02e-168) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (y4 <= 1.9e-35) {
		tmp = a * -(x * (y1 * y2));
	} else {
		tmp = b * (j * (t * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y4 <= -1e+67:
		tmp = j * (y1 * (y3 * -y4))
	elif y4 <= -1.5e-261:
		tmp = (y1 * y2) * (x * -a)
	elif y4 <= 2.02e-168:
		tmp = y0 * (y2 * (k * -y5))
	elif y4 <= 1.9e-35:
		tmp = a * -(x * (y1 * y2))
	else:
		tmp = b * (j * (t * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -1e+67)
		tmp = Float64(j * Float64(y1 * Float64(y3 * Float64(-y4))));
	elseif (y4 <= -1.5e-261)
		tmp = Float64(Float64(y1 * y2) * Float64(x * Float64(-a)));
	elseif (y4 <= 2.02e-168)
		tmp = Float64(y0 * Float64(y2 * Float64(k * Float64(-y5))));
	elseif (y4 <= 1.9e-35)
		tmp = Float64(a * Float64(-Float64(x * Float64(y1 * y2))));
	else
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y4 <= -1e+67)
		tmp = j * (y1 * (y3 * -y4));
	elseif (y4 <= -1.5e-261)
		tmp = (y1 * y2) * (x * -a);
	elseif (y4 <= 2.02e-168)
		tmp = y0 * (y2 * (k * -y5));
	elseif (y4 <= 1.9e-35)
		tmp = a * -(x * (y1 * y2));
	else
		tmp = b * (j * (t * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -1e+67], N[(j * N[(y1 * N[(y3 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -1.5e-261], N[(N[(y1 * y2), $MachinePrecision] * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2.02e-168], N[(y0 * N[(y2 * N[(k * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.9e-35], N[(a * (-N[(x * N[(y1 * y2), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y4 < -9.99999999999999983e66

   1. Initial program 27.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 42.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 42.2%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 42.2%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 42.2%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around -inf 42.4%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 44.7%

         \[\leadsto \color{blue}{\left(y1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} \]

   8. Simplified 44.7%

      \[\leadsto \color{blue}{\left(y1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} \]

   9. Taylor expanded in k around 0 44.4%

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 44.4%

          \[\leadsto \color{blue}{-j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)} \]

       2. *-commutative 44.4%

          \[\leadsto -j \cdot \left(y1 \cdot \color{blue}{\left(y4 \cdot y3\right)}\right) \]

   11. Simplified 44.4%

       \[\leadsto \color{blue}{-j \cdot \left(y1 \cdot \left(y4 \cdot y3\right)\right)} \]

   if -9.99999999999999983e66 < y4 < -1.5e-261

   1. Initial program 43.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 46.3%

      \[\leadsto \left(\left(\left(\color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. associate-*r* 43.9%

         \[\leadsto \left(\left(\left(\color{blue}{\left(i \cdot y1\right) \cdot \left(j \cdot x - k \cdot z\right)} + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. *-commutative 43.9%

         \[\leadsto \left(\left(\left(\left(i \cdot y1\right) \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 43.9%

      \[\leadsto \left(\left(\left(\color{blue}{\left(i \cdot y1\right) \cdot \left(j \cdot x - z \cdot k\right)} + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in a around -inf 45.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 45.7%

         \[\leadsto \color{blue}{-a \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   8. Simplified 45.7%

      \[\leadsto \color{blue}{-a \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in x around inf 24.6%

      \[\leadsto -\color{blue}{a \cdot \left(x \cdot \left(y1 \cdot y2\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 25.7%

          \[\leadsto -\color{blue}{\left(a \cdot x\right) \cdot \left(y1 \cdot y2\right)} \]

       2. *-commutative 25.7%

          \[\leadsto -\left(a \cdot x\right) \cdot \color{blue}{\left(y2 \cdot y1\right)} \]

   11. Simplified 25.7%

       \[\leadsto -\color{blue}{\left(a \cdot x\right) \cdot \left(y2 \cdot y1\right)} \]

   if -1.5e-261 < y4 < 2.0199999999999999e-168

   1. Initial program 44.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 51.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 51.8%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 51.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 51.8%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 51.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 51.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 51.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 51.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 51.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y2 around inf 42.9%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(c \cdot x - k \cdot y5\right)\right)} \]

   7. Taylor expanded in c around 0 36.2%

      \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(-1 \cdot \left(k \cdot y5\right)\right)}\right) \]
   8. Step-by-step derivation

      1. neg-mul-1 36.2%

         \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(-k \cdot y5\right)}\right) \]

      2. distribute-rgt-neg-in 36.2%

         \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot \left(-y5\right)\right)}\right) \]

   9. Simplified 36.2%

      \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(k \cdot \left(-y5\right)\right)}\right) \]

   if 2.0199999999999999e-168 < y4 < 1.9000000000000001e-35

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 33.3%

      \[\leadsto \left(\left(\left(\color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. associate-*r* 33.3%

         \[\leadsto \left(\left(\left(\color{blue}{\left(i \cdot y1\right) \cdot \left(j \cdot x - k \cdot z\right)} + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. *-commutative 33.3%

         \[\leadsto \left(\left(\left(\left(i \cdot y1\right) \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 33.3%

      \[\leadsto \left(\left(\left(\color{blue}{\left(i \cdot y1\right) \cdot \left(j \cdot x - z \cdot k\right)} + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in a around -inf 52.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 52.2%

         \[\leadsto \color{blue}{-a \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   8. Simplified 52.2%

      \[\leadsto \color{blue}{-a \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in x around inf 41.7%

      \[\leadsto -\color{blue}{a \cdot \left(x \cdot \left(y1 \cdot y2\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 41.7%

          \[\leadsto -a \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \]

   11. Simplified 41.7%

       \[\leadsto -\color{blue}{a \cdot \left(x \cdot \left(y2 \cdot y1\right)\right)} \]

   if 1.9000000000000001e-35 < y4

   1. Initial program 35.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 41.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 39.2%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   5. Taylor expanded in j around inf 33.5%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 33.5%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   7. Simplified 33.5%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1 \cdot 10^{+67}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -1.5 \cdot 10^{-261}:\\ \;\;\;\;\left(y1 \cdot y2\right) \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y4 \leq 2.02 \cdot 10^{-168}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 1.9 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \left(-x \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 20.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y4 \cdot \left(t \cdot j\right)\right)\\ \mathbf{if}\;j \leq -1 \cdot 10^{+206}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -2 \cdot 10^{+62}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-201}:\\ \;\;\;\;a \cdot \left(-x \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{-56}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y4 (* t j)))))
   (if (<= j -1e+206)
     t_1
     (if (<= j -2e+62)
       (* c (* x (* y0 y2)))
       (if (<= j -6e-201)
         (* a (- (* x (* y1 y2))))
         (if (<= j 1.85e-56) (* a (* y1 (* z y3))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y4 * (t * j));
	double tmp;
	if (j <= -1e+206) {
		tmp = t_1;
	} else if (j <= -2e+62) {
		tmp = c * (x * (y0 * y2));
	} else if (j <= -6e-201) {
		tmp = a * -(x * (y1 * y2));
	} else if (j <= 1.85e-56) {
		tmp = a * (y1 * (z * y3));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (y4 * (t * j))
    if (j <= (-1d+206)) then
        tmp = t_1
    else if (j <= (-2d+62)) then
        tmp = c * (x * (y0 * y2))
    else if (j <= (-6d-201)) then
        tmp = a * -(x * (y1 * y2))
    else if (j <= 1.85d-56) then
        tmp = a * (y1 * (z * y3))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y4 * (t * j));
	double tmp;
	if (j <= -1e+206) {
		tmp = t_1;
	} else if (j <= -2e+62) {
		tmp = c * (x * (y0 * y2));
	} else if (j <= -6e-201) {
		tmp = a * -(x * (y1 * y2));
	} else if (j <= 1.85e-56) {
		tmp = a * (y1 * (z * y3));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (y4 * (t * j))
	tmp = 0
	if j <= -1e+206:
		tmp = t_1
	elif j <= -2e+62:
		tmp = c * (x * (y0 * y2))
	elif j <= -6e-201:
		tmp = a * -(x * (y1 * y2))
	elif j <= 1.85e-56:
		tmp = a * (y1 * (z * y3))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(y4 * Float64(t * j)))
	tmp = 0.0
	if (j <= -1e+206)
		tmp = t_1;
	elseif (j <= -2e+62)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (j <= -6e-201)
		tmp = Float64(a * Float64(-Float64(x * Float64(y1 * y2))));
	elseif (j <= 1.85e-56)
		tmp = Float64(a * Float64(y1 * Float64(z * y3)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (y4 * (t * j));
	tmp = 0.0;
	if (j <= -1e+206)
		tmp = t_1;
	elseif (j <= -2e+62)
		tmp = c * (x * (y0 * y2));
	elseif (j <= -6e-201)
		tmp = a * -(x * (y1 * y2));
	elseif (j <= 1.85e-56)
		tmp = a * (y1 * (z * y3));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(y4 * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1e+206], t$95$1, If[LessEqual[j, -2e+62], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6e-201], N[(a * (-N[(x * N[(y1 * y2), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], If[LessEqual[j, 1.85e-56], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1e206 or 1.8500000000000001e-56 < j

   1. Initial program 32.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 38.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 36.1%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   5. Taylor expanded in j around inf 34.3%

      \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t\right)}\right) \]

   if -1e206 < j < -2.00000000000000007e62

   1. Initial program 26.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 66.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 66.2%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 66.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 66.2%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 66.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 66.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 66.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 66.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 66.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y2 around inf 40.1%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(c \cdot x - k \cdot y5\right)\right)} \]

   7. Taylor expanded in c around inf 37.7%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if -2.00000000000000007e62 < j < -6.00000000000000004e-201

   1. Initial program 37.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 50.3%

      \[\leadsto \left(\left(\left(\color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. associate-*r* 52.2%

         \[\leadsto \left(\left(\left(\color{blue}{\left(i \cdot y1\right) \cdot \left(j \cdot x - k \cdot z\right)} + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. *-commutative 52.2%

         \[\leadsto \left(\left(\left(\left(i \cdot y1\right) \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 52.2%

      \[\leadsto \left(\left(\left(\color{blue}{\left(i \cdot y1\right) \cdot \left(j \cdot x - z \cdot k\right)} + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in a around -inf 55.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 55.5%

         \[\leadsto \color{blue}{-a \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   8. Simplified 55.5%

      \[\leadsto \color{blue}{-a \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in x around inf 27.9%

      \[\leadsto -\color{blue}{a \cdot \left(x \cdot \left(y1 \cdot y2\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 27.9%

          \[\leadsto -a \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \]

   11. Simplified 27.9%

       \[\leadsto -\color{blue}{a \cdot \left(x \cdot \left(y2 \cdot y1\right)\right)} \]

   if -6.00000000000000004e-201 < j < 1.8500000000000001e-56

   1. Initial program 48.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 42.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 42.7%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 42.7%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 42.7%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 42.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 42.7%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 42.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 42.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 42.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 42.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 42.7%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in z around -inf 39.8%

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]

   7. Taylor expanded in a around inf 33.6%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 33.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1 \cdot 10^{+206}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -2 \cdot 10^{+62}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-201}:\\ \;\;\;\;a \cdot \left(-x \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{-56}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 20.5% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y4 \cdot \left(t \cdot j\right)\right)\\ \mathbf{if}\;j \leq -7.2 \cdot 10^{+205}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.25 \cdot 10^{+32}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{-56}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* y4 (* t j)))))
   (if (<= j -7.2e+205)
     t_1
     (if (<= j -1.25e+32)
       (* c (* x (* y0 y2)))
       (if (<= j 1.45e-56) (* a (* y1 (* z y3))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y4 * (t * j));
	double tmp;
	if (j <= -7.2e+205) {
		tmp = t_1;
	} else if (j <= -1.25e+32) {
		tmp = c * (x * (y0 * y2));
	} else if (j <= 1.45e-56) {
		tmp = a * (y1 * (z * y3));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (y4 * (t * j))
    if (j <= (-7.2d+205)) then
        tmp = t_1
    else if (j <= (-1.25d+32)) then
        tmp = c * (x * (y0 * y2))
    else if (j <= 1.45d-56) then
        tmp = a * (y1 * (z * y3))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (y4 * (t * j));
	double tmp;
	if (j <= -7.2e+205) {
		tmp = t_1;
	} else if (j <= -1.25e+32) {
		tmp = c * (x * (y0 * y2));
	} else if (j <= 1.45e-56) {
		tmp = a * (y1 * (z * y3));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (y4 * (t * j))
	tmp = 0
	if j <= -7.2e+205:
		tmp = t_1
	elif j <= -1.25e+32:
		tmp = c * (x * (y0 * y2))
	elif j <= 1.45e-56:
		tmp = a * (y1 * (z * y3))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(y4 * Float64(t * j)))
	tmp = 0.0
	if (j <= -7.2e+205)
		tmp = t_1;
	elseif (j <= -1.25e+32)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (j <= 1.45e-56)
		tmp = Float64(a * Float64(y1 * Float64(z * y3)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (y4 * (t * j));
	tmp = 0.0;
	if (j <= -7.2e+205)
		tmp = t_1;
	elseif (j <= -1.25e+32)
		tmp = c * (x * (y0 * y2));
	elseif (j <= 1.45e-56)
		tmp = a * (y1 * (z * y3));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(y4 * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7.2e+205], t$95$1, If[LessEqual[j, -1.25e+32], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.45e-56], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -7.20000000000000003e205 or 1.44999999999999996e-56 < j

   1. Initial program 32.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 38.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 36.1%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   5. Taylor expanded in j around inf 34.3%

      \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t\right)}\right) \]

   if -7.20000000000000003e205 < j < -1.2499999999999999e32

   1. Initial program 26.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 59.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 59.5%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 59.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 59.5%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 59.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 59.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 59.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 59.5%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 59.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y2 around inf 35.7%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(c \cdot x - k \cdot y5\right)\right)} \]

   7. Taylor expanded in c around inf 33.7%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if -1.2499999999999999e32 < j < 1.44999999999999996e-56

   1. Initial program 45.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 43.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 43.9%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 43.9%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 43.9%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 43.9%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 43.9%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 43.9%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 43.9%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 43.9%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 43.9%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 43.9%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in z around -inf 36.7%

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]

   7. Taylor expanded in a around inf 25.7%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 30.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.2 \cdot 10^{+205}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -1.25 \cdot 10^{+32}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{-56}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 21.4% accurate, 5.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -2 \cdot 10^{+68}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 7.2 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \left(-x \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -2e+68)
   (* j (* y1 (* y3 (- y4))))
   (if (<= y4 7.2e-40) (* a (- (* x (* y1 y2)))) (* b (* j (* t y4))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -2e+68) {
		tmp = j * (y1 * (y3 * -y4));
	} else if (y4 <= 7.2e-40) {
		tmp = a * -(x * (y1 * y2));
	} else {
		tmp = b * (j * (t * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y4 <= (-2d+68)) then
        tmp = j * (y1 * (y3 * -y4))
    else if (y4 <= 7.2d-40) then
        tmp = a * -(x * (y1 * y2))
    else
        tmp = b * (j * (t * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -2e+68) {
		tmp = j * (y1 * (y3 * -y4));
	} else if (y4 <= 7.2e-40) {
		tmp = a * -(x * (y1 * y2));
	} else {
		tmp = b * (j * (t * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y4 <= -2e+68:
		tmp = j * (y1 * (y3 * -y4))
	elif y4 <= 7.2e-40:
		tmp = a * -(x * (y1 * y2))
	else:
		tmp = b * (j * (t * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -2e+68)
		tmp = Float64(j * Float64(y1 * Float64(y3 * Float64(-y4))));
	elseif (y4 <= 7.2e-40)
		tmp = Float64(a * Float64(-Float64(x * Float64(y1 * y2))));
	else
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y4 <= -2e+68)
		tmp = j * (y1 * (y3 * -y4));
	elseif (y4 <= 7.2e-40)
		tmp = a * -(x * (y1 * y2));
	else
		tmp = b * (j * (t * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -2e+68], N[(j * N[(y1 * N[(y3 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 7.2e-40], N[(a * (-N[(x * N[(y1 * y2), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y4 < -1.99999999999999991e68

   1. Initial program 27.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 42.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 42.2%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 42.2%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 42.2%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around -inf 42.4%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 44.7%

         \[\leadsto \color{blue}{\left(y1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} \]

   8. Simplified 44.7%

      \[\leadsto \color{blue}{\left(y1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)} \]

   9. Taylor expanded in k around 0 44.4%

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 44.4%

          \[\leadsto \color{blue}{-j \cdot \left(y1 \cdot \left(y3 \cdot y4\right)\right)} \]

       2. *-commutative 44.4%

          \[\leadsto -j \cdot \left(y1 \cdot \color{blue}{\left(y4 \cdot y3\right)}\right) \]

   11. Simplified 44.4%

       \[\leadsto \color{blue}{-j \cdot \left(y1 \cdot \left(y4 \cdot y3\right)\right)} \]

   if -1.99999999999999991e68 < y4 < 7.2e-40

   1. Initial program 39.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around inf 44.7%

      \[\leadsto \left(\left(\left(\color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   4. Step-by-step derivation

      1. associate-*r* 43.4%

         \[\leadsto \left(\left(\left(\color{blue}{\left(i \cdot y1\right) \cdot \left(j \cdot x - k \cdot z\right)} + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. *-commutative 43.4%

         \[\leadsto \left(\left(\left(\left(i \cdot y1\right) \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Simplified 43.4%

      \[\leadsto \left(\left(\left(\color{blue}{\left(i \cdot y1\right) \cdot \left(j \cdot x - z \cdot k\right)} + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   6. Taylor expanded in a around -inf 44.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 44.7%

         \[\leadsto \color{blue}{-a \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   8. Simplified 44.7%

      \[\leadsto \color{blue}{-a \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   9. Taylor expanded in x around inf 25.1%

      \[\leadsto -\color{blue}{a \cdot \left(x \cdot \left(y1 \cdot y2\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 25.1%

          \[\leadsto -a \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \]

   11. Simplified 25.1%

       \[\leadsto -\color{blue}{a \cdot \left(x \cdot \left(y2 \cdot y1\right)\right)} \]

   if 7.2e-40 < y4

   1. Initial program 35.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 41.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 39.2%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   5. Taylor expanded in j around inf 33.5%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 33.5%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   7. Simplified 33.5%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 30.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -2 \cdot 10^{+68}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 7.2 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \left(-x \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 21.3% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -4.1 \cdot 10^{+74} \lor \neg \left(j \leq 1.3 \cdot 10^{-56}\right):\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= j -4.1e+74) (not (<= j 1.3e-56)))
   (* b (* y4 (* t j)))
   (* a (* y1 (* z y3)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((j <= -4.1e+74) || !(j <= 1.3e-56)) {
		tmp = b * (y4 * (t * j));
	} else {
		tmp = a * (y1 * (z * y3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((j <= (-4.1d+74)) .or. (.not. (j <= 1.3d-56))) then
        tmp = b * (y4 * (t * j))
    else
        tmp = a * (y1 * (z * y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((j <= -4.1e+74) || !(j <= 1.3e-56)) {
		tmp = b * (y4 * (t * j));
	} else {
		tmp = a * (y1 * (z * y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (j <= -4.1e+74) or not (j <= 1.3e-56):
		tmp = b * (y4 * (t * j))
	else:
		tmp = a * (y1 * (z * y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((j <= -4.1e+74) || !(j <= 1.3e-56))
		tmp = Float64(b * Float64(y4 * Float64(t * j)));
	else
		tmp = Float64(a * Float64(y1 * Float64(z * y3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((j <= -4.1e+74) || ~((j <= 1.3e-56)))
		tmp = b * (y4 * (t * j));
	else
		tmp = a * (y1 * (z * y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[j, -4.1e+74], N[Not[LessEqual[j, 1.3e-56]], $MachinePrecision]], N[(b * N[(y4 * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -4.1e74 or 1.29999999999999998e-56 < j

   1. Initial program 31.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 37.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 33.5%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   5. Taylor expanded in j around inf 30.7%

      \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t\right)}\right) \]

   if -4.1e74 < j < 1.29999999999999998e-56

   1. Initial program 42.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 43.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 43.1%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 43.1%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 43.1%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 43.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 43.1%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 43.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 43.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 43.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 43.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 43.1%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in z around -inf 34.5%

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]

   7. Taylor expanded in a around inf 23.5%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 27.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.1 \cdot 10^{+74} \lor \neg \left(j \leq 1.3 \cdot 10^{-56}\right):\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 19.4% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -1.36 \cdot 10^{+237} \lor \neg \left(y1 \leq 2.6 \cdot 10^{-57}\right):\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y1 -1.36e+237) (not (<= y1 2.6e-57)))
   (* a (* y1 (* z y3)))
   (* b (* j (* t y4)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y1 <= -1.36e+237) || !(y1 <= 2.6e-57)) {
		tmp = a * (y1 * (z * y3));
	} else {
		tmp = b * (j * (t * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y1 <= (-1.36d+237)) .or. (.not. (y1 <= 2.6d-57))) then
        tmp = a * (y1 * (z * y3))
    else
        tmp = b * (j * (t * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y1 <= -1.36e+237) || !(y1 <= 2.6e-57)) {
		tmp = a * (y1 * (z * y3));
	} else {
		tmp = b * (j * (t * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y1 <= -1.36e+237) or not (y1 <= 2.6e-57):
		tmp = a * (y1 * (z * y3))
	else:
		tmp = b * (j * (t * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y1 <= -1.36e+237) || !(y1 <= 2.6e-57))
		tmp = Float64(a * Float64(y1 * Float64(z * y3)));
	else
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y1 <= -1.36e+237) || ~((y1 <= 2.6e-57)))
		tmp = a * (y1 * (z * y3));
	else
		tmp = b * (j * (t * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y1, -1.36e+237], N[Not[LessEqual[y1, 2.6e-57]], $MachinePrecision]], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y1 < -1.36000000000000003e237 or 2.59999999999999985e-57 < y1

   1. Initial program 29.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 52.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 52.8%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 52.8%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 52.8%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 52.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 52.8%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 52.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 52.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 52.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 52.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 52.8%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in z around -inf 38.7%

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]

   7. Taylor expanded in a around inf 32.2%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

   if -1.36000000000000003e237 < y1 < 2.59999999999999985e-57

   1. Initial program 40.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 42.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 30.5%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   5. Taylor expanded in j around inf 24.2%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 24.2%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   7. Simplified 24.2%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 26.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.36 \cdot 10^{+237} \lor \neg \left(y1 \leq 2.6 \cdot 10^{-57}\right):\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 17.4% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* y1 (* z y3))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y1 * (z * y3));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * (y1 * (z * y3))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y1 * (z * y3));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (y1 * (z * y3))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(y1 * Float64(z * y3)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (y1 * (z * y3));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 36.8%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Add Preprocessing

3. Taylor expanded in y1 around -inf 38.7%

   \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
4. Step-by-step derivation

   1. associate-*r* 38.7%

      \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   2. neg-mul-1 38.7%

      \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   3. +-commutative 38.7%

      \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   4. mul-1-neg 38.7%

      \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   5. unsub-neg 38.7%

      \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   6. *-commutative 38.7%

      \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   7. *-commutative 38.7%

      \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   8. *-commutative 38.7%

      \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   9. *-commutative 38.7%

      \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

5. Simplified 38.7%

   \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

6. Taylor expanded in z around -inf 25.6%

   \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]

7. Taylor expanded in a around inf 17.6%

   \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

8. Final simplification 17.6%

   \[\leadsto a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right) \]
9. Add Preprocessing

Developer target: 28.7% 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 2024108 
(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)))))