Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.6% → 43.1%

Time: 1.9min

Alternatives: 32

Speedup: 2.3×

• 89.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 30.6% 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: 43.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot y1 - c \cdot y0\\ t_2 := x \cdot y - z \cdot t\\ t_3 := y1 \cdot y4 - y0 \cdot y5\\ t_4 := b \cdot y0 - i \cdot y1\\ t_5 := k \cdot \left(\left(y2 \cdot t\_3 - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot t\_4\right)\\ t_6 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_7 := t \cdot j - y \cdot k\\ t_8 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot t\_2 + y5 \cdot t\_7\right)\right)\\ \mathbf{if}\;k \leq -1.4 \cdot 10^{+173}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;k \leq -3.1 \cdot 10^{-26}:\\ \;\;\;\;t\_8\\ \mathbf{elif}\;k \leq -2.4 \cdot 10^{-120}:\\ \;\;\;\;z \cdot \left(k \cdot t\_4 + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot t\_1\right)\right)\\ \mathbf{elif}\;k \leq -1.02 \cdot 10^{-230}:\\ \;\;\;\;t\_8\\ \mathbf{elif}\;k \leq 3.5 \cdot 10^{-251}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;k \leq 3.8 \cdot 10^{-184}:\\ \;\;\;\;b \cdot \left(\left(a \cdot t\_2 + y4 \cdot t\_7\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;k \leq 2.1 \cdot 10^{-30}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;k \leq 1960000000000:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(z \cdot t\_1 - j \cdot t\_3\right)\right)\\ \mathbf{elif}\;k \leq 4.8 \cdot 10^{+122}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a y1) (* c y0)))
        (t_2 (- (* x y) (* z t)))
        (t_3 (- (* y1 y4) (* y0 y5)))
        (t_4 (- (* b y0) (* i y1)))
        (t_5 (* k (+ (- (* y2 t_3) (* y (- (* b y4) (* i y5)))) (* z t_4))))
        (t_6
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
           (* j (- (* i y1) (* b y0))))))
        (t_7 (- (* t j) (* y k)))
        (t_8 (* i (- (* y1 (- (* x j) (* z k))) (+ (* c t_2) (* y5 t_7))))))
   (if (<= k -1.4e+173)
     t_5
     (if (<= k -3.1e-26)
       t_8
       (if (<= k -2.4e-120)
         (* z (+ (* k t_4) (+ (* t (- (* c i) (* a b))) (* y3 t_1))))
         (if (<= k -1.02e-230)
           t_8
           (if (<= k 3.5e-251)
             t_6
             (if (<= k 3.8e-184)
               (* b (+ (+ (* a t_2) (* y4 t_7)) (* y0 (- (* z k) (* x j)))))
               (if (<= k 2.1e-30)
                 t_6
                 (if (<= k 1960000000000.0)
                   (*
                    y3
                    (+ (* y (- (* c y4) (* a y5))) (- (* z t_1) (* j t_3))))
                   (if (<= k 4.8e+122)
                     (* i (* y5 (- (* y k) (* t j))))
                     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 = (a * y1) - (c * y0);
	double t_2 = (x * y) - (z * t);
	double t_3 = (y1 * y4) - (y0 * y5);
	double t_4 = (b * y0) - (i * y1);
	double t_5 = k * (((y2 * t_3) - (y * ((b * y4) - (i * y5)))) + (z * t_4));
	double t_6 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double t_7 = (t * j) - (y * k);
	double t_8 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_2) + (y5 * t_7)));
	double tmp;
	if (k <= -1.4e+173) {
		tmp = t_5;
	} else if (k <= -3.1e-26) {
		tmp = t_8;
	} else if (k <= -2.4e-120) {
		tmp = z * ((k * t_4) + ((t * ((c * i) - (a * b))) + (y3 * t_1)));
	} else if (k <= -1.02e-230) {
		tmp = t_8;
	} else if (k <= 3.5e-251) {
		tmp = t_6;
	} else if (k <= 3.8e-184) {
		tmp = b * (((a * t_2) + (y4 * t_7)) + (y0 * ((z * k) - (x * j))));
	} else if (k <= 2.1e-30) {
		tmp = t_6;
	} else if (k <= 1960000000000.0) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((z * t_1) - (j * t_3)));
	} else if (k <= 4.8e+122) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} 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) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_1 = (a * y1) - (c * y0)
    t_2 = (x * y) - (z * t)
    t_3 = (y1 * y4) - (y0 * y5)
    t_4 = (b * y0) - (i * y1)
    t_5 = k * (((y2 * t_3) - (y * ((b * y4) - (i * y5)))) + (z * t_4))
    t_6 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    t_7 = (t * j) - (y * k)
    t_8 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_2) + (y5 * t_7)))
    if (k <= (-1.4d+173)) then
        tmp = t_5
    else if (k <= (-3.1d-26)) then
        tmp = t_8
    else if (k <= (-2.4d-120)) then
        tmp = z * ((k * t_4) + ((t * ((c * i) - (a * b))) + (y3 * t_1)))
    else if (k <= (-1.02d-230)) then
        tmp = t_8
    else if (k <= 3.5d-251) then
        tmp = t_6
    else if (k <= 3.8d-184) then
        tmp = b * (((a * t_2) + (y4 * t_7)) + (y0 * ((z * k) - (x * j))))
    else if (k <= 2.1d-30) then
        tmp = t_6
    else if (k <= 1960000000000.0d0) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((z * t_1) - (j * t_3)))
    else if (k <= 4.8d+122) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    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 = (a * y1) - (c * y0);
	double t_2 = (x * y) - (z * t);
	double t_3 = (y1 * y4) - (y0 * y5);
	double t_4 = (b * y0) - (i * y1);
	double t_5 = k * (((y2 * t_3) - (y * ((b * y4) - (i * y5)))) + (z * t_4));
	double t_6 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double t_7 = (t * j) - (y * k);
	double t_8 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_2) + (y5 * t_7)));
	double tmp;
	if (k <= -1.4e+173) {
		tmp = t_5;
	} else if (k <= -3.1e-26) {
		tmp = t_8;
	} else if (k <= -2.4e-120) {
		tmp = z * ((k * t_4) + ((t * ((c * i) - (a * b))) + (y3 * t_1)));
	} else if (k <= -1.02e-230) {
		tmp = t_8;
	} else if (k <= 3.5e-251) {
		tmp = t_6;
	} else if (k <= 3.8e-184) {
		tmp = b * (((a * t_2) + (y4 * t_7)) + (y0 * ((z * k) - (x * j))));
	} else if (k <= 2.1e-30) {
		tmp = t_6;
	} else if (k <= 1960000000000.0) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((z * t_1) - (j * t_3)));
	} else if (k <= 4.8e+122) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} 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 = (a * y1) - (c * y0)
	t_2 = (x * y) - (z * t)
	t_3 = (y1 * y4) - (y0 * y5)
	t_4 = (b * y0) - (i * y1)
	t_5 = k * (((y2 * t_3) - (y * ((b * y4) - (i * y5)))) + (z * t_4))
	t_6 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	t_7 = (t * j) - (y * k)
	t_8 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_2) + (y5 * t_7)))
	tmp = 0
	if k <= -1.4e+173:
		tmp = t_5
	elif k <= -3.1e-26:
		tmp = t_8
	elif k <= -2.4e-120:
		tmp = z * ((k * t_4) + ((t * ((c * i) - (a * b))) + (y3 * t_1)))
	elif k <= -1.02e-230:
		tmp = t_8
	elif k <= 3.5e-251:
		tmp = t_6
	elif k <= 3.8e-184:
		tmp = b * (((a * t_2) + (y4 * t_7)) + (y0 * ((z * k) - (x * j))))
	elif k <= 2.1e-30:
		tmp = t_6
	elif k <= 1960000000000.0:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((z * t_1) - (j * t_3)))
	elif k <= 4.8e+122:
		tmp = i * (y5 * ((y * k) - (t * j)))
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(a * y1) - Float64(c * y0))
	t_2 = Float64(Float64(x * y) - Float64(z * t))
	t_3 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_4 = Float64(Float64(b * y0) - Float64(i * y1))
	t_5 = Float64(k * Float64(Float64(Float64(y2 * t_3) - Float64(y * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(z * t_4)))
	t_6 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_7 = Float64(Float64(t * j) - Float64(y * k))
	t_8 = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) - Float64(Float64(c * t_2) + Float64(y5 * t_7))))
	tmp = 0.0
	if (k <= -1.4e+173)
		tmp = t_5;
	elseif (k <= -3.1e-26)
		tmp = t_8;
	elseif (k <= -2.4e-120)
		tmp = Float64(z * Float64(Float64(k * t_4) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) + Float64(y3 * t_1))));
	elseif (k <= -1.02e-230)
		tmp = t_8;
	elseif (k <= 3.5e-251)
		tmp = t_6;
	elseif (k <= 3.8e-184)
		tmp = Float64(b * Float64(Float64(Float64(a * t_2) + Float64(y4 * t_7)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (k <= 2.1e-30)
		tmp = t_6;
	elseif (k <= 1960000000000.0)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(z * t_1) - Float64(j * t_3))));
	elseif (k <= 4.8e+122)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	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 = (a * y1) - (c * y0);
	t_2 = (x * y) - (z * t);
	t_3 = (y1 * y4) - (y0 * y5);
	t_4 = (b * y0) - (i * y1);
	t_5 = k * (((y2 * t_3) - (y * ((b * y4) - (i * y5)))) + (z * t_4));
	t_6 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	t_7 = (t * j) - (y * k);
	t_8 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_2) + (y5 * t_7)));
	tmp = 0.0;
	if (k <= -1.4e+173)
		tmp = t_5;
	elseif (k <= -3.1e-26)
		tmp = t_8;
	elseif (k <= -2.4e-120)
		tmp = z * ((k * t_4) + ((t * ((c * i) - (a * b))) + (y3 * t_1)));
	elseif (k <= -1.02e-230)
		tmp = t_8;
	elseif (k <= 3.5e-251)
		tmp = t_6;
	elseif (k <= 3.8e-184)
		tmp = b * (((a * t_2) + (y4 * t_7)) + (y0 * ((z * k) - (x * j))));
	elseif (k <= 2.1e-30)
		tmp = t_6;
	elseif (k <= 1960000000000.0)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((z * t_1) - (j * t_3)));
	elseif (k <= 4.8e+122)
		tmp = i * (y5 * ((y * k) - (t * j)));
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(k * N[(N[(N[(y2 * t$95$3), $MachinePrecision] - N[(y * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(c * t$95$2), $MachinePrecision] + N[(y5 * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -1.4e+173], t$95$5, If[LessEqual[k, -3.1e-26], t$95$8, If[LessEqual[k, -2.4e-120], N[(z * N[(N[(k * t$95$4), $MachinePrecision] + N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.02e-230], t$95$8, If[LessEqual[k, 3.5e-251], t$95$6, If[LessEqual[k, 3.8e-184], N[(b * N[(N[(N[(a * t$95$2), $MachinePrecision] + N[(y4 * t$95$7), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.1e-30], t$95$6, If[LessEqual[k, 1960000000000.0], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * t$95$1), $MachinePrecision] - N[(j * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.8e+122], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if k < -1.39999999999999991e173 or 4.8000000000000004e122 < k

   1. Initial program 26.4%

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

   3. Taylor expanded in k around inf 61.5%

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

      1. sub-neg 61.5%

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

      2. +-commutative 61.5%

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

      3. mul-1-neg 61.5%

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

      4. unsub-neg 61.5%

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

      5. *-commutative 61.5%

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

      6. mul-1-neg 61.5%

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

      7. remove-double-neg 61.5%

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

   5. Simplified 61.5%

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

   if -1.39999999999999991e173 < k < -3.09999999999999983e-26 or -2.3999999999999999e-120 < k < -1.02e-230

   1. Initial program 25.6%

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

   3. Taylor expanded in i around -inf 59.8%

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

   if -3.09999999999999983e-26 < k < -2.3999999999999999e-120

   1. Initial program 29.2%

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

   3. Taylor expanded in z around -inf 52.9%

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

   if -1.02e-230 < k < 3.50000000000000034e-251 or 3.80000000000000017e-184 < k < 2.1000000000000002e-30

   1. Initial program 39.4%

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

   3. Taylor expanded in x around inf 62.8%

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

   if 3.50000000000000034e-251 < k < 3.80000000000000017e-184

   1. Initial program 34.0%

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

   3. Taylor expanded in b around inf 74.3%

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

   if 2.1000000000000002e-30 < k < 1.96e12

   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 y3 around -inf 66.9%

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

   if 1.96e12 < k < 4.8000000000000004e122

   1. Initial program 29.8%

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

   3. Taylor expanded in y5 around -inf 64.7%

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

   4. Taylor expanded in i around inf 82.5%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.4 \cdot 10^{+173}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -3.1 \cdot 10^{-26}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot \left(x \cdot y - z \cdot t\right) + y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;k \leq -2.4 \cdot 10^{-120}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;k \leq -1.02 \cdot 10^{-230}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot \left(x \cdot y - z \cdot t\right) + y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;k \leq 3.5 \cdot 10^{-251}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 3.8 \cdot 10^{-184}:\\ \;\;\;\;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}\;k \leq 2.1 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 1960000000000:\\ \;\;\;\;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(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)\\ \mathbf{elif}\;k \leq 4.8 \cdot 10^{+122}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 53.2% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a y1) (* c y0)))
        (t_2
         (+
          (+
           (-
            (* (- (* b y4) (* i y5)) (- (* t j) (* y k)))
            (-
             (* (- (* x y2) (* z y3)) t_1)
             (-
              (* (- (* a b) (* c i)) (- (* x y) (* z t)))
              (* (- (* i y1) (* b y0)) (- (* z k) (* x j))))))
           (* (- (* t y2) (* y y3)) (- (* a y5) (* c y4))))
          (* (- (* y1 y4) (* y0 y5)) (- (* k y2) (* j y3))))))
   (if (<= t_2 INFINITY)
     t_2
     (*
      z
      (+
       (* k (- (* b y0) (* i y1)))
       (+ (* t (- (* c i) (* a b))) (* 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 = (a * y1) - (c * y0);
	double t_2 = (((((b * y4) - (i * y5)) * ((t * j) - (y * k))) - ((((x * y2) - (z * y3)) * t_1) - ((((a * b) - (c * i)) * ((x * y) - (z * t))) - (((i * y1) - (b * y0)) * ((z * k) - (x * j)))))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (((y1 * y4) - (y0 * y5)) * ((k * y2) - (j * y3)));
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * 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 = (a * y1) - (c * y0);
	double t_2 = (((((b * y4) - (i * y5)) * ((t * j) - (y * k))) - ((((x * y2) - (z * y3)) * t_1) - ((((a * b) - (c * i)) * ((x * y) - (z * t))) - (((i * y1) - (b * y0)) * ((z * k) - (x * j)))))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (((y1 * y4) - (y0 * y5)) * ((k * y2) - (j * y3)));
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((t * ((c * i) - (a * b))) + (y3 * t_1)));
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 89.1%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around -inf 39.4%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.3%

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

Alternative 3: 35.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot i\right) \cdot \left(k \cdot y5 - x \cdot c\right)\\ t_2 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;y1 \leq -4.7 \cdot 10^{+83}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -8.6 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -3.5 \cdot 10^{-179}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y1 \leq -2.4 \cdot 10^{-208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -3.6 \cdot 10^{-212}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y1 \leq 1.35 \cdot 10^{-254}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 7.6 \cdot 10^{-215}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 5.7 \cdot 10^{-185}:\\ \;\;\;\;\left(k \cdot y0\right) \cdot \left(z \cdot b - y2 \cdot y5\right)\\ \mathbf{elif}\;y1 \leq 3.5 \cdot 10^{-134}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq 3 \cdot 10^{-92}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 9.2 \cdot 10^{+36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y1 \leq 1.65 \cdot 10^{+190}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* y i) (- (* k y5) (* x c))))
        (t_2
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j)))))))
   (if (<= y1 -4.7e+83)
     (* k (* y1 (- (* y2 y4) (* z i))))
     (if (<= y1 -8.6e-56)
       t_1
       (if (<= y1 -3.5e-179)
         t_2
         (if (<= y1 -2.4e-208)
           t_1
           (if (<= y1 -3.6e-212)
             t_2
             (if (<= y1 1.35e-254)
               (* c (* y0 (- (* x y2) (* z y3))))
               (if (<= y1 7.6e-215)
                 (* b (* x (- (* y a) (* j y0))))
                 (if (<= y1 5.7e-185)
                   (* (* k y0) (- (* z b) (* y2 y5)))
                   (if (<= y1 3.5e-134)
                     (* x (* y (- (* a b) (* c i))))
                     (if (<= y1 3e-92)
                       (* i (* y5 (- (* y k) (* t j))))
                       (if (<= y1 9.2e+36)
                         t_2
                         (if (<= y1 1.65e+190)
                           (*
                            j
                            (+
                             (+
                              (* t (- (* b y4) (* i y5)))
                              (* y3 (- (* y0 y5) (* y1 y4))))
                             (* x (- (* i y1) (* b y0)))))
                           (* x (* y2 (- (* c y0) (* a y1))))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * i) * ((k * y5) - (x * c));
	double t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (y1 <= -4.7e+83) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (y1 <= -8.6e-56) {
		tmp = t_1;
	} else if (y1 <= -3.5e-179) {
		tmp = t_2;
	} else if (y1 <= -2.4e-208) {
		tmp = t_1;
	} else if (y1 <= -3.6e-212) {
		tmp = t_2;
	} else if (y1 <= 1.35e-254) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (y1 <= 7.6e-215) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y1 <= 5.7e-185) {
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	} else if (y1 <= 3.5e-134) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y1 <= 3e-92) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y1 <= 9.2e+36) {
		tmp = t_2;
	} else if (y1 <= 1.65e+190) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	} else {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * i) * ((k * y5) - (x * c))
    t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    if (y1 <= (-4.7d+83)) then
        tmp = k * (y1 * ((y2 * y4) - (z * i)))
    else if (y1 <= (-8.6d-56)) then
        tmp = t_1
    else if (y1 <= (-3.5d-179)) then
        tmp = t_2
    else if (y1 <= (-2.4d-208)) then
        tmp = t_1
    else if (y1 <= (-3.6d-212)) then
        tmp = t_2
    else if (y1 <= 1.35d-254) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (y1 <= 7.6d-215) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y1 <= 5.7d-185) then
        tmp = (k * y0) * ((z * b) - (y2 * y5))
    else if (y1 <= 3.5d-134) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y1 <= 3d-92) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (y1 <= 9.2d+36) then
        tmp = t_2
    else if (y1 <= 1.65d+190) then
        tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
    else
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * i) * ((k * y5) - (x * c));
	double t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (y1 <= -4.7e+83) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (y1 <= -8.6e-56) {
		tmp = t_1;
	} else if (y1 <= -3.5e-179) {
		tmp = t_2;
	} else if (y1 <= -2.4e-208) {
		tmp = t_1;
	} else if (y1 <= -3.6e-212) {
		tmp = t_2;
	} else if (y1 <= 1.35e-254) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (y1 <= 7.6e-215) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y1 <= 5.7e-185) {
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	} else if (y1 <= 3.5e-134) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y1 <= 3e-92) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y1 <= 9.2e+36) {
		tmp = t_2;
	} else if (y1 <= 1.65e+190) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	} else {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y * i) * ((k * y5) - (x * c))
	t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	tmp = 0
	if y1 <= -4.7e+83:
		tmp = k * (y1 * ((y2 * y4) - (z * i)))
	elif y1 <= -8.6e-56:
		tmp = t_1
	elif y1 <= -3.5e-179:
		tmp = t_2
	elif y1 <= -2.4e-208:
		tmp = t_1
	elif y1 <= -3.6e-212:
		tmp = t_2
	elif y1 <= 1.35e-254:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif y1 <= 7.6e-215:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y1 <= 5.7e-185:
		tmp = (k * y0) * ((z * b) - (y2 * y5))
	elif y1 <= 3.5e-134:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y1 <= 3e-92:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif y1 <= 9.2e+36:
		tmp = t_2
	elif y1 <= 1.65e+190:
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
	else:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * i) * Float64(Float64(k * y5) - Float64(x * c)))
	t_2 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	tmp = 0.0
	if (y1 <= -4.7e+83)
		tmp = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (y1 <= -8.6e-56)
		tmp = t_1;
	elseif (y1 <= -3.5e-179)
		tmp = t_2;
	elseif (y1 <= -2.4e-208)
		tmp = t_1;
	elseif (y1 <= -3.6e-212)
		tmp = t_2;
	elseif (y1 <= 1.35e-254)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (y1 <= 7.6e-215)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y1 <= 5.7e-185)
		tmp = Float64(Float64(k * y0) * Float64(Float64(z * b) - Float64(y2 * y5)));
	elseif (y1 <= 3.5e-134)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y1 <= 3e-92)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (y1 <= 9.2e+36)
		tmp = t_2;
	elseif (y1 <= 1.65e+190)
		tmp = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))));
	else
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y * i) * ((k * y5) - (x * c));
	t_2 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	tmp = 0.0;
	if (y1 <= -4.7e+83)
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	elseif (y1 <= -8.6e-56)
		tmp = t_1;
	elseif (y1 <= -3.5e-179)
		tmp = t_2;
	elseif (y1 <= -2.4e-208)
		tmp = t_1;
	elseif (y1 <= -3.6e-212)
		tmp = t_2;
	elseif (y1 <= 1.35e-254)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (y1 <= 7.6e-215)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y1 <= 5.7e-185)
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	elseif (y1 <= 3.5e-134)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y1 <= 3e-92)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (y1 <= 9.2e+36)
		tmp = t_2;
	elseif (y1 <= 1.65e+190)
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	else
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -4.7e+83], N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -8.6e-56], t$95$1, If[LessEqual[y1, -3.5e-179], t$95$2, If[LessEqual[y1, -2.4e-208], t$95$1, If[LessEqual[y1, -3.6e-212], t$95$2, If[LessEqual[y1, 1.35e-254], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 7.6e-215], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 5.7e-185], N[(N[(k * y0), $MachinePrecision] * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.5e-134], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3e-92], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 9.2e+36], t$95$2, If[LessEqual[y1, 1.65e+190], N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y1 < -4.6999999999999999e83

   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 61.5%

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

      1. mul-1-neg 61.5%

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

      2. *-commutative 61.5%

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

      3. distribute-rgt-neg-in 61.5%

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

   5. Simplified 61.5%

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

   6. Taylor expanded in k around -inf 70.9%

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

      1. mul-1-neg 70.9%

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

      2. *-commutative 70.9%

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

      3. distribute-rgt-neg-in 70.9%

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

      4. +-commutative 70.9%

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

      5. mul-1-neg 70.9%

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

      6. unsub-neg 70.9%

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

      7. *-commutative 70.9%

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

   8. Simplified 70.9%

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

   if -4.6999999999999999e83 < y1 < -8.6000000000000002e-56 or -3.50000000000000024e-179 < y1 < -2.3999999999999999e-208

   1. Initial program 25.9%

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

   3. Taylor expanded in y around inf 59.7%

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

   4. Taylor expanded in i around inf 60.3%

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

      1. associate-*r* 60.4%

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

      2. +-commutative 60.4%

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

      3. mul-1-neg 60.4%

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

      4. unsub-neg 60.4%

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

      5. *-commutative 60.4%

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

      6. *-commutative 60.4%

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

   6. Simplified 60.4%

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

   if -8.6000000000000002e-56 < y1 < -3.50000000000000024e-179 or -2.3999999999999999e-208 < y1 < -3.6000000000000001e-212 or 3.00000000000000013e-92 < y1 < 9.19999999999999986e36

   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 b around inf 57.4%

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

   if -3.6000000000000001e-212 < y1 < 1.35000000000000003e-254

   1. Initial program 38.0%

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

   3. Taylor expanded in y0 around inf 36.2%

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

      1. +-commutative 36.2%

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

      2. mul-1-neg 36.2%

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

      3. unsub-neg 36.2%

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

      4. *-commutative 36.2%

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

      5. *-commutative 36.2%

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

      6. *-commutative 36.2%

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

      7. *-commutative 36.2%

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

   5. Simplified 36.2%

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

   6. Taylor expanded in c around inf 50.8%

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

   if 1.35000000000000003e-254 < y1 < 7.59999999999999954e-215

   1. Initial program 33.2%

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

   3. Taylor expanded in b around inf 56.2%

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

   4. Taylor expanded in x around inf 67.1%

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

   if 7.59999999999999954e-215 < y1 < 5.69999999999999986e-185

   1. Initial program 45.0%

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

   3. Taylor expanded in y0 around inf 45.2%

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

      1. +-commutative 45.2%

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

      2. mul-1-neg 45.2%

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

      3. unsub-neg 45.2%

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

      4. *-commutative 45.2%

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

      5. *-commutative 45.2%

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

      6. *-commutative 45.2%

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

      7. *-commutative 45.2%

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

   5. Simplified 45.2%

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

   6. Taylor expanded in k around -inf 45.5%

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

      1. associate-*r* 55.9%

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

      2. *-commutative 55.9%

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

      3. +-commutative 55.9%

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

      4. mul-1-neg 55.9%

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

      5. unsub-neg 55.9%

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

      6. *-commutative 55.9%

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

   8. Simplified 55.9%

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

   if 5.69999999999999986e-185 < y1 < 3.4999999999999998e-134

   1. Initial program 9.1%

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

   3. Taylor expanded in x around inf 63.7%

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

   4. Taylor expanded in y around inf 63.7%

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

      1. *-commutative 63.7%

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

   6. Simplified 63.7%

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

   if 3.4999999999999998e-134 < y1 < 3.00000000000000013e-92

   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 y5 around -inf 30.7%

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

   4. Taylor expanded in i around inf 70.4%

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

   if 9.19999999999999986e36 < y1 < 1.65e190

   1. Initial program 19.7%

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

   3. Taylor expanded in j around inf 53.7%

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

      1. +-commutative 53.7%

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

      2. mul-1-neg 53.7%

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

      3. unsub-neg 53.7%

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

      4. *-commutative 53.7%

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

   5. Simplified 53.7%

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

   if 1.65e190 < y1

   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 x around inf 44.5%

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

   4. Taylor expanded in y2 around inf 67.5%

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

      1. *-commutative 67.5%

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

   6. Simplified 67.5%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -4.7 \cdot 10^{+83}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -8.6 \cdot 10^{-56}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(k \cdot y5 - x \cdot c\right)\\ \mathbf{elif}\;y1 \leq -3.5 \cdot 10^{-179}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq -2.4 \cdot 10^{-208}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(k \cdot y5 - x \cdot c\right)\\ \mathbf{elif}\;y1 \leq -3.6 \cdot 10^{-212}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 1.35 \cdot 10^{-254}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 7.6 \cdot 10^{-215}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 5.7 \cdot 10^{-185}:\\ \;\;\;\;\left(k \cdot y0\right) \cdot \left(z \cdot b - y2 \cdot y5\right)\\ \mathbf{elif}\;y1 \leq 3.5 \cdot 10^{-134}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq 3 \cdot 10^{-92}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 9.2 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 1.65 \cdot 10^{+190}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 36.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ t_2 := b \cdot y4 - i \cdot y5\\ \mathbf{if}\;y1 \leq -3.5 \cdot 10^{+83}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -1.36 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -2.9 \cdot 10^{-216}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot t\_2\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq 1.25 \cdot 10^{-254}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 3.6 \cdot 10^{-215}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 1.9 \cdot 10^{-188}:\\ \;\;\;\;\left(k \cdot y0\right) \cdot \left(z \cdot b - y2 \cdot y5\right)\\ \mathbf{elif}\;y1 \leq 8.4 \cdot 10^{-134}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq 9.4 \cdot 10^{-94}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 1.8 \cdot 10^{+40}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 5.4 \cdot 10^{+189}:\\ \;\;\;\;j \cdot \left(\left(t \cdot t\_2 + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* x (* y (- (* a b) (* c i))))) (t_2 (- (* b y4) (* i y5))))
   (if (<= y1 -3.5e+83)
     (* k (* y1 (- (* y2 y4) (* z i))))
     (if (<= y1 -1.36e-25)
       t_1
       (if (<= y1 -2.9e-216)
         (*
          k
          (+
           (- (* y2 (- (* y1 y4) (* y0 y5))) (* y t_2))
           (* z (- (* b y0) (* i y1)))))
         (if (<= y1 1.25e-254)
           (* c (* y0 (- (* x y2) (* z y3))))
           (if (<= y1 3.6e-215)
             (* b (* x (- (* y a) (* j y0))))
             (if (<= y1 1.9e-188)
               (* (* k y0) (- (* z b) (* y2 y5)))
               (if (<= y1 8.4e-134)
                 t_1
                 (if (<= y1 9.4e-94)
                   (* i (* y5 (- (* y k) (* t j))))
                   (if (<= y1 1.8e+40)
                     (*
                      b
                      (+
                       (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
                       (* y0 (- (* z k) (* x j)))))
                     (if (<= y1 5.4e+189)
                       (*
                        j
                        (+
                         (+ (* t t_2) (* y3 (- (* y0 y5) (* y1 y4))))
                         (* x (- (* i y1) (* b y0)))))
                       (* x (* y2 (- (* c y0) (* a y1))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (y * ((a * b) - (c * i)));
	double t_2 = (b * y4) - (i * y5);
	double tmp;
	if (y1 <= -3.5e+83) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (y1 <= -1.36e-25) {
		tmp = t_1;
	} else if (y1 <= -2.9e-216) {
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) - (y * t_2)) + (z * ((b * y0) - (i * y1))));
	} else if (y1 <= 1.25e-254) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (y1 <= 3.6e-215) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y1 <= 1.9e-188) {
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	} else if (y1 <= 8.4e-134) {
		tmp = t_1;
	} else if (y1 <= 9.4e-94) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y1 <= 1.8e+40) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y1 <= 5.4e+189) {
		tmp = j * (((t * t_2) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	} else {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y * ((a * b) - (c * i)))
    t_2 = (b * y4) - (i * y5)
    if (y1 <= (-3.5d+83)) then
        tmp = k * (y1 * ((y2 * y4) - (z * i)))
    else if (y1 <= (-1.36d-25)) then
        tmp = t_1
    else if (y1 <= (-2.9d-216)) then
        tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) - (y * t_2)) + (z * ((b * y0) - (i * y1))))
    else if (y1 <= 1.25d-254) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (y1 <= 3.6d-215) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y1 <= 1.9d-188) then
        tmp = (k * y0) * ((z * b) - (y2 * y5))
    else if (y1 <= 8.4d-134) then
        tmp = t_1
    else if (y1 <= 9.4d-94) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (y1 <= 1.8d+40) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    else if (y1 <= 5.4d+189) then
        tmp = j * (((t * t_2) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
    else
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (y * ((a * b) - (c * i)));
	double t_2 = (b * y4) - (i * y5);
	double tmp;
	if (y1 <= -3.5e+83) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (y1 <= -1.36e-25) {
		tmp = t_1;
	} else if (y1 <= -2.9e-216) {
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) - (y * t_2)) + (z * ((b * y0) - (i * y1))));
	} else if (y1 <= 1.25e-254) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (y1 <= 3.6e-215) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y1 <= 1.9e-188) {
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	} else if (y1 <= 8.4e-134) {
		tmp = t_1;
	} else if (y1 <= 9.4e-94) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y1 <= 1.8e+40) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y1 <= 5.4e+189) {
		tmp = j * (((t * t_2) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	} else {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = x * (y * ((a * b) - (c * i)))
	t_2 = (b * y4) - (i * y5)
	tmp = 0
	if y1 <= -3.5e+83:
		tmp = k * (y1 * ((y2 * y4) - (z * i)))
	elif y1 <= -1.36e-25:
		tmp = t_1
	elif y1 <= -2.9e-216:
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) - (y * t_2)) + (z * ((b * y0) - (i * y1))))
	elif y1 <= 1.25e-254:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif y1 <= 3.6e-215:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y1 <= 1.9e-188:
		tmp = (k * y0) * ((z * b) - (y2 * y5))
	elif y1 <= 8.4e-134:
		tmp = t_1
	elif y1 <= 9.4e-94:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif y1 <= 1.8e+40:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	elif y1 <= 5.4e+189:
		tmp = j * (((t * t_2) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
	else:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))))
	t_2 = Float64(Float64(b * y4) - Float64(i * y5))
	tmp = 0.0
	if (y1 <= -3.5e+83)
		tmp = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (y1 <= -1.36e-25)
		tmp = t_1;
	elseif (y1 <= -2.9e-216)
		tmp = Float64(k * Float64(Float64(Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) - Float64(y * t_2)) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))));
	elseif (y1 <= 1.25e-254)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (y1 <= 3.6e-215)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y1 <= 1.9e-188)
		tmp = Float64(Float64(k * y0) * Float64(Float64(z * b) - Float64(y2 * y5)));
	elseif (y1 <= 8.4e-134)
		tmp = t_1;
	elseif (y1 <= 9.4e-94)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (y1 <= 1.8e+40)
		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 (y1 <= 5.4e+189)
		tmp = Float64(j * Float64(Float64(Float64(t * t_2) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))));
	else
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = x * (y * ((a * b) - (c * i)));
	t_2 = (b * y4) - (i * y5);
	tmp = 0.0;
	if (y1 <= -3.5e+83)
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	elseif (y1 <= -1.36e-25)
		tmp = t_1;
	elseif (y1 <= -2.9e-216)
		tmp = k * (((y2 * ((y1 * y4) - (y0 * y5))) - (y * t_2)) + (z * ((b * y0) - (i * y1))));
	elseif (y1 <= 1.25e-254)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (y1 <= 3.6e-215)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y1 <= 1.9e-188)
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	elseif (y1 <= 8.4e-134)
		tmp = t_1;
	elseif (y1 <= 9.4e-94)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (y1 <= 1.8e+40)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	elseif (y1 <= 5.4e+189)
		tmp = j * (((t * t_2) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	else
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -3.5e+83], N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.36e-25], t$95$1, If[LessEqual[y1, -2.9e-216], N[(k * N[(N[(N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.25e-254], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.6e-215], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.9e-188], N[(N[(k * y0), $MachinePrecision] * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 8.4e-134], t$95$1, If[LessEqual[y1, 9.4e-94], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.8e+40], 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[y1, 5.4e+189], N[(j * N[(N[(N[(t * t$95$2), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y1 < -3.49999999999999977e83

   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 61.5%

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

      1. mul-1-neg 61.5%

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

      2. *-commutative 61.5%

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

      3. distribute-rgt-neg-in 61.5%

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

   5. Simplified 61.5%

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

   6. Taylor expanded in k around -inf 70.9%

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

      1. mul-1-neg 70.9%

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

      2. *-commutative 70.9%

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

      3. distribute-rgt-neg-in 70.9%

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

      4. +-commutative 70.9%

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

      5. mul-1-neg 70.9%

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

      6. unsub-neg 70.9%

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

      7. *-commutative 70.9%

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

   8. Simplified 70.9%

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

   if -3.49999999999999977e83 < y1 < -1.36000000000000005e-25 or 1.9e-188 < y1 < 8.3999999999999996e-134

   1. Initial program 13.8%

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

   3. Taylor expanded in x around inf 59.0%

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

   4. Taylor expanded in y around inf 59.1%

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

      1. *-commutative 59.1%

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

   6. Simplified 59.1%

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

   if -1.36000000000000005e-25 < y1 < -2.9000000000000001e-216

   1. Initial program 55.4%

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

   3. Taylor expanded in k around inf 55.9%

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

      1. sub-neg 55.9%

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

      2. +-commutative 55.9%

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

      3. mul-1-neg 55.9%

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

      4. unsub-neg 55.9%

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

      5. *-commutative 55.9%

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

      6. mul-1-neg 55.9%

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

      7. remove-double-neg 55.9%

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

   5. Simplified 55.9%

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

   if -2.9000000000000001e-216 < y1 < 1.2500000000000001e-254

   1. Initial program 35.0%

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

   3. Taylor expanded in y0 around inf 35.8%

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

      1. +-commutative 35.8%

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

      2. mul-1-neg 35.8%

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

      3. unsub-neg 35.8%

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

      4. *-commutative 35.8%

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

      5. *-commutative 35.8%

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

      6. *-commutative 35.8%

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

      7. *-commutative 35.8%

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

   5. Simplified 35.8%

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

   6. Taylor expanded in c around inf 49.1%

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

   if 1.2500000000000001e-254 < y1 < 3.5999999999999999e-215

   1. Initial program 33.2%

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

   3. Taylor expanded in b around inf 56.2%

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

   4. Taylor expanded in x around inf 67.1%

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

   if 3.5999999999999999e-215 < y1 < 1.9e-188

   1. Initial program 50.7%

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

   3. Taylor expanded in y0 around inf 50.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   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 k around -inf 51.2%

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

      1. associate-*r* 62.8%

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

      2. *-commutative 62.8%

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

      3. +-commutative 62.8%

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

      4. mul-1-neg 62.8%

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

      5. unsub-neg 62.8%

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

      6. *-commutative 62.8%

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

   8. Simplified 62.8%

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

   if 8.3999999999999996e-134 < y1 < 9.40000000000000007e-94

   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 y5 around -inf 30.7%

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

   4. Taylor expanded in i around inf 70.4%

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

   if 9.40000000000000007e-94 < y1 < 1.79999999999999998e40

   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 b around inf 56.0%

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

   if 1.79999999999999998e40 < y1 < 5.39999999999999988e189

   1. Initial program 20.3%

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

   3. Taylor expanded in j around inf 55.2%

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

      1. +-commutative 55.2%

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

      2. mul-1-neg 55.2%

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

      3. unsub-neg 55.2%

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

      4. *-commutative 55.2%

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

   5. Simplified 55.2%

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

   if 5.39999999999999988e189 < y1

   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 x around inf 44.5%

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

   4. Taylor expanded in y2 around inf 67.5%

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

      1. *-commutative 67.5%

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

   6. Simplified 67.5%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -3.5 \cdot 10^{+83}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -1.36 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -2.9 \cdot 10^{-216}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq 1.25 \cdot 10^{-254}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 3.6 \cdot 10^{-215}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 1.9 \cdot 10^{-188}:\\ \;\;\;\;\left(k \cdot y0\right) \cdot \left(z \cdot b - y2 \cdot y5\right)\\ \mathbf{elif}\;y1 \leq 8.4 \cdot 10^{-134}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq 9.4 \cdot 10^{-94}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 1.8 \cdot 10^{+40}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 5.4 \cdot 10^{+189}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 43.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot k - x \cdot j\\ t_2 := x \cdot y - z \cdot t\\ t_3 := y1 \cdot y4 - y0 \cdot y5\\ t_4 := k \cdot \left(\left(y2 \cdot t\_3 - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ t_5 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_6 := t \cdot j - y \cdot k\\ t_7 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot t\_2 + y5 \cdot t\_6\right)\right)\\ \mathbf{if}\;k \leq -4.3 \cdot 10^{+170}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;k \leq -4.9 \cdot 10^{-26}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;k \leq -1.25 \cdot 10^{-120}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot t\_1\right)\\ \mathbf{elif}\;k \leq -5.2 \cdot 10^{-224}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;k \leq 1.55 \cdot 10^{-251}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;k \leq 7.8 \cdot 10^{-184}:\\ \;\;\;\;b \cdot \left(\left(a \cdot t\_2 + y4 \cdot t\_6\right) + y0 \cdot t\_1\right)\\ \mathbf{elif}\;k \leq 1.95 \cdot 10^{-30}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;k \leq 245000000000:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(z \cdot \left(a \cdot y1 - c \cdot y0\right) - j \cdot t\_3\right)\right)\\ \mathbf{elif}\;k \leq 1.28 \cdot 10^{+126}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* z k) (* x j)))
        (t_2 (- (* x y) (* z t)))
        (t_3 (- (* y1 y4) (* y0 y5)))
        (t_4
         (*
          k
          (+
           (- (* y2 t_3) (* y (- (* b y4) (* i y5))))
           (* z (- (* b y0) (* i y1))))))
        (t_5
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
           (* j (- (* i y1) (* b y0))))))
        (t_6 (- (* t j) (* y k)))
        (t_7 (* i (- (* y1 (- (* x j) (* z k))) (+ (* c t_2) (* y5 t_6))))))
   (if (<= k -4.3e+170)
     t_4
     (if (<= k -4.9e-26)
       t_7
       (if (<= k -1.25e-120)
         (*
          y0
          (+
           (+ (* c (- (* x y2) (* z y3))) (* y5 (- (* j y3) (* k y2))))
           (* b t_1)))
         (if (<= k -5.2e-224)
           t_7
           (if (<= k 1.55e-251)
             t_5
             (if (<= k 7.8e-184)
               (* b (+ (+ (* a t_2) (* y4 t_6)) (* y0 t_1)))
               (if (<= k 1.95e-30)
                 t_5
                 (if (<= k 245000000000.0)
                   (*
                    y3
                    (+
                     (* y (- (* c y4) (* a y5)))
                     (- (* z (- (* a y1) (* c y0))) (* j t_3))))
                   (if (<= k 1.28e+126)
                     (* i (* y5 (- (* y k) (* t j))))
                     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 = (z * k) - (x * j);
	double t_2 = (x * y) - (z * t);
	double t_3 = (y1 * y4) - (y0 * y5);
	double t_4 = k * (((y2 * t_3) - (y * ((b * y4) - (i * y5)))) + (z * ((b * y0) - (i * y1))));
	double t_5 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double t_6 = (t * j) - (y * k);
	double t_7 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_2) + (y5 * t_6)));
	double tmp;
	if (k <= -4.3e+170) {
		tmp = t_4;
	} else if (k <= -4.9e-26) {
		tmp = t_7;
	} else if (k <= -1.25e-120) {
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * t_1));
	} else if (k <= -5.2e-224) {
		tmp = t_7;
	} else if (k <= 1.55e-251) {
		tmp = t_5;
	} else if (k <= 7.8e-184) {
		tmp = b * (((a * t_2) + (y4 * t_6)) + (y0 * t_1));
	} else if (k <= 1.95e-30) {
		tmp = t_5;
	} else if (k <= 245000000000.0) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((z * ((a * y1) - (c * y0))) - (j * t_3)));
	} else if (k <= 1.28e+126) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} 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) :: t_7
    real(8) :: tmp
    t_1 = (z * k) - (x * j)
    t_2 = (x * y) - (z * t)
    t_3 = (y1 * y4) - (y0 * y5)
    t_4 = k * (((y2 * t_3) - (y * ((b * y4) - (i * y5)))) + (z * ((b * y0) - (i * y1))))
    t_5 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    t_6 = (t * j) - (y * k)
    t_7 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_2) + (y5 * t_6)))
    if (k <= (-4.3d+170)) then
        tmp = t_4
    else if (k <= (-4.9d-26)) then
        tmp = t_7
    else if (k <= (-1.25d-120)) then
        tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * t_1))
    else if (k <= (-5.2d-224)) then
        tmp = t_7
    else if (k <= 1.55d-251) then
        tmp = t_5
    else if (k <= 7.8d-184) then
        tmp = b * (((a * t_2) + (y4 * t_6)) + (y0 * t_1))
    else if (k <= 1.95d-30) then
        tmp = t_5
    else if (k <= 245000000000.0d0) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((z * ((a * y1) - (c * y0))) - (j * t_3)))
    else if (k <= 1.28d+126) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    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 = (z * k) - (x * j);
	double t_2 = (x * y) - (z * t);
	double t_3 = (y1 * y4) - (y0 * y5);
	double t_4 = k * (((y2 * t_3) - (y * ((b * y4) - (i * y5)))) + (z * ((b * y0) - (i * y1))));
	double t_5 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double t_6 = (t * j) - (y * k);
	double t_7 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_2) + (y5 * t_6)));
	double tmp;
	if (k <= -4.3e+170) {
		tmp = t_4;
	} else if (k <= -4.9e-26) {
		tmp = t_7;
	} else if (k <= -1.25e-120) {
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * t_1));
	} else if (k <= -5.2e-224) {
		tmp = t_7;
	} else if (k <= 1.55e-251) {
		tmp = t_5;
	} else if (k <= 7.8e-184) {
		tmp = b * (((a * t_2) + (y4 * t_6)) + (y0 * t_1));
	} else if (k <= 1.95e-30) {
		tmp = t_5;
	} else if (k <= 245000000000.0) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((z * ((a * y1) - (c * y0))) - (j * t_3)));
	} else if (k <= 1.28e+126) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} 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 = (z * k) - (x * j)
	t_2 = (x * y) - (z * t)
	t_3 = (y1 * y4) - (y0 * y5)
	t_4 = k * (((y2 * t_3) - (y * ((b * y4) - (i * y5)))) + (z * ((b * y0) - (i * y1))))
	t_5 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	t_6 = (t * j) - (y * k)
	t_7 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_2) + (y5 * t_6)))
	tmp = 0
	if k <= -4.3e+170:
		tmp = t_4
	elif k <= -4.9e-26:
		tmp = t_7
	elif k <= -1.25e-120:
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * t_1))
	elif k <= -5.2e-224:
		tmp = t_7
	elif k <= 1.55e-251:
		tmp = t_5
	elif k <= 7.8e-184:
		tmp = b * (((a * t_2) + (y4 * t_6)) + (y0 * t_1))
	elif k <= 1.95e-30:
		tmp = t_5
	elif k <= 245000000000.0:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((z * ((a * y1) - (c * y0))) - (j * t_3)))
	elif k <= 1.28e+126:
		tmp = i * (y5 * ((y * k) - (t * j)))
	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(z * k) - Float64(x * j))
	t_2 = Float64(Float64(x * y) - Float64(z * t))
	t_3 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_4 = Float64(k * Float64(Float64(Float64(y2 * t_3) - Float64(y * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))))
	t_5 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_6 = Float64(Float64(t * j) - Float64(y * k))
	t_7 = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) - Float64(Float64(c * t_2) + Float64(y5 * t_6))))
	tmp = 0.0
	if (k <= -4.3e+170)
		tmp = t_4;
	elseif (k <= -4.9e-26)
		tmp = t_7;
	elseif (k <= -1.25e-120)
		tmp = Float64(y0 * Float64(Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2)))) + Float64(b * t_1)));
	elseif (k <= -5.2e-224)
		tmp = t_7;
	elseif (k <= 1.55e-251)
		tmp = t_5;
	elseif (k <= 7.8e-184)
		tmp = Float64(b * Float64(Float64(Float64(a * t_2) + Float64(y4 * t_6)) + Float64(y0 * t_1)));
	elseif (k <= 1.95e-30)
		tmp = t_5;
	elseif (k <= 245000000000.0)
		tmp = 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_3))));
	elseif (k <= 1.28e+126)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	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 = (z * k) - (x * j);
	t_2 = (x * y) - (z * t);
	t_3 = (y1 * y4) - (y0 * y5);
	t_4 = k * (((y2 * t_3) - (y * ((b * y4) - (i * y5)))) + (z * ((b * y0) - (i * y1))));
	t_5 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	t_6 = (t * j) - (y * k);
	t_7 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_2) + (y5 * t_6)));
	tmp = 0.0;
	if (k <= -4.3e+170)
		tmp = t_4;
	elseif (k <= -4.9e-26)
		tmp = t_7;
	elseif (k <= -1.25e-120)
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * t_1));
	elseif (k <= -5.2e-224)
		tmp = t_7;
	elseif (k <= 1.55e-251)
		tmp = t_5;
	elseif (k <= 7.8e-184)
		tmp = b * (((a * t_2) + (y4 * t_6)) + (y0 * t_1));
	elseif (k <= 1.95e-30)
		tmp = t_5;
	elseif (k <= 245000000000.0)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((z * ((a * y1) - (c * y0))) - (j * t_3)));
	elseif (k <= 1.28e+126)
		tmp = i * (y5 * ((y * k) - (t * j)));
	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[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(k * N[(N[(N[(y2 * t$95$3), $MachinePrecision] - N[(y * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(c * t$95$2), $MachinePrecision] + N[(y5 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -4.3e+170], t$95$4, If[LessEqual[k, -4.9e-26], t$95$7, If[LessEqual[k, -1.25e-120], N[(y0 * N[(N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -5.2e-224], t$95$7, If[LessEqual[k, 1.55e-251], t$95$5, If[LessEqual[k, 7.8e-184], N[(b * N[(N[(N[(a * t$95$2), $MachinePrecision] + N[(y4 * t$95$6), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.95e-30], t$95$5, If[LessEqual[k, 245000000000.0], 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$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.28e+126], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if k < -4.2999999999999999e170 or 1.27999999999999993e126 < k

   1. Initial program 26.4%

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

   3. Taylor expanded in k around inf 61.5%

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

      1. sub-neg 61.5%

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

      2. +-commutative 61.5%

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

      3. mul-1-neg 61.5%

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

      4. unsub-neg 61.5%

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

      5. *-commutative 61.5%

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

      6. mul-1-neg 61.5%

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

      7. remove-double-neg 61.5%

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

   5. Simplified 61.5%

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

   if -4.2999999999999999e170 < k < -4.8999999999999999e-26 or -1.25000000000000002e-120 < k < -5.2000000000000004e-224

   1. Initial program 25.6%

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

   3. Taylor expanded in i around -inf 59.8%

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

   if -4.8999999999999999e-26 < k < -1.25000000000000002e-120

   1. Initial program 29.2%

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

   3. Taylor expanded in y0 around inf 52.7%

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

      1. +-commutative 52.7%

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

      2. mul-1-neg 52.7%

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

      3. unsub-neg 52.7%

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

      4. *-commutative 52.7%

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

      5. *-commutative 52.7%

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

      6. *-commutative 52.7%

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

      7. *-commutative 52.7%

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

   5. Simplified 52.7%

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

   if -5.2000000000000004e-224 < k < 1.55000000000000001e-251 or 7.79999999999999988e-184 < k < 1.9500000000000002e-30

   1. Initial program 39.4%

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

   3. Taylor expanded in x around inf 62.8%

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

   if 1.55000000000000001e-251 < k < 7.79999999999999988e-184

   1. Initial program 34.0%

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

   3. Taylor expanded in b around inf 74.3%

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

   if 1.9500000000000002e-30 < k < 2.45e11

   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 y3 around -inf 66.9%

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

   if 2.45e11 < k < 1.27999999999999993e126

   1. Initial program 29.8%

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

   3. Taylor expanded in y5 around -inf 64.7%

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

   4. Taylor expanded in i around inf 82.5%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -4.3 \cdot 10^{+170}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -4.9 \cdot 10^{-26}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot \left(x \cdot y - z \cdot t\right) + y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;k \leq -1.25 \cdot 10^{-120}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;k \leq -5.2 \cdot 10^{-224}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot \left(x \cdot y - z \cdot t\right) + y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;k \leq 1.55 \cdot 10^{-251}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 7.8 \cdot 10^{-184}:\\ \;\;\;\;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}\;k \leq 1.95 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 245000000000:\\ \;\;\;\;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(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)\\ \mathbf{elif}\;k \leq 1.28 \cdot 10^{+126}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 31.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y0 \cdot y2\right) \cdot \left(x \cdot c - k \cdot y5\right)\\ t_2 := y2 \cdot y4 - z \cdot i\\ t_3 := x \cdot y2 - z \cdot y3\\ \mathbf{if}\;y0 \leq -2.15 \cdot 10^{+159}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k - c \cdot y3\right)\\ \mathbf{elif}\;y0 \leq -4.5 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq -1.16 \cdot 10^{+39}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -2.35 \cdot 10^{-58}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -3.1 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq -3.9 \cdot 10^{-202}:\\ \;\;\;\;t\_3 \cdot \left(c \cdot y0\right)\\ \mathbf{elif}\;y0 \leq -3 \cdot 10^{-267}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)\\ \mathbf{elif}\;y0 \leq 2 \cdot 10^{-306}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq 6.5 \cdot 10^{-191}:\\ \;\;\;\;k \cdot \left(y1 \cdot t\_2\right)\\ \mathbf{elif}\;y0 \leq 8.4 \cdot 10^{-122}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 1.6 \cdot 10^{-22}:\\ \;\;\;\;\left(k \cdot y1\right) \cdot t\_2\\ \mathbf{elif}\;y0 \leq 1.8 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot t\_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* y0 y2) (- (* x c) (* k y5))))
        (t_2 (- (* y2 y4) (* z i)))
        (t_3 (- (* x y2) (* z y3))))
   (if (<= y0 -2.15e+159)
     (* (* z y0) (- (* b k) (* c y3)))
     (if (<= y0 -4.5e+133)
       t_1
       (if (<= y0 -1.16e+39)
         (* b (* y0 (- (* z k) (* x j))))
         (if (<= y0 -2.35e-58)
           (* z (* c (- (* t i) (* y0 y3))))
           (if (<= y0 -3.1e-196)
             (* y (* x (- (* a b) (* c i))))
             (if (<= y0 -3.9e-202)
               (* t_3 (* c y0))
               (if (<= y0 -3e-267)
                 (* (* t b) (- (* j y4) (* z a)))
                 (if (<= y0 2e-306)
                   (* i (* y5 (- (* y k) (* t j))))
                   (if (<= y0 6.5e-191)
                     (* k (* y1 t_2))
                     (if (<= y0 8.4e-122)
                       (* b (* y4 (- (* t j) (* y k))))
                       (if (<= y0 1.6e-22)
                         (* (* k y1) t_2)
                         (if (<= y0 1.8e+106)
                           t_1
                           (* c (* y0 t_3))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * y2) * ((x * c) - (k * y5));
	double t_2 = (y2 * y4) - (z * i);
	double t_3 = (x * y2) - (z * y3);
	double tmp;
	if (y0 <= -2.15e+159) {
		tmp = (z * y0) * ((b * k) - (c * y3));
	} else if (y0 <= -4.5e+133) {
		tmp = t_1;
	} else if (y0 <= -1.16e+39) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y0 <= -2.35e-58) {
		tmp = z * (c * ((t * i) - (y0 * y3)));
	} else if (y0 <= -3.1e-196) {
		tmp = y * (x * ((a * b) - (c * i)));
	} else if (y0 <= -3.9e-202) {
		tmp = t_3 * (c * y0);
	} else if (y0 <= -3e-267) {
		tmp = (t * b) * ((j * y4) - (z * a));
	} else if (y0 <= 2e-306) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y0 <= 6.5e-191) {
		tmp = k * (y1 * t_2);
	} else if (y0 <= 8.4e-122) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y0 <= 1.6e-22) {
		tmp = (k * y1) * t_2;
	} else if (y0 <= 1.8e+106) {
		tmp = t_1;
	} else {
		tmp = c * (y0 * t_3);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y0 * y2) * ((x * c) - (k * y5))
    t_2 = (y2 * y4) - (z * i)
    t_3 = (x * y2) - (z * y3)
    if (y0 <= (-2.15d+159)) then
        tmp = (z * y0) * ((b * k) - (c * y3))
    else if (y0 <= (-4.5d+133)) then
        tmp = t_1
    else if (y0 <= (-1.16d+39)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y0 <= (-2.35d-58)) then
        tmp = z * (c * ((t * i) - (y0 * y3)))
    else if (y0 <= (-3.1d-196)) then
        tmp = y * (x * ((a * b) - (c * i)))
    else if (y0 <= (-3.9d-202)) then
        tmp = t_3 * (c * y0)
    else if (y0 <= (-3d-267)) then
        tmp = (t * b) * ((j * y4) - (z * a))
    else if (y0 <= 2d-306) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (y0 <= 6.5d-191) then
        tmp = k * (y1 * t_2)
    else if (y0 <= 8.4d-122) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y0 <= 1.6d-22) then
        tmp = (k * y1) * t_2
    else if (y0 <= 1.8d+106) then
        tmp = t_1
    else
        tmp = c * (y0 * t_3)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * y2) * ((x * c) - (k * y5));
	double t_2 = (y2 * y4) - (z * i);
	double t_3 = (x * y2) - (z * y3);
	double tmp;
	if (y0 <= -2.15e+159) {
		tmp = (z * y0) * ((b * k) - (c * y3));
	} else if (y0 <= -4.5e+133) {
		tmp = t_1;
	} else if (y0 <= -1.16e+39) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y0 <= -2.35e-58) {
		tmp = z * (c * ((t * i) - (y0 * y3)));
	} else if (y0 <= -3.1e-196) {
		tmp = y * (x * ((a * b) - (c * i)));
	} else if (y0 <= -3.9e-202) {
		tmp = t_3 * (c * y0);
	} else if (y0 <= -3e-267) {
		tmp = (t * b) * ((j * y4) - (z * a));
	} else if (y0 <= 2e-306) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y0 <= 6.5e-191) {
		tmp = k * (y1 * t_2);
	} else if (y0 <= 8.4e-122) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y0 <= 1.6e-22) {
		tmp = (k * y1) * t_2;
	} else if (y0 <= 1.8e+106) {
		tmp = t_1;
	} else {
		tmp = c * (y0 * t_3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y0 * y2) * ((x * c) - (k * y5))
	t_2 = (y2 * y4) - (z * i)
	t_3 = (x * y2) - (z * y3)
	tmp = 0
	if y0 <= -2.15e+159:
		tmp = (z * y0) * ((b * k) - (c * y3))
	elif y0 <= -4.5e+133:
		tmp = t_1
	elif y0 <= -1.16e+39:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y0 <= -2.35e-58:
		tmp = z * (c * ((t * i) - (y0 * y3)))
	elif y0 <= -3.1e-196:
		tmp = y * (x * ((a * b) - (c * i)))
	elif y0 <= -3.9e-202:
		tmp = t_3 * (c * y0)
	elif y0 <= -3e-267:
		tmp = (t * b) * ((j * y4) - (z * a))
	elif y0 <= 2e-306:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif y0 <= 6.5e-191:
		tmp = k * (y1 * t_2)
	elif y0 <= 8.4e-122:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y0 <= 1.6e-22:
		tmp = (k * y1) * t_2
	elif y0 <= 1.8e+106:
		tmp = t_1
	else:
		tmp = c * (y0 * t_3)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y0 * y2) * Float64(Float64(x * c) - Float64(k * y5)))
	t_2 = Float64(Float64(y2 * y4) - Float64(z * i))
	t_3 = Float64(Float64(x * y2) - Float64(z * y3))
	tmp = 0.0
	if (y0 <= -2.15e+159)
		tmp = Float64(Float64(z * y0) * Float64(Float64(b * k) - Float64(c * y3)));
	elseif (y0 <= -4.5e+133)
		tmp = t_1;
	elseif (y0 <= -1.16e+39)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y0 <= -2.35e-58)
		tmp = Float64(z * Float64(c * Float64(Float64(t * i) - Float64(y0 * y3))));
	elseif (y0 <= -3.1e-196)
		tmp = Float64(y * Float64(x * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y0 <= -3.9e-202)
		tmp = Float64(t_3 * Float64(c * y0));
	elseif (y0 <= -3e-267)
		tmp = Float64(Float64(t * b) * Float64(Float64(j * y4) - Float64(z * a)));
	elseif (y0 <= 2e-306)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (y0 <= 6.5e-191)
		tmp = Float64(k * Float64(y1 * t_2));
	elseif (y0 <= 8.4e-122)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y0 <= 1.6e-22)
		tmp = Float64(Float64(k * y1) * t_2);
	elseif (y0 <= 1.8e+106)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(y0 * t_3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y0 * y2) * ((x * c) - (k * y5));
	t_2 = (y2 * y4) - (z * i);
	t_3 = (x * y2) - (z * y3);
	tmp = 0.0;
	if (y0 <= -2.15e+159)
		tmp = (z * y0) * ((b * k) - (c * y3));
	elseif (y0 <= -4.5e+133)
		tmp = t_1;
	elseif (y0 <= -1.16e+39)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y0 <= -2.35e-58)
		tmp = z * (c * ((t * i) - (y0 * y3)));
	elseif (y0 <= -3.1e-196)
		tmp = y * (x * ((a * b) - (c * i)));
	elseif (y0 <= -3.9e-202)
		tmp = t_3 * (c * y0);
	elseif (y0 <= -3e-267)
		tmp = (t * b) * ((j * y4) - (z * a));
	elseif (y0 <= 2e-306)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (y0 <= 6.5e-191)
		tmp = k * (y1 * t_2);
	elseif (y0 <= 8.4e-122)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y0 <= 1.6e-22)
		tmp = (k * y1) * t_2;
	elseif (y0 <= 1.8e+106)
		tmp = t_1;
	else
		tmp = c * (y0 * t_3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y0 * y2), $MachinePrecision] * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -2.15e+159], N[(N[(z * y0), $MachinePrecision] * N[(N[(b * k), $MachinePrecision] - N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -4.5e+133], t$95$1, If[LessEqual[y0, -1.16e+39], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -2.35e-58], N[(z * N[(c * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -3.1e-196], N[(y * N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -3.9e-202], N[(t$95$3 * N[(c * y0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -3e-267], N[(N[(t * b), $MachinePrecision] * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2e-306], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 6.5e-191], N[(k * N[(y1 * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 8.4e-122], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.6e-22], N[(N[(k * y1), $MachinePrecision] * t$95$2), $MachinePrecision], If[LessEqual[y0, 1.8e+106], t$95$1, N[(c * N[(y0 * t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 12 regimes

2. if y0 < -2.1500000000000001e159

   1. Initial program 18.1%

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

   3. Taylor expanded in y0 around inf 60.7%

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

      1. +-commutative 60.7%

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

      2. mul-1-neg 60.7%

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

      3. unsub-neg 60.7%

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

      4. *-commutative 60.7%

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

      5. *-commutative 60.7%

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

      6. *-commutative 60.7%

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

      7. *-commutative 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in z around inf 61.4%

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

      1. associate-*r* 61.5%

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

      2. distribute-lft-out-- 61.5%

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

   8. Simplified 61.5%

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

   if -2.1500000000000001e159 < y0 < -4.49999999999999985e133 or 1.59999999999999994e-22 < y0 < 1.8e106

   1. Initial program 27.6%

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

   3. Taylor expanded in y0 around inf 45.7%

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

      1. +-commutative 45.7%

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

      2. mul-1-neg 45.7%

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

      3. unsub-neg 45.7%

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

      4. *-commutative 45.7%

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

      5. *-commutative 45.7%

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

      6. *-commutative 45.7%

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

      7. *-commutative 45.7%

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

   5. Simplified 45.7%

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

   6. Taylor expanded in y2 around inf 56.0%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(c \cdot x - k \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 55.9%

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

   8. Simplified 55.9%

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

   if -4.49999999999999985e133 < y0 < -1.16000000000000003e39

   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 y0 around inf 78.0%

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

      1. +-commutative 78.0%

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

      2. mul-1-neg 78.0%

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

      3. unsub-neg 78.0%

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

      4. *-commutative 78.0%

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

      5. *-commutative 78.0%

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

      6. *-commutative 78.0%

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

      7. *-commutative 78.0%

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

   5. Simplified 78.0%

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

   6. Taylor expanded in b around inf 67.5%

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

   if -1.16000000000000003e39 < y0 < -2.34999999999999997e-58

   1. Initial program 54.8%

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

   3. Taylor expanded in z around -inf 55.2%

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

   4. Taylor expanded in c around inf 42.0%

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

      1. +-commutative 42.0%

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

      2. mul-1-neg 42.0%

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

      3. unsub-neg 42.0%

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

      4. *-commutative 42.0%

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

   6. Simplified 42.0%

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

   if -2.34999999999999997e-58 < y0 < -3.09999999999999993e-196

   1. Initial program 14.4%

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

   3. Taylor expanded in y around inf 36.9%

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

   4. Taylor expanded in x around inf 42.0%

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

      1. *-commutative 42.0%

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

      2. *-commutative 42.0%

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

      3. *-commutative 42.0%

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

      4. associate-*r* 42.0%

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

      5. *-commutative 42.0%

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

      6. *-commutative 42.0%

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

      7. *-commutative 42.0%

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

   6. Simplified 42.0%

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

   if -3.09999999999999993e-196 < y0 < -3.8999999999999999e-202

   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 8.5%

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

      1. +-commutative 8.5%

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

      2. mul-1-neg 8.5%

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

      3. unsub-neg 8.5%

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

      4. *-commutative 8.5%

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

      5. *-commutative 8.5%

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

      6. *-commutative 8.5%

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

      7. *-commutative 8.5%

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

   5. Simplified 8.5%

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

   6. Taylor expanded in c around inf 51.3%

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

      1. associate-*r* 52.1%

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

      2. *-commutative 52.1%

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

   8. Simplified 52.1%

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

   if -3.8999999999999999e-202 < y0 < -3e-267

   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 b around inf 51.0%

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

   4. Taylor expanded in t around inf 57.2%

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

      1. associate-*r* 51.4%

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

      2. +-commutative 51.4%

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

      3. mul-1-neg 51.4%

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

      4. unsub-neg 51.4%

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

      5. *-commutative 51.4%

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

   6. Simplified 51.4%

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

   if -3e-267 < y0 < 2.00000000000000006e-306

   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 y5 around -inf 25.5%

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

   4. Taylor expanded in i around inf 62.9%

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

   if 2.00000000000000006e-306 < y0 < 6.4999999999999995e-191

   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 59.8%

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

      1. mul-1-neg 59.8%

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

      2. *-commutative 59.8%

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

      3. distribute-rgt-neg-in 59.8%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in k around -inf 52.6%

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

      1. mul-1-neg 52.6%

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

      2. *-commutative 52.6%

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

      3. distribute-rgt-neg-in 52.6%

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

      4. +-commutative 52.6%

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

      5. mul-1-neg 52.6%

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

      6. unsub-neg 52.6%

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

      7. *-commutative 52.6%

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

   8. Simplified 52.6%

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

   if 6.4999999999999995e-191 < y0 < 8.39999999999999969e-122

   1. Initial program 13.3%

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

   3. Taylor expanded in b around inf 53.3%

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

   4. Taylor expanded in y4 around inf 66.9%

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

   if 8.39999999999999969e-122 < y0 < 1.59999999999999994e-22

   1. Initial program 56.2%

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

   3. Taylor expanded in y1 around -inf 57.2%

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

      1. mul-1-neg 57.2%

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

      2. *-commutative 57.2%

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

      3. distribute-rgt-neg-in 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in k around inf 51.6%

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

      1. associate-*r* 51.6%

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

      2. +-commutative 51.6%

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

      3. mul-1-neg 51.6%

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

      4. unsub-neg 51.6%

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

      5. *-commutative 51.6%

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

   8. Simplified 51.6%

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

   if 1.8e106 < y0

   1. Initial program 19.2%

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

   3. Taylor expanded in y0 around inf 58.1%

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

      1. +-commutative 58.1%

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

      2. mul-1-neg 58.1%

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

      3. unsub-neg 58.1%

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

      4. *-commutative 58.1%

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

      5. *-commutative 58.1%

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

      6. *-commutative 58.1%

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

      7. *-commutative 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in c around inf 58.0%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
3. Recombined 12 regimes into one program.

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -2.15 \cdot 10^{+159}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k - c \cdot y3\right)\\ \mathbf{elif}\;y0 \leq -4.5 \cdot 10^{+133}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c - k \cdot y5\right)\\ \mathbf{elif}\;y0 \leq -1.16 \cdot 10^{+39}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -2.35 \cdot 10^{-58}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -3.1 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq -3.9 \cdot 10^{-202}:\\ \;\;\;\;\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0\right)\\ \mathbf{elif}\;y0 \leq -3 \cdot 10^{-267}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)\\ \mathbf{elif}\;y0 \leq 2 \cdot 10^{-306}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq 6.5 \cdot 10^{-191}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 8.4 \cdot 10^{-122}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 1.6 \cdot 10^{-22}:\\ \;\;\;\;\left(k \cdot y1\right) \cdot \left(y2 \cdot y4 - z \cdot i\right)\\ \mathbf{elif}\;y0 \leq 1.8 \cdot 10^{+106}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c - k \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 42.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ t_2 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;k \leq -3.1 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq -9.5 \cdot 10^{-17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;k \leq -2.4 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq -5 \cdot 10^{-108}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 3.8 \cdot 10^{-251}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;k \leq 1.45 \cdot 10^{-183}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;k \leq 2.1 \cdot 10^{-8}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;k \leq 6 \cdot 10^{+129}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          k
          (+
           (- (* y2 (- (* y1 y4) (* y0 y5))) (* y (- (* b y4) (* i y5))))
           (* z (- (* b y0) (* i y1))))))
        (t_2
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
           (* j (- (* i y1) (* b y0)))))))
   (if (<= k -3.1e+137)
     t_1
     (if (<= k -9.5e-17)
       t_2
       (if (<= k -2.4e-44)
         t_1
         (if (<= k -5e-108)
           (* c (* y0 (- (* x y2) (* z y3))))
           (if (<= k 3.8e-251)
             t_2
             (if (<= k 1.45e-183)
               (*
                b
                (+
                 (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
                 (* y0 (- (* z k) (* x j)))))
               (if (<= k 2.1e-8)
                 t_2
                 (if (<= k 6e+129)
                   (* i (* y5 (- (* y k) (* t j))))
                   t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (((y2 * ((y1 * y4) - (y0 * y5))) - (y * ((b * y4) - (i * y5)))) + (z * ((b * y0) - (i * y1))));
	double t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (k <= -3.1e+137) {
		tmp = t_1;
	} else if (k <= -9.5e-17) {
		tmp = t_2;
	} else if (k <= -2.4e-44) {
		tmp = t_1;
	} else if (k <= -5e-108) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (k <= 3.8e-251) {
		tmp = t_2;
	} else if (k <= 1.45e-183) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (k <= 2.1e-8) {
		tmp = t_2;
	} else if (k <= 6e+129) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = k * (((y2 * ((y1 * y4) - (y0 * y5))) - (y * ((b * y4) - (i * y5)))) + (z * ((b * y0) - (i * y1))))
    t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    if (k <= (-3.1d+137)) then
        tmp = t_1
    else if (k <= (-9.5d-17)) then
        tmp = t_2
    else if (k <= (-2.4d-44)) then
        tmp = t_1
    else if (k <= (-5d-108)) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (k <= 3.8d-251) then
        tmp = t_2
    else if (k <= 1.45d-183) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    else if (k <= 2.1d-8) then
        tmp = t_2
    else if (k <= 6d+129) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (((y2 * ((y1 * y4) - (y0 * y5))) - (y * ((b * y4) - (i * y5)))) + (z * ((b * y0) - (i * y1))));
	double t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (k <= -3.1e+137) {
		tmp = t_1;
	} else if (k <= -9.5e-17) {
		tmp = t_2;
	} else if (k <= -2.4e-44) {
		tmp = t_1;
	} else if (k <= -5e-108) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (k <= 3.8e-251) {
		tmp = t_2;
	} else if (k <= 1.45e-183) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (k <= 2.1e-8) {
		tmp = t_2;
	} else if (k <= 6e+129) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (((y2 * ((y1 * y4) - (y0 * y5))) - (y * ((b * y4) - (i * y5)))) + (z * ((b * y0) - (i * y1))))
	t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	tmp = 0
	if k <= -3.1e+137:
		tmp = t_1
	elif k <= -9.5e-17:
		tmp = t_2
	elif k <= -2.4e-44:
		tmp = t_1
	elif k <= -5e-108:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif k <= 3.8e-251:
		tmp = t_2
	elif k <= 1.45e-183:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	elif k <= 2.1e-8:
		tmp = t_2
	elif k <= 6e+129:
		tmp = i * (y5 * ((y * k) - (t * j)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(Float64(Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) - Float64(y * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))))
	t_2 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (k <= -3.1e+137)
		tmp = t_1;
	elseif (k <= -9.5e-17)
		tmp = t_2;
	elseif (k <= -2.4e-44)
		tmp = t_1;
	elseif (k <= -5e-108)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (k <= 3.8e-251)
		tmp = t_2;
	elseif (k <= 1.45e-183)
		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 (k <= 2.1e-8)
		tmp = t_2;
	elseif (k <= 6e+129)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (((y2 * ((y1 * y4) - (y0 * y5))) - (y * ((b * y4) - (i * y5)))) + (z * ((b * y0) - (i * y1))));
	t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (k <= -3.1e+137)
		tmp = t_1;
	elseif (k <= -9.5e-17)
		tmp = t_2;
	elseif (k <= -2.4e-44)
		tmp = t_1;
	elseif (k <= -5e-108)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (k <= 3.8e-251)
		tmp = t_2;
	elseif (k <= 1.45e-183)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	elseif (k <= 2.1e-8)
		tmp = t_2;
	elseif (k <= 6e+129)
		tmp = i * (y5 * ((y * k) - (t * j)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(N[(N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -3.1e+137], t$95$1, If[LessEqual[k, -9.5e-17], t$95$2, If[LessEqual[k, -2.4e-44], t$95$1, If[LessEqual[k, -5e-108], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.8e-251], t$95$2, If[LessEqual[k, 1.45e-183], 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[k, 2.1e-8], t$95$2, If[LessEqual[k, 6e+129], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if k < -3.0999999999999999e137 or -9.50000000000000029e-17 < k < -2.40000000000000009e-44 or 6.0000000000000006e129 < k

   1. Initial program 27.0%

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

   3. Taylor expanded in k around inf 61.1%

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

      1. sub-neg 61.1%

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

      2. +-commutative 61.1%

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

      3. mul-1-neg 61.1%

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

      4. unsub-neg 61.1%

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

      5. *-commutative 61.1%

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

      6. mul-1-neg 61.1%

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

      7. remove-double-neg 61.1%

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

   5. Simplified 61.1%

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

   if -3.0999999999999999e137 < k < -9.50000000000000029e-17 or -5e-108 < k < 3.7999999999999997e-251 or 1.45e-183 < k < 2.09999999999999994e-8

   1. Initial program 33.1%

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

   3. Taylor expanded in x around inf 54.0%

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

   if -2.40000000000000009e-44 < k < -5e-108

   1. Initial program 29.0%

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

   3. Taylor expanded in y0 around inf 43.2%

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

      1. +-commutative 43.2%

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

      2. mul-1-neg 43.2%

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

      3. unsub-neg 43.2%

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

      4. *-commutative 43.2%

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

      5. *-commutative 43.2%

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

      6. *-commutative 43.2%

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

      7. *-commutative 43.2%

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

   5. Simplified 43.2%

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

   6. Taylor expanded in c around inf 50.8%

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

   if 3.7999999999999997e-251 < k < 1.45e-183

   1. Initial program 34.0%

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

   3. Taylor expanded in b around inf 74.3%

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

   if 2.09999999999999994e-8 < k < 6.0000000000000006e129

   1. Initial program 28.9%

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

   3. Taylor expanded in y5 around -inf 57.2%

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

   4. Taylor expanded in i around inf 76.6%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3.1 \cdot 10^{+137}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -9.5 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq -2.4 \cdot 10^{-44}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -5 \cdot 10^{-108}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 3.8 \cdot 10^{-251}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 1.45 \cdot 10^{-183}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;k \leq 2.1 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 6 \cdot 10^{+129}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 42.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ t_2 := z \cdot k - x \cdot j\\ t_3 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;k \leq -1.35 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq -8.8 \cdot 10^{+60}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;k \leq -2.2 \cdot 10^{-26}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq -2.02 \cdot 10^{-227}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot t\_2\right)\\ \mathbf{elif}\;k \leq 2.3 \cdot 10^{-251}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;k \leq 3.9 \cdot 10^{-184}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot t\_2\right)\\ \mathbf{elif}\;k \leq 8.2 \cdot 10^{-8}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;k \leq 4.6 \cdot 10^{+122}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          k
          (+
           (- (* y2 (- (* y1 y4) (* y0 y5))) (* y (- (* b y4) (* i y5))))
           (* z (- (* b y0) (* i y1))))))
        (t_2 (- (* z k) (* x j)))
        (t_3
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
           (* j (- (* i y1) (* b y0)))))))
   (if (<= k -1.35e+137)
     t_1
     (if (<= k -8.8e+60)
       t_3
       (if (<= k -2.2e-26)
         (* z (* c (- (* t i) (* y0 y3))))
         (if (<= k -2.02e-227)
           (*
            y0
            (+
             (+ (* c (- (* x y2) (* z y3))) (* y5 (- (* j y3) (* k y2))))
             (* b t_2)))
           (if (<= k 2.3e-251)
             t_3
             (if (<= k 3.9e-184)
               (*
                b
                (+
                 (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
                 (* y0 t_2)))
               (if (<= k 8.2e-8)
                 t_3
                 (if (<= k 4.6e+122)
                   (* i (* y5 (- (* y k) (* t j))))
                   t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (((y2 * ((y1 * y4) - (y0 * y5))) - (y * ((b * y4) - (i * y5)))) + (z * ((b * y0) - (i * y1))));
	double t_2 = (z * k) - (x * j);
	double t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (k <= -1.35e+137) {
		tmp = t_1;
	} else if (k <= -8.8e+60) {
		tmp = t_3;
	} else if (k <= -2.2e-26) {
		tmp = z * (c * ((t * i) - (y0 * y3)));
	} else if (k <= -2.02e-227) {
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * t_2));
	} else if (k <= 2.3e-251) {
		tmp = t_3;
	} else if (k <= 3.9e-184) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * t_2));
	} else if (k <= 8.2e-8) {
		tmp = t_3;
	} else if (k <= 4.6e+122) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = k * (((y2 * ((y1 * y4) - (y0 * y5))) - (y * ((b * y4) - (i * y5)))) + (z * ((b * y0) - (i * y1))))
    t_2 = (z * k) - (x * j)
    t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    if (k <= (-1.35d+137)) then
        tmp = t_1
    else if (k <= (-8.8d+60)) then
        tmp = t_3
    else if (k <= (-2.2d-26)) then
        tmp = z * (c * ((t * i) - (y0 * y3)))
    else if (k <= (-2.02d-227)) then
        tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * t_2))
    else if (k <= 2.3d-251) then
        tmp = t_3
    else if (k <= 3.9d-184) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * t_2))
    else if (k <= 8.2d-8) then
        tmp = t_3
    else if (k <= 4.6d+122) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (((y2 * ((y1 * y4) - (y0 * y5))) - (y * ((b * y4) - (i * y5)))) + (z * ((b * y0) - (i * y1))));
	double t_2 = (z * k) - (x * j);
	double t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (k <= -1.35e+137) {
		tmp = t_1;
	} else if (k <= -8.8e+60) {
		tmp = t_3;
	} else if (k <= -2.2e-26) {
		tmp = z * (c * ((t * i) - (y0 * y3)));
	} else if (k <= -2.02e-227) {
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * t_2));
	} else if (k <= 2.3e-251) {
		tmp = t_3;
	} else if (k <= 3.9e-184) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * t_2));
	} else if (k <= 8.2e-8) {
		tmp = t_3;
	} else if (k <= 4.6e+122) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (((y2 * ((y1 * y4) - (y0 * y5))) - (y * ((b * y4) - (i * y5)))) + (z * ((b * y0) - (i * y1))))
	t_2 = (z * k) - (x * j)
	t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	tmp = 0
	if k <= -1.35e+137:
		tmp = t_1
	elif k <= -8.8e+60:
		tmp = t_3
	elif k <= -2.2e-26:
		tmp = z * (c * ((t * i) - (y0 * y3)))
	elif k <= -2.02e-227:
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * t_2))
	elif k <= 2.3e-251:
		tmp = t_3
	elif k <= 3.9e-184:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * t_2))
	elif k <= 8.2e-8:
		tmp = t_3
	elif k <= 4.6e+122:
		tmp = i * (y5 * ((y * k) - (t * j)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(Float64(Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) - Float64(y * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))))
	t_2 = Float64(Float64(z * k) - Float64(x * j))
	t_3 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (k <= -1.35e+137)
		tmp = t_1;
	elseif (k <= -8.8e+60)
		tmp = t_3;
	elseif (k <= -2.2e-26)
		tmp = Float64(z * Float64(c * Float64(Float64(t * i) - Float64(y0 * y3))));
	elseif (k <= -2.02e-227)
		tmp = Float64(y0 * Float64(Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2)))) + Float64(b * t_2)));
	elseif (k <= 2.3e-251)
		tmp = t_3;
	elseif (k <= 3.9e-184)
		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 * t_2)));
	elseif (k <= 8.2e-8)
		tmp = t_3;
	elseif (k <= 4.6e+122)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (((y2 * ((y1 * y4) - (y0 * y5))) - (y * ((b * y4) - (i * y5)))) + (z * ((b * y0) - (i * y1))));
	t_2 = (z * k) - (x * j);
	t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (k <= -1.35e+137)
		tmp = t_1;
	elseif (k <= -8.8e+60)
		tmp = t_3;
	elseif (k <= -2.2e-26)
		tmp = z * (c * ((t * i) - (y0 * y3)));
	elseif (k <= -2.02e-227)
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * t_2));
	elseif (k <= 2.3e-251)
		tmp = t_3;
	elseif (k <= 3.9e-184)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * t_2));
	elseif (k <= 8.2e-8)
		tmp = t_3;
	elseif (k <= 4.6e+122)
		tmp = i * (y5 * ((y * k) - (t * j)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(N[(N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $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[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -1.35e+137], t$95$1, If[LessEqual[k, -8.8e+60], t$95$3, If[LessEqual[k, -2.2e-26], N[(z * N[(c * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2.02e-227], N[(y0 * N[(N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.3e-251], t$95$3, If[LessEqual[k, 3.9e-184], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 8.2e-8], t$95$3, If[LessEqual[k, 4.6e+122], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if k < -1.35000000000000009e137 or 4.6000000000000001e122 < k

   1. Initial program 24.9%

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

   3. Taylor expanded in k around inf 60.9%

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

      1. sub-neg 60.9%

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

      2. +-commutative 60.9%

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

      3. mul-1-neg 60.9%

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

      4. unsub-neg 60.9%

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

      5. *-commutative 60.9%

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

      6. mul-1-neg 60.9%

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

      7. remove-double-neg 60.9%

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

   5. Simplified 60.9%

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

   if -1.35000000000000009e137 < k < -8.79999999999999984e60 or -2.0200000000000001e-227 < k < 2.30000000000000017e-251 or 3.89999999999999994e-184 < k < 8.20000000000000063e-8

   1. Initial program 34.7%

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

   3. Taylor expanded in x around inf 59.3%

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

   if -8.79999999999999984e60 < k < -2.2000000000000001e-26

   1. Initial program 38.9%

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

   3. Taylor expanded in z around -inf 39.3%

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

   4. Taylor expanded in c around inf 50.6%

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

      1. +-commutative 50.6%

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

      2. mul-1-neg 50.6%

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

      3. unsub-neg 50.6%

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

      4. *-commutative 50.6%

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

   6. Simplified 50.6%

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

   if -2.2000000000000001e-26 < k < -2.0200000000000001e-227

   1. Initial program 29.5%

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

   3. Taylor expanded in y0 around inf 45.9%

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

      1. +-commutative 45.9%

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

      2. mul-1-neg 45.9%

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

      3. unsub-neg 45.9%

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

      4. *-commutative 45.9%

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

      5. *-commutative 45.9%

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

      6. *-commutative 45.9%

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

      7. *-commutative 45.9%

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

   5. Simplified 45.9%

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

   if 2.30000000000000017e-251 < k < 3.89999999999999994e-184

   1. Initial program 34.0%

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

   3. Taylor expanded in b around inf 74.3%

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

   if 8.20000000000000063e-8 < k < 4.6000000000000001e122

   1. Initial program 28.9%

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

   3. Taylor expanded in y5 around -inf 57.2%

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

   4. Taylor expanded in i around inf 76.6%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.35 \cdot 10^{+137}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -8.8 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq -2.2 \cdot 10^{-26}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq -2.02 \cdot 10^{-227}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;k \leq 2.3 \cdot 10^{-251}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 3.9 \cdot 10^{-184}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;k \leq 8.2 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 4.6 \cdot 10^{+122}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 43.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot k - x \cdot j\\ t_2 := k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ t_3 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_4 := x \cdot y - z \cdot t\\ t_5 := t \cdot j - y \cdot k\\ t_6 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot t\_4 + y5 \cdot t\_5\right)\right)\\ \mathbf{if}\;k \leq -3.4 \cdot 10^{+170}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;k \leq -5.2 \cdot 10^{-26}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;k \leq -7.6 \cdot 10^{-121}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot t\_1\right)\\ \mathbf{elif}\;k \leq -2.25 \cdot 10^{-229}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;k \leq 8.5 \cdot 10^{-251}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{-184}:\\ \;\;\;\;b \cdot \left(\left(a \cdot t\_4 + y4 \cdot t\_5\right) + y0 \cdot t\_1\right)\\ \mathbf{elif}\;k \leq 0.115:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;k \leq 4.6 \cdot 10^{+125}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* z k) (* x j)))
        (t_2
         (*
          k
          (+
           (- (* y2 (- (* y1 y4) (* y0 y5))) (* y (- (* b y4) (* i y5))))
           (* z (- (* b y0) (* i y1))))))
        (t_3
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
           (* j (- (* i y1) (* b y0))))))
        (t_4 (- (* x y) (* z t)))
        (t_5 (- (* t j) (* y k)))
        (t_6 (* i (- (* y1 (- (* x j) (* z k))) (+ (* c t_4) (* y5 t_5))))))
   (if (<= k -3.4e+170)
     t_2
     (if (<= k -5.2e-26)
       t_6
       (if (<= k -7.6e-121)
         (*
          y0
          (+
           (+ (* c (- (* x y2) (* z y3))) (* y5 (- (* j y3) (* k y2))))
           (* b t_1)))
         (if (<= k -2.25e-229)
           t_6
           (if (<= k 8.5e-251)
             t_3
             (if (<= k 7.5e-184)
               (* b (+ (+ (* a t_4) (* y4 t_5)) (* y0 t_1)))
               (if (<= k 0.115)
                 t_3
                 (if (<= k 4.6e+125)
                   (* i (* y5 (- (* y k) (* t j))))
                   t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * k) - (x * j);
	double t_2 = k * (((y2 * ((y1 * y4) - (y0 * y5))) - (y * ((b * y4) - (i * y5)))) + (z * ((b * y0) - (i * y1))));
	double t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double t_4 = (x * y) - (z * t);
	double t_5 = (t * j) - (y * k);
	double t_6 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_4) + (y5 * t_5)));
	double tmp;
	if (k <= -3.4e+170) {
		tmp = t_2;
	} else if (k <= -5.2e-26) {
		tmp = t_6;
	} else if (k <= -7.6e-121) {
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * t_1));
	} else if (k <= -2.25e-229) {
		tmp = t_6;
	} else if (k <= 8.5e-251) {
		tmp = t_3;
	} else if (k <= 7.5e-184) {
		tmp = b * (((a * t_4) + (y4 * t_5)) + (y0 * t_1));
	} else if (k <= 0.115) {
		tmp = t_3;
	} else if (k <= 4.6e+125) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = (z * k) - (x * j)
    t_2 = k * (((y2 * ((y1 * y4) - (y0 * y5))) - (y * ((b * y4) - (i * y5)))) + (z * ((b * y0) - (i * y1))))
    t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    t_4 = (x * y) - (z * t)
    t_5 = (t * j) - (y * k)
    t_6 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_4) + (y5 * t_5)))
    if (k <= (-3.4d+170)) then
        tmp = t_2
    else if (k <= (-5.2d-26)) then
        tmp = t_6
    else if (k <= (-7.6d-121)) then
        tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * t_1))
    else if (k <= (-2.25d-229)) then
        tmp = t_6
    else if (k <= 8.5d-251) then
        tmp = t_3
    else if (k <= 7.5d-184) then
        tmp = b * (((a * t_4) + (y4 * t_5)) + (y0 * t_1))
    else if (k <= 0.115d0) then
        tmp = t_3
    else if (k <= 4.6d+125) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * k) - (x * j);
	double t_2 = k * (((y2 * ((y1 * y4) - (y0 * y5))) - (y * ((b * y4) - (i * y5)))) + (z * ((b * y0) - (i * y1))));
	double t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double t_4 = (x * y) - (z * t);
	double t_5 = (t * j) - (y * k);
	double t_6 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_4) + (y5 * t_5)));
	double tmp;
	if (k <= -3.4e+170) {
		tmp = t_2;
	} else if (k <= -5.2e-26) {
		tmp = t_6;
	} else if (k <= -7.6e-121) {
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * t_1));
	} else if (k <= -2.25e-229) {
		tmp = t_6;
	} else if (k <= 8.5e-251) {
		tmp = t_3;
	} else if (k <= 7.5e-184) {
		tmp = b * (((a * t_4) + (y4 * t_5)) + (y0 * t_1));
	} else if (k <= 0.115) {
		tmp = t_3;
	} else if (k <= 4.6e+125) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (z * k) - (x * j)
	t_2 = k * (((y2 * ((y1 * y4) - (y0 * y5))) - (y * ((b * y4) - (i * y5)))) + (z * ((b * y0) - (i * y1))))
	t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	t_4 = (x * y) - (z * t)
	t_5 = (t * j) - (y * k)
	t_6 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_4) + (y5 * t_5)))
	tmp = 0
	if k <= -3.4e+170:
		tmp = t_2
	elif k <= -5.2e-26:
		tmp = t_6
	elif k <= -7.6e-121:
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * t_1))
	elif k <= -2.25e-229:
		tmp = t_6
	elif k <= 8.5e-251:
		tmp = t_3
	elif k <= 7.5e-184:
		tmp = b * (((a * t_4) + (y4 * t_5)) + (y0 * t_1))
	elif k <= 0.115:
		tmp = t_3
	elif k <= 4.6e+125:
		tmp = i * (y5 * ((y * k) - (t * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(z * k) - Float64(x * j))
	t_2 = Float64(k * Float64(Float64(Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) - Float64(y * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(z * Float64(Float64(b * y0) - Float64(i * y1)))))
	t_3 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_4 = Float64(Float64(x * y) - Float64(z * t))
	t_5 = Float64(Float64(t * j) - Float64(y * k))
	t_6 = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) - Float64(Float64(c * t_4) + Float64(y5 * t_5))))
	tmp = 0.0
	if (k <= -3.4e+170)
		tmp = t_2;
	elseif (k <= -5.2e-26)
		tmp = t_6;
	elseif (k <= -7.6e-121)
		tmp = Float64(y0 * Float64(Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2)))) + Float64(b * t_1)));
	elseif (k <= -2.25e-229)
		tmp = t_6;
	elseif (k <= 8.5e-251)
		tmp = t_3;
	elseif (k <= 7.5e-184)
		tmp = Float64(b * Float64(Float64(Float64(a * t_4) + Float64(y4 * t_5)) + Float64(y0 * t_1)));
	elseif (k <= 0.115)
		tmp = t_3;
	elseif (k <= 4.6e+125)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (z * k) - (x * j);
	t_2 = k * (((y2 * ((y1 * y4) - (y0 * y5))) - (y * ((b * y4) - (i * y5)))) + (z * ((b * y0) - (i * y1))));
	t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	t_4 = (x * y) - (z * t);
	t_5 = (t * j) - (y * k);
	t_6 = i * ((y1 * ((x * j) - (z * k))) - ((c * t_4) + (y5 * t_5)));
	tmp = 0.0;
	if (k <= -3.4e+170)
		tmp = t_2;
	elseif (k <= -5.2e-26)
		tmp = t_6;
	elseif (k <= -7.6e-121)
		tmp = y0 * (((c * ((x * y2) - (z * y3))) + (y5 * ((j * y3) - (k * y2)))) + (b * t_1));
	elseif (k <= -2.25e-229)
		tmp = t_6;
	elseif (k <= 8.5e-251)
		tmp = t_3;
	elseif (k <= 7.5e-184)
		tmp = b * (((a * t_4) + (y4 * t_5)) + (y0 * t_1));
	elseif (k <= 0.115)
		tmp = t_3;
	elseif (k <= 4.6e+125)
		tmp = i * (y5 * ((y * k) - (t * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(N[(N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(c * t$95$4), $MachinePrecision] + N[(y5 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -3.4e+170], t$95$2, If[LessEqual[k, -5.2e-26], t$95$6, If[LessEqual[k, -7.6e-121], N[(y0 * N[(N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2.25e-229], t$95$6, If[LessEqual[k, 8.5e-251], t$95$3, If[LessEqual[k, 7.5e-184], N[(b * N[(N[(N[(a * t$95$4), $MachinePrecision] + N[(y4 * t$95$5), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 0.115], t$95$3, If[LessEqual[k, 4.6e+125], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if k < -3.4000000000000001e170 or 4.60000000000000026e125 < k

   1. Initial program 26.4%

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

   3. Taylor expanded in k around inf 61.5%

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

      1. sub-neg 61.5%

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

      2. +-commutative 61.5%

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

      3. mul-1-neg 61.5%

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

      4. unsub-neg 61.5%

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

      5. *-commutative 61.5%

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

      6. mul-1-neg 61.5%

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

      7. remove-double-neg 61.5%

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

   5. Simplified 61.5%

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

   if -3.4000000000000001e170 < k < -5.2000000000000002e-26 or -7.6000000000000002e-121 < k < -2.2500000000000001e-229

   1. Initial program 25.6%

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

   3. Taylor expanded in i around -inf 59.8%

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

   if -5.2000000000000002e-26 < k < -7.6000000000000002e-121

   1. Initial program 29.2%

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

   3. Taylor expanded in y0 around inf 52.7%

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

      1. +-commutative 52.7%

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

      2. mul-1-neg 52.7%

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

      3. unsub-neg 52.7%

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

      4. *-commutative 52.7%

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

      5. *-commutative 52.7%

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

      6. *-commutative 52.7%

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

      7. *-commutative 52.7%

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

   5. Simplified 52.7%

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

   if -2.2500000000000001e-229 < k < 8.49999999999999984e-251 or 7.4999999999999995e-184 < k < 0.115000000000000005

   1. Initial program 38.9%

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

   3. Taylor expanded in x around inf 57.1%

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

   if 8.49999999999999984e-251 < k < 7.4999999999999995e-184

   1. Initial program 34.0%

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

   3. Taylor expanded in b around inf 74.3%

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

   if 0.115000000000000005 < k < 4.60000000000000026e125

   1. Initial program 28.9%

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

   3. Taylor expanded in y5 around -inf 57.2%

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

   4. Taylor expanded in i around inf 76.6%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3.4 \cdot 10^{+170}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq -5.2 \cdot 10^{-26}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot \left(x \cdot y - z \cdot t\right) + y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;k \leq -7.6 \cdot 10^{-121}:\\ \;\;\;\;y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;k \leq -2.25 \cdot 10^{-229}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \left(c \cdot \left(x \cdot y - z \cdot t\right) + y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;k \leq 8.5 \cdot 10^{-251}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{-184}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;k \leq 0.115:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 4.6 \cdot 10^{+125}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(\left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) - y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 31.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot i\right) \cdot \left(k \cdot y5 - x \cdot c\right)\\ t_2 := y0 \cdot \left(z \cdot k - x \cdot j\right)\\ \mathbf{if}\;i \leq -8.1 \cdot 10^{+179}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -7 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{elif}\;i \leq -6 \cdot 10^{+35}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(-x \cdot a\right)\right)\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{-17}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;i \leq -2.5 \cdot 10^{-66}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(t \cdot i - y0 \cdot y3\right)\\ \mathbf{elif}\;i \leq -2.4 \cdot 10^{-265}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 4.4 \cdot 10^{-81}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + t\_2\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{+81}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{+221}:\\ \;\;\;\;b \cdot t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* y i) (- (* k y5) (* x c))))
        (t_2 (* y0 (- (* z k) (* x j)))))
   (if (<= i -8.1e+179)
     t_1
     (if (<= i -7e+49)
       (* t (* y5 (- (* a y2) (* i j))))
       (if (<= i -6e+35)
         (* y1 (* y2 (- (* x a))))
         (if (<= i -2.1e-17)
           (* i (* y5 (- (* y k) (* t j))))
           (if (<= i -2.5e-66)
             (* (* z c) (- (* t i) (* y0 y3)))
             (if (<= i -2.4e-265)
               (* y5 (* y2 (- (* t a) (* k y0))))
               (if (<= i 4.4e-81)
                 (*
                  b
                  (+
                   (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
                   t_2))
                 (if (<= i 2.6e+81)
                   (* k (* y1 (- (* y2 y4) (* z i))))
                   (if (<= i 1.15e+221) (* b t_2) t_1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * i) * ((k * y5) - (x * c));
	double t_2 = y0 * ((z * k) - (x * j));
	double tmp;
	if (i <= -8.1e+179) {
		tmp = t_1;
	} else if (i <= -7e+49) {
		tmp = t * (y5 * ((a * y2) - (i * j)));
	} else if (i <= -6e+35) {
		tmp = y1 * (y2 * -(x * a));
	} else if (i <= -2.1e-17) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (i <= -2.5e-66) {
		tmp = (z * c) * ((t * i) - (y0 * y3));
	} else if (i <= -2.4e-265) {
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	} else if (i <= 4.4e-81) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + t_2);
	} else if (i <= 2.6e+81) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (i <= 1.15e+221) {
		tmp = b * t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * i) * ((k * y5) - (x * c))
    t_2 = y0 * ((z * k) - (x * j))
    if (i <= (-8.1d+179)) then
        tmp = t_1
    else if (i <= (-7d+49)) then
        tmp = t * (y5 * ((a * y2) - (i * j)))
    else if (i <= (-6d+35)) then
        tmp = y1 * (y2 * -(x * a))
    else if (i <= (-2.1d-17)) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (i <= (-2.5d-66)) then
        tmp = (z * c) * ((t * i) - (y0 * y3))
    else if (i <= (-2.4d-265)) then
        tmp = y5 * (y2 * ((t * a) - (k * y0)))
    else if (i <= 4.4d-81) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + t_2)
    else if (i <= 2.6d+81) then
        tmp = k * (y1 * ((y2 * y4) - (z * i)))
    else if (i <= 1.15d+221) then
        tmp = b * t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * i) * ((k * y5) - (x * c));
	double t_2 = y0 * ((z * k) - (x * j));
	double tmp;
	if (i <= -8.1e+179) {
		tmp = t_1;
	} else if (i <= -7e+49) {
		tmp = t * (y5 * ((a * y2) - (i * j)));
	} else if (i <= -6e+35) {
		tmp = y1 * (y2 * -(x * a));
	} else if (i <= -2.1e-17) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (i <= -2.5e-66) {
		tmp = (z * c) * ((t * i) - (y0 * y3));
	} else if (i <= -2.4e-265) {
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	} else if (i <= 4.4e-81) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + t_2);
	} else if (i <= 2.6e+81) {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	} else if (i <= 1.15e+221) {
		tmp = b * t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y * i) * ((k * y5) - (x * c))
	t_2 = y0 * ((z * k) - (x * j))
	tmp = 0
	if i <= -8.1e+179:
		tmp = t_1
	elif i <= -7e+49:
		tmp = t * (y5 * ((a * y2) - (i * j)))
	elif i <= -6e+35:
		tmp = y1 * (y2 * -(x * a))
	elif i <= -2.1e-17:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif i <= -2.5e-66:
		tmp = (z * c) * ((t * i) - (y0 * y3))
	elif i <= -2.4e-265:
		tmp = y5 * (y2 * ((t * a) - (k * y0)))
	elif i <= 4.4e-81:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + t_2)
	elif i <= 2.6e+81:
		tmp = k * (y1 * ((y2 * y4) - (z * i)))
	elif i <= 1.15e+221:
		tmp = b * t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * i) * Float64(Float64(k * y5) - Float64(x * c)))
	t_2 = Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))
	tmp = 0.0
	if (i <= -8.1e+179)
		tmp = t_1;
	elseif (i <= -7e+49)
		tmp = Float64(t * Float64(y5 * Float64(Float64(a * y2) - Float64(i * j))));
	elseif (i <= -6e+35)
		tmp = Float64(y1 * Float64(y2 * Float64(-Float64(x * a))));
	elseif (i <= -2.1e-17)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (i <= -2.5e-66)
		tmp = Float64(Float64(z * c) * Float64(Float64(t * i) - Float64(y0 * y3)));
	elseif (i <= -2.4e-265)
		tmp = Float64(y5 * Float64(y2 * Float64(Float64(t * a) - Float64(k * y0))));
	elseif (i <= 4.4e-81)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + t_2));
	elseif (i <= 2.6e+81)
		tmp = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))));
	elseif (i <= 1.15e+221)
		tmp = Float64(b * t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y * i) * ((k * y5) - (x * c));
	t_2 = y0 * ((z * k) - (x * j));
	tmp = 0.0;
	if (i <= -8.1e+179)
		tmp = t_1;
	elseif (i <= -7e+49)
		tmp = t * (y5 * ((a * y2) - (i * j)));
	elseif (i <= -6e+35)
		tmp = y1 * (y2 * -(x * a));
	elseif (i <= -2.1e-17)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (i <= -2.5e-66)
		tmp = (z * c) * ((t * i) - (y0 * y3));
	elseif (i <= -2.4e-265)
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	elseif (i <= 4.4e-81)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + t_2);
	elseif (i <= 2.6e+81)
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	elseif (i <= 1.15e+221)
		tmp = b * t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] * N[(N[(k * y5), $MachinePrecision] - N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -8.1e+179], t$95$1, If[LessEqual[i, -7e+49], N[(t * N[(y5 * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -6e+35], N[(y1 * N[(y2 * (-N[(x * a), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.1e-17], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.5e-66], N[(N[(z * c), $MachinePrecision] * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.4e-265], N[(y5 * N[(y2 * N[(N[(t * a), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.4e-81], 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] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.6e+81], N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.15e+221], N[(b * t$95$2), $MachinePrecision], t$95$1]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if i < -8.1e179 or 1.14999999999999993e221 < i

   1. Initial program 26.7%

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

   3. Taylor expanded in y around inf 46.9%

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

   4. Taylor expanded in i around inf 56.6%

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

      1. associate-*r* 60.8%

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

      2. +-commutative 60.8%

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

      3. mul-1-neg 60.8%

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

      4. unsub-neg 60.8%

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

      5. *-commutative 60.8%

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

      6. *-commutative 60.8%

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

   6. Simplified 60.8%

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

   if -8.1e179 < i < -6.9999999999999995e49

   1. Initial program 36.0%

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

   3. Taylor expanded in y5 around -inf 50.4%

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

   4. Taylor expanded in t around inf 54.6%

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

   if -6.9999999999999995e49 < i < -5.99999999999999981e35

   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 y1 around -inf 60.1%

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

      1. mul-1-neg 60.1%

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

      2. *-commutative 60.1%

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

      3. distribute-rgt-neg-in 60.1%

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

   5. Simplified 60.1%

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

   6. Taylor expanded in y2 around inf 61.4%

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

      1. *-commutative 61.4%

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

   8. Simplified 61.4%

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

   9. Taylor expanded in x around inf 80.9%

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

   if -5.99999999999999981e35 < i < -2.09999999999999992e-17

   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 y5 around -inf 45.7%

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

   4. Taylor expanded in i around inf 45.8%

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

   if -2.09999999999999992e-17 < i < -2.49999999999999981e-66

   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 z around -inf 72.5%

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

   4. Taylor expanded in c around inf 72.4%

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

      1. associate-*r* 72.3%

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

      2. +-commutative 72.3%

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

      3. mul-1-neg 72.3%

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

      4. unsub-neg 72.3%

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

      5. *-commutative 72.3%

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

   6. Simplified 72.3%

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

   if -2.49999999999999981e-66 < i < -2.4e-265

   1. Initial program 25.5%

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

   3. Taylor expanded in y5 around -inf 50.9%

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

   4. Taylor expanded in y2 around inf 50.7%

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

      1. *-commutative 50.7%

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

      2. *-commutative 50.7%

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

   6. Simplified 50.7%

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

   if -2.4e-265 < i < 4.3999999999999998e-81

   1. Initial program 30.9%

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

   3. Taylor expanded in b around inf 55.1%

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

   if 4.3999999999999998e-81 < i < 2.59999999999999992e81

   1. Initial program 36.1%

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

   3. Taylor expanded in y1 around -inf 52.3%

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

      1. mul-1-neg 52.3%

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

      2. *-commutative 52.3%

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

      3. distribute-rgt-neg-in 52.3%

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

   5. Simplified 52.3%

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

   6. Taylor expanded in k around -inf 47.3%

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

      1. mul-1-neg 47.3%

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

      2. *-commutative 47.3%

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

      3. distribute-rgt-neg-in 47.3%

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

      4. +-commutative 47.3%

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

      5. mul-1-neg 47.3%

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

      6. unsub-neg 47.3%

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

      7. *-commutative 47.3%

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

   8. Simplified 47.3%

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

   if 2.59999999999999992e81 < i < 1.14999999999999993e221

   1. Initial program 27.6%

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

   3. Taylor expanded in y0 around inf 42.2%

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

      1. +-commutative 42.2%

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

      2. mul-1-neg 42.2%

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

      3. unsub-neg 42.2%

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

      4. *-commutative 42.2%

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

      5. *-commutative 42.2%

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

      6. *-commutative 42.2%

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

      7. *-commutative 42.2%

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

   5. Simplified 42.2%

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

   6. Taylor expanded in b around inf 52.6%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8.1 \cdot 10^{+179}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(k \cdot y5 - x \cdot c\right)\\ \mathbf{elif}\;i \leq -7 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{elif}\;i \leq -6 \cdot 10^{+35}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(-x \cdot a\right)\right)\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{-17}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;i \leq -2.5 \cdot 10^{-66}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(t \cdot i - y0 \cdot y3\right)\\ \mathbf{elif}\;i \leq -2.4 \cdot 10^{-265}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 4.4 \cdot 10^{-81}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{+81}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{+221}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(k \cdot y5 - x \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 32.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y2 \cdot y4 - z \cdot i\\ t_2 := x \cdot y2 - z \cdot y3\\ \mathbf{if}\;y0 \leq -7.2 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -5.8 \cdot 10^{-58}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -2.05 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq -1.15 \cdot 10^{-202}:\\ \;\;\;\;t\_2 \cdot \left(c \cdot y0\right)\\ \mathbf{elif}\;y0 \leq -1.65 \cdot 10^{-267}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)\\ \mathbf{elif}\;y0 \leq 2.9 \cdot 10^{-307}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq 6.2 \cdot 10^{-191}:\\ \;\;\;\;k \cdot \left(y1 \cdot t\_1\right)\\ \mathbf{elif}\;y0 \leq 1.4 \cdot 10^{-120}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 1.6 \cdot 10^{-22}:\\ \;\;\;\;\left(k \cdot y1\right) \cdot t\_1\\ \mathbf{elif}\;y0 \leq 1.66 \cdot 10^{+106}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c - k \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot t\_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y2 y4) (* z i))) (t_2 (- (* x y2) (* z y3))))
   (if (<= y0 -7.2e+36)
     (* b (* y0 (- (* z k) (* x j))))
     (if (<= y0 -5.8e-58)
       (* z (* c (- (* t i) (* y0 y3))))
       (if (<= y0 -2.05e-196)
         (* y (* x (- (* a b) (* c i))))
         (if (<= y0 -1.15e-202)
           (* t_2 (* c y0))
           (if (<= y0 -1.65e-267)
             (* (* t b) (- (* j y4) (* z a)))
             (if (<= y0 2.9e-307)
               (* i (* y5 (- (* y k) (* t j))))
               (if (<= y0 6.2e-191)
                 (* k (* y1 t_1))
                 (if (<= y0 1.4e-120)
                   (* b (* y4 (- (* t j) (* y k))))
                   (if (<= y0 1.6e-22)
                     (* (* k y1) t_1)
                     (if (<= y0 1.66e+106)
                       (* (* y0 y2) (- (* x c) (* k y5)))
                       (* c (* y0 t_2))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y2 * y4) - (z * i);
	double t_2 = (x * y2) - (z * y3);
	double tmp;
	if (y0 <= -7.2e+36) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y0 <= -5.8e-58) {
		tmp = z * (c * ((t * i) - (y0 * y3)));
	} else if (y0 <= -2.05e-196) {
		tmp = y * (x * ((a * b) - (c * i)));
	} else if (y0 <= -1.15e-202) {
		tmp = t_2 * (c * y0);
	} else if (y0 <= -1.65e-267) {
		tmp = (t * b) * ((j * y4) - (z * a));
	} else if (y0 <= 2.9e-307) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y0 <= 6.2e-191) {
		tmp = k * (y1 * t_1);
	} else if (y0 <= 1.4e-120) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y0 <= 1.6e-22) {
		tmp = (k * y1) * t_1;
	} else if (y0 <= 1.66e+106) {
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	} else {
		tmp = c * (y0 * 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 = (y2 * y4) - (z * i)
    t_2 = (x * y2) - (z * y3)
    if (y0 <= (-7.2d+36)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y0 <= (-5.8d-58)) then
        tmp = z * (c * ((t * i) - (y0 * y3)))
    else if (y0 <= (-2.05d-196)) then
        tmp = y * (x * ((a * b) - (c * i)))
    else if (y0 <= (-1.15d-202)) then
        tmp = t_2 * (c * y0)
    else if (y0 <= (-1.65d-267)) then
        tmp = (t * b) * ((j * y4) - (z * a))
    else if (y0 <= 2.9d-307) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (y0 <= 6.2d-191) then
        tmp = k * (y1 * t_1)
    else if (y0 <= 1.4d-120) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y0 <= 1.6d-22) then
        tmp = (k * y1) * t_1
    else if (y0 <= 1.66d+106) then
        tmp = (y0 * y2) * ((x * c) - (k * y5))
    else
        tmp = c * (y0 * 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 = (y2 * y4) - (z * i);
	double t_2 = (x * y2) - (z * y3);
	double tmp;
	if (y0 <= -7.2e+36) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y0 <= -5.8e-58) {
		tmp = z * (c * ((t * i) - (y0 * y3)));
	} else if (y0 <= -2.05e-196) {
		tmp = y * (x * ((a * b) - (c * i)));
	} else if (y0 <= -1.15e-202) {
		tmp = t_2 * (c * y0);
	} else if (y0 <= -1.65e-267) {
		tmp = (t * b) * ((j * y4) - (z * a));
	} else if (y0 <= 2.9e-307) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y0 <= 6.2e-191) {
		tmp = k * (y1 * t_1);
	} else if (y0 <= 1.4e-120) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y0 <= 1.6e-22) {
		tmp = (k * y1) * t_1;
	} else if (y0 <= 1.66e+106) {
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	} else {
		tmp = c * (y0 * 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 = (y2 * y4) - (z * i)
	t_2 = (x * y2) - (z * y3)
	tmp = 0
	if y0 <= -7.2e+36:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y0 <= -5.8e-58:
		tmp = z * (c * ((t * i) - (y0 * y3)))
	elif y0 <= -2.05e-196:
		tmp = y * (x * ((a * b) - (c * i)))
	elif y0 <= -1.15e-202:
		tmp = t_2 * (c * y0)
	elif y0 <= -1.65e-267:
		tmp = (t * b) * ((j * y4) - (z * a))
	elif y0 <= 2.9e-307:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif y0 <= 6.2e-191:
		tmp = k * (y1 * t_1)
	elif y0 <= 1.4e-120:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y0 <= 1.6e-22:
		tmp = (k * y1) * t_1
	elif y0 <= 1.66e+106:
		tmp = (y0 * y2) * ((x * c) - (k * y5))
	else:
		tmp = c * (y0 * t_2)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y2 * y4) - Float64(z * i))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	tmp = 0.0
	if (y0 <= -7.2e+36)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y0 <= -5.8e-58)
		tmp = Float64(z * Float64(c * Float64(Float64(t * i) - Float64(y0 * y3))));
	elseif (y0 <= -2.05e-196)
		tmp = Float64(y * Float64(x * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y0 <= -1.15e-202)
		tmp = Float64(t_2 * Float64(c * y0));
	elseif (y0 <= -1.65e-267)
		tmp = Float64(Float64(t * b) * Float64(Float64(j * y4) - Float64(z * a)));
	elseif (y0 <= 2.9e-307)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (y0 <= 6.2e-191)
		tmp = Float64(k * Float64(y1 * t_1));
	elseif (y0 <= 1.4e-120)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y0 <= 1.6e-22)
		tmp = Float64(Float64(k * y1) * t_1);
	elseif (y0 <= 1.66e+106)
		tmp = Float64(Float64(y0 * y2) * Float64(Float64(x * c) - Float64(k * y5)));
	else
		tmp = Float64(c * Float64(y0 * 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 = (y2 * y4) - (z * i);
	t_2 = (x * y2) - (z * y3);
	tmp = 0.0;
	if (y0 <= -7.2e+36)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y0 <= -5.8e-58)
		tmp = z * (c * ((t * i) - (y0 * y3)));
	elseif (y0 <= -2.05e-196)
		tmp = y * (x * ((a * b) - (c * i)));
	elseif (y0 <= -1.15e-202)
		tmp = t_2 * (c * y0);
	elseif (y0 <= -1.65e-267)
		tmp = (t * b) * ((j * y4) - (z * a));
	elseif (y0 <= 2.9e-307)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (y0 <= 6.2e-191)
		tmp = k * (y1 * t_1);
	elseif (y0 <= 1.4e-120)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y0 <= 1.6e-22)
		tmp = (k * y1) * t_1;
	elseif (y0 <= 1.66e+106)
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	else
		tmp = c * (y0 * t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -7.2e+36], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -5.8e-58], N[(z * N[(c * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -2.05e-196], N[(y * N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.15e-202], N[(t$95$2 * N[(c * y0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.65e-267], N[(N[(t * b), $MachinePrecision] * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.9e-307], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 6.2e-191], N[(k * N[(y1 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.4e-120], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.6e-22], N[(N[(k * y1), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[y0, 1.66e+106], N[(N[(y0 * y2), $MachinePrecision] * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y0 * t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if y0 < -7.1999999999999995e36

   1. Initial program 25.1%

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

   3. Taylor expanded in y0 around inf 66.3%

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

      1. +-commutative 66.3%

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

      2. mul-1-neg 66.3%

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

      3. unsub-neg 66.3%

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

      4. *-commutative 66.3%

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

      5. *-commutative 66.3%

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

      6. *-commutative 66.3%

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

      7. *-commutative 66.3%

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

   5. Simplified 66.3%

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

   6. Taylor expanded in b around inf 54.3%

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

   if -7.1999999999999995e36 < y0 < -5.7999999999999998e-58

   1. Initial program 54.8%

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

   3. Taylor expanded in z around -inf 55.2%

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

   4. Taylor expanded in c around inf 42.0%

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

      1. +-commutative 42.0%

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

      2. mul-1-neg 42.0%

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

      3. unsub-neg 42.0%

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

      4. *-commutative 42.0%

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

   6. Simplified 42.0%

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

   if -5.7999999999999998e-58 < y0 < -2.05000000000000011e-196

   1. Initial program 14.4%

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

   3. Taylor expanded in y around inf 36.9%

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

   4. Taylor expanded in x around inf 42.0%

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

      1. *-commutative 42.0%

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

      2. *-commutative 42.0%

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

      3. *-commutative 42.0%

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

      4. associate-*r* 42.0%

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

      5. *-commutative 42.0%

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

      6. *-commutative 42.0%

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

      7. *-commutative 42.0%

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

   6. Simplified 42.0%

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

   if -2.05000000000000011e-196 < y0 < -1.1499999999999999e-202

   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 8.5%

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

      1. +-commutative 8.5%

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

      2. mul-1-neg 8.5%

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

      3. unsub-neg 8.5%

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

      4. *-commutative 8.5%

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

      5. *-commutative 8.5%

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

      6. *-commutative 8.5%

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

      7. *-commutative 8.5%

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

   5. Simplified 8.5%

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

   6. Taylor expanded in c around inf 51.3%

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

      1. associate-*r* 52.1%

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

      2. *-commutative 52.1%

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

   8. Simplified 52.1%

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

   if -1.1499999999999999e-202 < y0 < -1.65000000000000002e-267

   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 b around inf 51.0%

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

   4. Taylor expanded in t around inf 57.2%

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

      1. associate-*r* 51.4%

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

      2. +-commutative 51.4%

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

      3. mul-1-neg 51.4%

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

      4. unsub-neg 51.4%

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

      5. *-commutative 51.4%

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

   6. Simplified 51.4%

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

   if -1.65000000000000002e-267 < y0 < 2.9e-307

   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 y5 around -inf 25.5%

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

   4. Taylor expanded in i around inf 62.9%

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

   if 2.9e-307 < y0 < 6.2000000000000004e-191

   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 59.8%

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

      1. mul-1-neg 59.8%

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

      2. *-commutative 59.8%

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

      3. distribute-rgt-neg-in 59.8%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in k around -inf 52.6%

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

      1. mul-1-neg 52.6%

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

      2. *-commutative 52.6%

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

      3. distribute-rgt-neg-in 52.6%

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

      4. +-commutative 52.6%

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

      5. mul-1-neg 52.6%

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

      6. unsub-neg 52.6%

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

      7. *-commutative 52.6%

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

   8. Simplified 52.6%

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

   if 6.2000000000000004e-191 < y0 < 1.39999999999999997e-120

   1. Initial program 13.3%

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

   3. Taylor expanded in b around inf 53.3%

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

   4. Taylor expanded in y4 around inf 66.9%

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

   if 1.39999999999999997e-120 < y0 < 1.59999999999999994e-22

   1. Initial program 56.2%

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

   3. Taylor expanded in y1 around -inf 57.2%

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

      1. mul-1-neg 57.2%

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

      2. *-commutative 57.2%

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

      3. distribute-rgt-neg-in 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in k around inf 51.6%

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

      1. associate-*r* 51.6%

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

      2. +-commutative 51.6%

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

      3. mul-1-neg 51.6%

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

      4. unsub-neg 51.6%

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

      5. *-commutative 51.6%

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

   8. Simplified 51.6%

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

   if 1.59999999999999994e-22 < y0 < 1.66e106

   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 40.7%

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

      1. +-commutative 40.7%

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

      2. mul-1-neg 40.7%

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

      3. unsub-neg 40.7%

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

      4. *-commutative 40.7%

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

      5. *-commutative 40.7%

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

      6. *-commutative 40.7%

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

      7. *-commutative 40.7%

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

   5. Simplified 40.7%

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

   6. Taylor expanded in y2 around inf 51.3%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(c \cdot x - k \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 51.1%

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

   8. Simplified 51.1%

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

   if 1.66e106 < y0

   1. Initial program 19.2%

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

   3. Taylor expanded in y0 around inf 58.1%

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

      1. +-commutative 58.1%

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

      2. mul-1-neg 58.1%

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

      3. unsub-neg 58.1%

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

      4. *-commutative 58.1%

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

      5. *-commutative 58.1%

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

      6. *-commutative 58.1%

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

      7. *-commutative 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in c around inf 58.0%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
3. Recombined 11 regimes into one program.

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -7.2 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -5.8 \cdot 10^{-58}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -2.05 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq -1.15 \cdot 10^{-202}:\\ \;\;\;\;\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0\right)\\ \mathbf{elif}\;y0 \leq -1.65 \cdot 10^{-267}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)\\ \mathbf{elif}\;y0 \leq 2.9 \cdot 10^{-307}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq 6.2 \cdot 10^{-191}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 1.4 \cdot 10^{-120}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 1.6 \cdot 10^{-22}:\\ \;\;\;\;\left(k \cdot y1\right) \cdot \left(y2 \cdot y4 - z \cdot i\right)\\ \mathbf{elif}\;y0 \leq 1.66 \cdot 10^{+106}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c - k \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 31.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y0 \cdot y2\right) \cdot \left(x \cdot c - k \cdot y5\right)\\ t_2 := y2 \cdot y4 - z \cdot i\\ \mathbf{if}\;y0 \leq -1.7 \cdot 10^{+160}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k - c \cdot y3\right)\\ \mathbf{elif}\;y0 \leq -2.4 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq -1.7 \cdot 10^{+40}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(k \cdot y0 - t \cdot a\right)\\ \mathbf{elif}\;y0 \leq -6 \cdot 10^{-58}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -1.15 \cdot 10^{-187}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 7 \cdot 10^{-308}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq 4.9 \cdot 10^{-191}:\\ \;\;\;\;k \cdot \left(y1 \cdot t\_2\right)\\ \mathbf{elif}\;y0 \leq 3.8 \cdot 10^{-111}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 1.6 \cdot 10^{-22}:\\ \;\;\;\;\left(k \cdot y1\right) \cdot t\_2\\ \mathbf{elif}\;y0 \leq 1.6 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* y0 y2) (- (* x c) (* k y5)))) (t_2 (- (* y2 y4) (* z i))))
   (if (<= y0 -1.7e+160)
     (* (* z y0) (- (* b k) (* c y3)))
     (if (<= y0 -2.4e+121)
       t_1
       (if (<= y0 -1.7e+40)
         (* (* z b) (- (* k y0) (* t a)))
         (if (<= y0 -6e-58)
           (* z (* c (- (* t i) (* y0 y3))))
           (if (<= y0 -1.15e-187)
             (* y (* x (- (* a b) (* c i))))
             (if (<= y0 7e-308)
               (* i (* y5 (- (* y k) (* t j))))
               (if (<= y0 4.9e-191)
                 (* k (* y1 t_2))
                 (if (<= y0 3.8e-111)
                   (* b (* y4 (- (* t j) (* y k))))
                   (if (<= y0 1.6e-22)
                     (* (* k y1) t_2)
                     (if (<= y0 1.6e+106)
                       t_1
                       (* c (* y0 (- (* x y2) (* z y3))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * y2) * ((x * c) - (k * y5));
	double t_2 = (y2 * y4) - (z * i);
	double tmp;
	if (y0 <= -1.7e+160) {
		tmp = (z * y0) * ((b * k) - (c * y3));
	} else if (y0 <= -2.4e+121) {
		tmp = t_1;
	} else if (y0 <= -1.7e+40) {
		tmp = (z * b) * ((k * y0) - (t * a));
	} else if (y0 <= -6e-58) {
		tmp = z * (c * ((t * i) - (y0 * y3)));
	} else if (y0 <= -1.15e-187) {
		tmp = y * (x * ((a * b) - (c * i)));
	} else if (y0 <= 7e-308) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y0 <= 4.9e-191) {
		tmp = k * (y1 * t_2);
	} else if (y0 <= 3.8e-111) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y0 <= 1.6e-22) {
		tmp = (k * y1) * t_2;
	} else if (y0 <= 1.6e+106) {
		tmp = t_1;
	} else {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y0 * y2) * ((x * c) - (k * y5))
    t_2 = (y2 * y4) - (z * i)
    if (y0 <= (-1.7d+160)) then
        tmp = (z * y0) * ((b * k) - (c * y3))
    else if (y0 <= (-2.4d+121)) then
        tmp = t_1
    else if (y0 <= (-1.7d+40)) then
        tmp = (z * b) * ((k * y0) - (t * a))
    else if (y0 <= (-6d-58)) then
        tmp = z * (c * ((t * i) - (y0 * y3)))
    else if (y0 <= (-1.15d-187)) then
        tmp = y * (x * ((a * b) - (c * i)))
    else if (y0 <= 7d-308) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (y0 <= 4.9d-191) then
        tmp = k * (y1 * t_2)
    else if (y0 <= 3.8d-111) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y0 <= 1.6d-22) then
        tmp = (k * y1) * t_2
    else if (y0 <= 1.6d+106) then
        tmp = t_1
    else
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * y2) * ((x * c) - (k * y5));
	double t_2 = (y2 * y4) - (z * i);
	double tmp;
	if (y0 <= -1.7e+160) {
		tmp = (z * y0) * ((b * k) - (c * y3));
	} else if (y0 <= -2.4e+121) {
		tmp = t_1;
	} else if (y0 <= -1.7e+40) {
		tmp = (z * b) * ((k * y0) - (t * a));
	} else if (y0 <= -6e-58) {
		tmp = z * (c * ((t * i) - (y0 * y3)));
	} else if (y0 <= -1.15e-187) {
		tmp = y * (x * ((a * b) - (c * i)));
	} else if (y0 <= 7e-308) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y0 <= 4.9e-191) {
		tmp = k * (y1 * t_2);
	} else if (y0 <= 3.8e-111) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y0 <= 1.6e-22) {
		tmp = (k * y1) * t_2;
	} else if (y0 <= 1.6e+106) {
		tmp = t_1;
	} else {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y0 * y2) * ((x * c) - (k * y5))
	t_2 = (y2 * y4) - (z * i)
	tmp = 0
	if y0 <= -1.7e+160:
		tmp = (z * y0) * ((b * k) - (c * y3))
	elif y0 <= -2.4e+121:
		tmp = t_1
	elif y0 <= -1.7e+40:
		tmp = (z * b) * ((k * y0) - (t * a))
	elif y0 <= -6e-58:
		tmp = z * (c * ((t * i) - (y0 * y3)))
	elif y0 <= -1.15e-187:
		tmp = y * (x * ((a * b) - (c * i)))
	elif y0 <= 7e-308:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif y0 <= 4.9e-191:
		tmp = k * (y1 * t_2)
	elif y0 <= 3.8e-111:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y0 <= 1.6e-22:
		tmp = (k * y1) * t_2
	elif y0 <= 1.6e+106:
		tmp = t_1
	else:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y0 * y2) * Float64(Float64(x * c) - Float64(k * y5)))
	t_2 = Float64(Float64(y2 * y4) - Float64(z * i))
	tmp = 0.0
	if (y0 <= -1.7e+160)
		tmp = Float64(Float64(z * y0) * Float64(Float64(b * k) - Float64(c * y3)));
	elseif (y0 <= -2.4e+121)
		tmp = t_1;
	elseif (y0 <= -1.7e+40)
		tmp = Float64(Float64(z * b) * Float64(Float64(k * y0) - Float64(t * a)));
	elseif (y0 <= -6e-58)
		tmp = Float64(z * Float64(c * Float64(Float64(t * i) - Float64(y0 * y3))));
	elseif (y0 <= -1.15e-187)
		tmp = Float64(y * Float64(x * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y0 <= 7e-308)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (y0 <= 4.9e-191)
		tmp = Float64(k * Float64(y1 * t_2));
	elseif (y0 <= 3.8e-111)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y0 <= 1.6e-22)
		tmp = Float64(Float64(k * y1) * t_2);
	elseif (y0 <= 1.6e+106)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - 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)
	t_1 = (y0 * y2) * ((x * c) - (k * y5));
	t_2 = (y2 * y4) - (z * i);
	tmp = 0.0;
	if (y0 <= -1.7e+160)
		tmp = (z * y0) * ((b * k) - (c * y3));
	elseif (y0 <= -2.4e+121)
		tmp = t_1;
	elseif (y0 <= -1.7e+40)
		tmp = (z * b) * ((k * y0) - (t * a));
	elseif (y0 <= -6e-58)
		tmp = z * (c * ((t * i) - (y0 * y3)));
	elseif (y0 <= -1.15e-187)
		tmp = y * (x * ((a * b) - (c * i)));
	elseif (y0 <= 7e-308)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (y0 <= 4.9e-191)
		tmp = k * (y1 * t_2);
	elseif (y0 <= 3.8e-111)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y0 <= 1.6e-22)
		tmp = (k * y1) * t_2;
	elseif (y0 <= 1.6e+106)
		tmp = t_1;
	else
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y0 * y2), $MachinePrecision] * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -1.7e+160], N[(N[(z * y0), $MachinePrecision] * N[(N[(b * k), $MachinePrecision] - N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -2.4e+121], t$95$1, If[LessEqual[y0, -1.7e+40], N[(N[(z * b), $MachinePrecision] * N[(N[(k * y0), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -6e-58], N[(z * N[(c * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.15e-187], N[(y * N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 7e-308], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.9e-191], N[(k * N[(y1 * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 3.8e-111], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.6e-22], N[(N[(k * y1), $MachinePrecision] * t$95$2), $MachinePrecision], If[LessEqual[y0, 1.6e+106], t$95$1, N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y0 < -1.70000000000000015e160

   1. Initial program 18.1%

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

   3. Taylor expanded in y0 around inf 60.7%

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

      1. +-commutative 60.7%

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

      2. mul-1-neg 60.7%

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

      3. unsub-neg 60.7%

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

      4. *-commutative 60.7%

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

      5. *-commutative 60.7%

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

      6. *-commutative 60.7%

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

      7. *-commutative 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in z around inf 61.4%

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

      1. associate-*r* 61.5%

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

      2. distribute-lft-out-- 61.5%

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

   8. Simplified 61.5%

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

   if -1.70000000000000015e160 < y0 < -2.4e121 or 1.59999999999999994e-22 < y0 < 1.5999999999999999e106

   1. Initial program 28.0%

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

   3. Taylor expanded in y0 around inf 47.1%

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

      1. +-commutative 47.1%

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

      2. mul-1-neg 47.1%

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

      3. unsub-neg 47.1%

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

      4. *-commutative 47.1%

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

      5. *-commutative 47.1%

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

      6. *-commutative 47.1%

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

      7. *-commutative 47.1%

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

   5. Simplified 47.1%

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

   6. Taylor expanded in y2 around inf 54.5%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(c \cdot x - k \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 54.3%

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

   8. Simplified 54.3%

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

   if -2.4e121 < y0 < -1.69999999999999994e40

   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 54.0%

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

   4. Taylor expanded in z around inf 74.0%

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

      1. associate-*r* 67.6%

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

      2. *-commutative 67.6%

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

      3. distribute-lft-out-- 67.6%

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

      4. *-commutative 67.6%

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

      5. *-commutative 67.6%

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

   6. Simplified 67.6%

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

   if -1.69999999999999994e40 < y0 < -6.00000000000000015e-58

   1. Initial program 54.8%

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

   3. Taylor expanded in z around -inf 55.2%

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

   4. Taylor expanded in c around inf 42.0%

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

      1. +-commutative 42.0%

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

      2. mul-1-neg 42.0%

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

      3. unsub-neg 42.0%

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

      4. *-commutative 42.0%

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

   6. Simplified 42.0%

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

   if -6.00000000000000015e-58 < y0 < -1.14999999999999999e-187

   1. Initial program 14.4%

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

   3. Taylor expanded in y around inf 36.9%

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

   4. Taylor expanded in x around inf 42.0%

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

      1. *-commutative 42.0%

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

      2. *-commutative 42.0%

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

      3. *-commutative 42.0%

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

      4. associate-*r* 42.0%

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

      5. *-commutative 42.0%

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

      6. *-commutative 42.0%

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

      7. *-commutative 42.0%

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

   6. Simplified 42.0%

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

   if -1.14999999999999999e-187 < y0 < 7e-308

   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 y5 around -inf 32.1%

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

   4. Taylor expanded in i around inf 50.9%

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

   if 7e-308 < y0 < 4.9e-191

   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 59.8%

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

      1. mul-1-neg 59.8%

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

      2. *-commutative 59.8%

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

      3. distribute-rgt-neg-in 59.8%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in k around -inf 52.6%

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

      1. mul-1-neg 52.6%

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

      2. *-commutative 52.6%

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

      3. distribute-rgt-neg-in 52.6%

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

      4. +-commutative 52.6%

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

      5. mul-1-neg 52.6%

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

      6. unsub-neg 52.6%

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

      7. *-commutative 52.6%

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

   8. Simplified 52.6%

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

   if 4.9e-191 < y0 < 3.80000000000000022e-111

   1. Initial program 13.3%

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

   3. Taylor expanded in b around inf 53.3%

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

   4. Taylor expanded in y4 around inf 66.9%

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

   if 3.80000000000000022e-111 < y0 < 1.59999999999999994e-22

   1. Initial program 56.2%

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

   3. Taylor expanded in y1 around -inf 57.2%

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

      1. mul-1-neg 57.2%

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

      2. *-commutative 57.2%

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

      3. distribute-rgt-neg-in 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in k around inf 51.6%

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

      1. associate-*r* 51.6%

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

      2. +-commutative 51.6%

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

      3. mul-1-neg 51.6%

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

      4. unsub-neg 51.6%

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

      5. *-commutative 51.6%

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

   8. Simplified 51.6%

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

   if 1.5999999999999999e106 < y0

   1. Initial program 19.2%

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

   3. Taylor expanded in y0 around inf 58.1%

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

      1. +-commutative 58.1%

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

      2. mul-1-neg 58.1%

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

      3. unsub-neg 58.1%

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

      4. *-commutative 58.1%

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

      5. *-commutative 58.1%

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

      6. *-commutative 58.1%

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

      7. *-commutative 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in c around inf 58.0%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.7 \cdot 10^{+160}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k - c \cdot y3\right)\\ \mathbf{elif}\;y0 \leq -2.4 \cdot 10^{+121}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c - k \cdot y5\right)\\ \mathbf{elif}\;y0 \leq -1.7 \cdot 10^{+40}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(k \cdot y0 - t \cdot a\right)\\ \mathbf{elif}\;y0 \leq -6 \cdot 10^{-58}:\\ \;\;\;\;z \cdot \left(c \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -1.15 \cdot 10^{-187}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 7 \cdot 10^{-308}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq 4.9 \cdot 10^{-191}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 3.8 \cdot 10^{-111}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 1.6 \cdot 10^{-22}:\\ \;\;\;\;\left(k \cdot y1\right) \cdot \left(y2 \cdot y4 - z \cdot i\right)\\ \mathbf{elif}\;y0 \leq 1.6 \cdot 10^{+106}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c - k \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 32.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y2 \cdot y4 - z \cdot i\\ \mathbf{if}\;y0 \leq -7 \cdot 10^{+33}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -1.4 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq -3.4 \cdot 10^{-268}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)\\ \mathbf{elif}\;y0 \leq 6.8 \cdot 10^{-307}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq 5.2 \cdot 10^{-191}:\\ \;\;\;\;k \cdot \left(y1 \cdot t\_1\right)\\ \mathbf{elif}\;y0 \leq 1.35 \cdot 10^{-112}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 1.65 \cdot 10^{-22}:\\ \;\;\;\;\left(k \cdot y1\right) \cdot t\_1\\ \mathbf{elif}\;y0 \leq 2.9 \cdot 10^{+106}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c - k \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y2 y4) (* z i))))
   (if (<= y0 -7e+33)
     (* b (* y0 (- (* z k) (* x j))))
     (if (<= y0 -1.4e-183)
       (* x (* y (- (* a b) (* c i))))
       (if (<= y0 -3.4e-268)
         (* (* t b) (- (* j y4) (* z a)))
         (if (<= y0 6.8e-307)
           (* i (* y5 (- (* y k) (* t j))))
           (if (<= y0 5.2e-191)
             (* k (* y1 t_1))
             (if (<= y0 1.35e-112)
               (* b (* y4 (- (* t j) (* y k))))
               (if (<= y0 1.65e-22)
                 (* (* k y1) t_1)
                 (if (<= y0 2.9e+106)
                   (* (* y0 y2) (- (* x c) (* k y5)))
                   (* c (* y0 (- (* x y2) (* z y3))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y2 * y4) - (z * i);
	double tmp;
	if (y0 <= -7e+33) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y0 <= -1.4e-183) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y0 <= -3.4e-268) {
		tmp = (t * b) * ((j * y4) - (z * a));
	} else if (y0 <= 6.8e-307) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y0 <= 5.2e-191) {
		tmp = k * (y1 * t_1);
	} else if (y0 <= 1.35e-112) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y0 <= 1.65e-22) {
		tmp = (k * y1) * t_1;
	} else if (y0 <= 2.9e+106) {
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	} else {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y2 * y4) - (z * i)
    if (y0 <= (-7d+33)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y0 <= (-1.4d-183)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y0 <= (-3.4d-268)) then
        tmp = (t * b) * ((j * y4) - (z * a))
    else if (y0 <= 6.8d-307) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (y0 <= 5.2d-191) then
        tmp = k * (y1 * t_1)
    else if (y0 <= 1.35d-112) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y0 <= 1.65d-22) then
        tmp = (k * y1) * t_1
    else if (y0 <= 2.9d+106) then
        tmp = (y0 * y2) * ((x * c) - (k * y5))
    else
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y2 * y4) - (z * i);
	double tmp;
	if (y0 <= -7e+33) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y0 <= -1.4e-183) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y0 <= -3.4e-268) {
		tmp = (t * b) * ((j * y4) - (z * a));
	} else if (y0 <= 6.8e-307) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y0 <= 5.2e-191) {
		tmp = k * (y1 * t_1);
	} else if (y0 <= 1.35e-112) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y0 <= 1.65e-22) {
		tmp = (k * y1) * t_1;
	} else if (y0 <= 2.9e+106) {
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	} else {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y2 * y4) - (z * i)
	tmp = 0
	if y0 <= -7e+33:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y0 <= -1.4e-183:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y0 <= -3.4e-268:
		tmp = (t * b) * ((j * y4) - (z * a))
	elif y0 <= 6.8e-307:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif y0 <= 5.2e-191:
		tmp = k * (y1 * t_1)
	elif y0 <= 1.35e-112:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y0 <= 1.65e-22:
		tmp = (k * y1) * t_1
	elif y0 <= 2.9e+106:
		tmp = (y0 * y2) * ((x * c) - (k * y5))
	else:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y2 * y4) - Float64(z * i))
	tmp = 0.0
	if (y0 <= -7e+33)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y0 <= -1.4e-183)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y0 <= -3.4e-268)
		tmp = Float64(Float64(t * b) * Float64(Float64(j * y4) - Float64(z * a)));
	elseif (y0 <= 6.8e-307)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (y0 <= 5.2e-191)
		tmp = Float64(k * Float64(y1 * t_1));
	elseif (y0 <= 1.35e-112)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y0 <= 1.65e-22)
		tmp = Float64(Float64(k * y1) * t_1);
	elseif (y0 <= 2.9e+106)
		tmp = Float64(Float64(y0 * y2) * Float64(Float64(x * c) - Float64(k * y5)));
	else
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - 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)
	t_1 = (y2 * y4) - (z * i);
	tmp = 0.0;
	if (y0 <= -7e+33)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y0 <= -1.4e-183)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y0 <= -3.4e-268)
		tmp = (t * b) * ((j * y4) - (z * a));
	elseif (y0 <= 6.8e-307)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (y0 <= 5.2e-191)
		tmp = k * (y1 * t_1);
	elseif (y0 <= 1.35e-112)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y0 <= 1.65e-22)
		tmp = (k * y1) * t_1;
	elseif (y0 <= 2.9e+106)
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	else
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -7e+33], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.4e-183], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -3.4e-268], N[(N[(t * b), $MachinePrecision] * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 6.8e-307], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 5.2e-191], N[(k * N[(y1 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.35e-112], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.65e-22], N[(N[(k * y1), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[y0, 2.9e+106], N[(N[(y0 * y2), $MachinePrecision] * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y0 < -7.0000000000000002e33

   1. Initial program 24.7%

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

   3. Taylor expanded in y0 around inf 66.9%

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

      1. +-commutative 66.9%

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

      2. mul-1-neg 66.9%

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

      3. unsub-neg 66.9%

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

      4. *-commutative 66.9%

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

      5. *-commutative 66.9%

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

      6. *-commutative 66.9%

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

      7. *-commutative 66.9%

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

   5. Simplified 66.9%

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

   6. Taylor expanded in b around inf 53.4%

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

   if -7.0000000000000002e33 < y0 < -1.39999999999999992e-183

   1. Initial program 36.3%

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

   3. Taylor expanded in x around inf 41.4%

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

   4. Taylor expanded in y around inf 34.4%

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

      1. *-commutative 34.4%

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

   6. Simplified 34.4%

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

   if -1.39999999999999992e-183 < y0 < -3.4e-268

   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 b around inf 42.9%

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

   4. Taylor expanded in t around inf 53.4%

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

      1. associate-*r* 48.6%

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

      2. +-commutative 48.6%

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

      3. mul-1-neg 48.6%

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

      4. unsub-neg 48.6%

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

      5. *-commutative 48.6%

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

   6. Simplified 48.6%

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

   if -3.4e-268 < y0 < 6.79999999999999978e-307

   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 y5 around -inf 25.5%

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

   4. Taylor expanded in i around inf 62.9%

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

   if 6.79999999999999978e-307 < y0 < 5.19999999999999972e-191

   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 59.8%

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

      1. mul-1-neg 59.8%

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

      2. *-commutative 59.8%

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

      3. distribute-rgt-neg-in 59.8%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in k around -inf 52.6%

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

      1. mul-1-neg 52.6%

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

      2. *-commutative 52.6%

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

      3. distribute-rgt-neg-in 52.6%

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

      4. +-commutative 52.6%

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

      5. mul-1-neg 52.6%

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

      6. unsub-neg 52.6%

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

      7. *-commutative 52.6%

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

   8. Simplified 52.6%

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

   if 5.19999999999999972e-191 < y0 < 1.35e-112

   1. Initial program 13.3%

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

   3. Taylor expanded in b around inf 53.3%

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

   4. Taylor expanded in y4 around inf 66.9%

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

   if 1.35e-112 < y0 < 1.65e-22

   1. Initial program 56.2%

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

   3. Taylor expanded in y1 around -inf 57.2%

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

      1. mul-1-neg 57.2%

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

      2. *-commutative 57.2%

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

      3. distribute-rgt-neg-in 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in k around inf 51.6%

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

      1. associate-*r* 51.6%

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

      2. +-commutative 51.6%

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

      3. mul-1-neg 51.6%

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

      4. unsub-neg 51.6%

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

      5. *-commutative 51.6%

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

   8. Simplified 51.6%

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

   if 1.65e-22 < y0 < 2.9000000000000002e106

   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 40.7%

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

      1. +-commutative 40.7%

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

      2. mul-1-neg 40.7%

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

      3. unsub-neg 40.7%

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

      4. *-commutative 40.7%

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

      5. *-commutative 40.7%

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

      6. *-commutative 40.7%

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

      7. *-commutative 40.7%

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

   5. Simplified 40.7%

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

   6. Taylor expanded in y2 around inf 51.3%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(c \cdot x - k \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 51.1%

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

   8. Simplified 51.1%

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

   if 2.9000000000000002e106 < y0

   1. Initial program 19.2%

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

   3. Taylor expanded in y0 around inf 58.1%

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

      1. +-commutative 58.1%

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

      2. mul-1-neg 58.1%

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

      3. unsub-neg 58.1%

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

      4. *-commutative 58.1%

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

      5. *-commutative 58.1%

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

      6. *-commutative 58.1%

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

      7. *-commutative 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in c around inf 58.0%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -7 \cdot 10^{+33}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -1.4 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq -3.4 \cdot 10^{-268}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)\\ \mathbf{elif}\;y0 \leq 6.8 \cdot 10^{-307}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq 5.2 \cdot 10^{-191}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 1.35 \cdot 10^{-112}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 1.65 \cdot 10^{-22}:\\ \;\;\;\;\left(k \cdot y1\right) \cdot \left(y2 \cdot y4 - z \cdot i\right)\\ \mathbf{elif}\;y0 \leq 2.9 \cdot 10^{+106}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c - k \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 32.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(k \cdot y1\right) \cdot \left(y2 \cdot y4 - z \cdot i\right)\\ \mathbf{if}\;y0 \leq -5 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -1 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 4.7 \cdot 10^{-306}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)\\ \mathbf{elif}\;y0 \leq 5.3 \cdot 10^{-191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq 2.8 \cdot 10^{-123}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 1.6 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq 1.7 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* k y1) (- (* y2 y4) (* z i)))))
   (if (<= y0 -5e+36)
     (* b (* y0 (- (* z k) (* x j))))
     (if (<= y0 -1e-185)
       (* x (* y (- (* a b) (* c i))))
       (if (<= y0 4.7e-306)
         (* (* t b) (- (* j y4) (* z a)))
         (if (<= y0 5.3e-191)
           t_1
           (if (<= y0 2.8e-123)
             (* b (* y4 (- (* t j) (* y k))))
             (if (<= y0 1.6e-22)
               t_1
               (if (<= y0 1.7e+71)
                 (* y (* y3 (- (* c y4) (* a y5))))
                 (* c (* y0 (- (* x y2) (* z y3)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y1) * ((y2 * y4) - (z * i));
	double tmp;
	if (y0 <= -5e+36) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y0 <= -1e-185) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y0 <= 4.7e-306) {
		tmp = (t * b) * ((j * y4) - (z * a));
	} else if (y0 <= 5.3e-191) {
		tmp = t_1;
	} else if (y0 <= 2.8e-123) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y0 <= 1.6e-22) {
		tmp = t_1;
	} else if (y0 <= 1.7e+71) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (k * y1) * ((y2 * y4) - (z * i))
    if (y0 <= (-5d+36)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y0 <= (-1d-185)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y0 <= 4.7d-306) then
        tmp = (t * b) * ((j * y4) - (z * a))
    else if (y0 <= 5.3d-191) then
        tmp = t_1
    else if (y0 <= 2.8d-123) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y0 <= 1.6d-22) then
        tmp = t_1
    else if (y0 <= 1.7d+71) then
        tmp = y * (y3 * ((c * y4) - (a * y5)))
    else
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y1) * ((y2 * y4) - (z * i));
	double tmp;
	if (y0 <= -5e+36) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y0 <= -1e-185) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y0 <= 4.7e-306) {
		tmp = (t * b) * ((j * y4) - (z * a));
	} else if (y0 <= 5.3e-191) {
		tmp = t_1;
	} else if (y0 <= 2.8e-123) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y0 <= 1.6e-22) {
		tmp = t_1;
	} else if (y0 <= 1.7e+71) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (k * y1) * ((y2 * y4) - (z * i))
	tmp = 0
	if y0 <= -5e+36:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y0 <= -1e-185:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y0 <= 4.7e-306:
		tmp = (t * b) * ((j * y4) - (z * a))
	elif y0 <= 5.3e-191:
		tmp = t_1
	elif y0 <= 2.8e-123:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y0 <= 1.6e-22:
		tmp = t_1
	elif y0 <= 1.7e+71:
		tmp = y * (y3 * ((c * y4) - (a * y5)))
	else:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(k * y1) * Float64(Float64(y2 * y4) - Float64(z * i)))
	tmp = 0.0
	if (y0 <= -5e+36)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y0 <= -1e-185)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y0 <= 4.7e-306)
		tmp = Float64(Float64(t * b) * Float64(Float64(j * y4) - Float64(z * a)));
	elseif (y0 <= 5.3e-191)
		tmp = t_1;
	elseif (y0 <= 2.8e-123)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y0 <= 1.6e-22)
		tmp = t_1;
	elseif (y0 <= 1.7e+71)
		tmp = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))));
	else
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - 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)
	t_1 = (k * y1) * ((y2 * y4) - (z * i));
	tmp = 0.0;
	if (y0 <= -5e+36)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y0 <= -1e-185)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y0 <= 4.7e-306)
		tmp = (t * b) * ((j * y4) - (z * a));
	elseif (y0 <= 5.3e-191)
		tmp = t_1;
	elseif (y0 <= 2.8e-123)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y0 <= 1.6e-22)
		tmp = t_1;
	elseif (y0 <= 1.7e+71)
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	else
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(k * y1), $MachinePrecision] * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -5e+36], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1e-185], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.7e-306], N[(N[(t * b), $MachinePrecision] * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 5.3e-191], t$95$1, If[LessEqual[y0, 2.8e-123], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.6e-22], t$95$1, If[LessEqual[y0, 1.7e+71], N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y0 < -4.99999999999999977e36

   1. Initial program 24.7%

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

   3. Taylor expanded in y0 around inf 66.9%

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

      1. +-commutative 66.9%

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

      2. mul-1-neg 66.9%

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

      3. unsub-neg 66.9%

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

      4. *-commutative 66.9%

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

      5. *-commutative 66.9%

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

      6. *-commutative 66.9%

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

      7. *-commutative 66.9%

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

   5. Simplified 66.9%

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

   6. Taylor expanded in b around inf 53.4%

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

   if -4.99999999999999977e36 < y0 < -9.9999999999999999e-186

   1. Initial program 36.3%

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

   3. Taylor expanded in x around inf 41.4%

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

   4. Taylor expanded in y around inf 34.4%

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

      1. *-commutative 34.4%

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

   6. Simplified 34.4%

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

   if -9.9999999999999999e-186 < y0 < 4.7000000000000001e-306

   1. Initial program 37.3%

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

   3. Taylor expanded in b around inf 37.7%

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

   4. Taylor expanded in t around inf 49.7%

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

      1. associate-*r* 46.3%

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

      2. +-commutative 46.3%

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

      3. mul-1-neg 46.3%

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

      4. unsub-neg 46.3%

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

      5. *-commutative 46.3%

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

   6. Simplified 46.3%

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

   if 4.7000000000000001e-306 < y0 < 5.29999999999999985e-191 or 2.7999999999999999e-123 < y0 < 1.59999999999999994e-22

   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 58.9%

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

      1. mul-1-neg 58.9%

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

      2. *-commutative 58.9%

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

      3. distribute-rgt-neg-in 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in k around inf 52.2%

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

      1. associate-*r* 50.0%

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

      2. +-commutative 50.0%

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

      3. mul-1-neg 50.0%

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

      4. unsub-neg 50.0%

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

      5. *-commutative 50.0%

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

   8. Simplified 50.0%

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

   if 5.29999999999999985e-191 < y0 < 2.7999999999999999e-123

   1. Initial program 13.3%

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

   3. Taylor expanded in b around inf 53.3%

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

   4. Taylor expanded in y4 around inf 66.9%

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

   if 1.59999999999999994e-22 < y0 < 1.6999999999999999e71

   1. Initial program 26.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 16.3%

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   4. Taylor expanded in y3 around inf 53.3%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   if 1.6999999999999999e71 < y0

   1. Initial program 20.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 53.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 53.9%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 53.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 53.9%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 53.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 53.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 53.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 53.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 53.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 53.9%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -5 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -1 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 4.7 \cdot 10^{-306}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)\\ \mathbf{elif}\;y0 \leq 5.3 \cdot 10^{-191}:\\ \;\;\;\;\left(k \cdot y1\right) \cdot \left(y2 \cdot y4 - z \cdot i\right)\\ \mathbf{elif}\;y0 \leq 2.8 \cdot 10^{-123}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 1.6 \cdot 10^{-22}:\\ \;\;\;\;\left(k \cdot y1\right) \cdot \left(y2 \cdot y4 - z \cdot i\right)\\ \mathbf{elif}\;y0 \leq 1.7 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 32.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(k \cdot y1\right) \cdot \left(y2 \cdot y4 - z \cdot i\right)\\ \mathbf{if}\;y0 \leq -5.2 \cdot 10^{+34}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -8.5 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 2 \cdot 10^{-307}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)\\ \mathbf{elif}\;y0 \leq 5 \cdot 10^{-191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq 9.5 \cdot 10^{-105}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 1.65 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq 1.56 \cdot 10^{+106}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c - k \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* k y1) (- (* y2 y4) (* z i)))))
   (if (<= y0 -5.2e+34)
     (* b (* y0 (- (* z k) (* x j))))
     (if (<= y0 -8.5e-186)
       (* x (* y (- (* a b) (* c i))))
       (if (<= y0 2e-307)
         (* (* t b) (- (* j y4) (* z a)))
         (if (<= y0 5e-191)
           t_1
           (if (<= y0 9.5e-105)
             (* b (* y4 (- (* t j) (* y k))))
             (if (<= y0 1.65e-22)
               t_1
               (if (<= y0 1.56e+106)
                 (* (* y0 y2) (- (* x c) (* k y5)))
                 (* c (* y0 (- (* x y2) (* z y3)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y1) * ((y2 * y4) - (z * i));
	double tmp;
	if (y0 <= -5.2e+34) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y0 <= -8.5e-186) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y0 <= 2e-307) {
		tmp = (t * b) * ((j * y4) - (z * a));
	} else if (y0 <= 5e-191) {
		tmp = t_1;
	} else if (y0 <= 9.5e-105) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y0 <= 1.65e-22) {
		tmp = t_1;
	} else if (y0 <= 1.56e+106) {
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	} else {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (k * y1) * ((y2 * y4) - (z * i))
    if (y0 <= (-5.2d+34)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y0 <= (-8.5d-186)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y0 <= 2d-307) then
        tmp = (t * b) * ((j * y4) - (z * a))
    else if (y0 <= 5d-191) then
        tmp = t_1
    else if (y0 <= 9.5d-105) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y0 <= 1.65d-22) then
        tmp = t_1
    else if (y0 <= 1.56d+106) then
        tmp = (y0 * y2) * ((x * c) - (k * y5))
    else
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y1) * ((y2 * y4) - (z * i));
	double tmp;
	if (y0 <= -5.2e+34) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y0 <= -8.5e-186) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y0 <= 2e-307) {
		tmp = (t * b) * ((j * y4) - (z * a));
	} else if (y0 <= 5e-191) {
		tmp = t_1;
	} else if (y0 <= 9.5e-105) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y0 <= 1.65e-22) {
		tmp = t_1;
	} else if (y0 <= 1.56e+106) {
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	} else {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (k * y1) * ((y2 * y4) - (z * i))
	tmp = 0
	if y0 <= -5.2e+34:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y0 <= -8.5e-186:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y0 <= 2e-307:
		tmp = (t * b) * ((j * y4) - (z * a))
	elif y0 <= 5e-191:
		tmp = t_1
	elif y0 <= 9.5e-105:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y0 <= 1.65e-22:
		tmp = t_1
	elif y0 <= 1.56e+106:
		tmp = (y0 * y2) * ((x * c) - (k * y5))
	else:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(k * y1) * Float64(Float64(y2 * y4) - Float64(z * i)))
	tmp = 0.0
	if (y0 <= -5.2e+34)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y0 <= -8.5e-186)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y0 <= 2e-307)
		tmp = Float64(Float64(t * b) * Float64(Float64(j * y4) - Float64(z * a)));
	elseif (y0 <= 5e-191)
		tmp = t_1;
	elseif (y0 <= 9.5e-105)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y0 <= 1.65e-22)
		tmp = t_1;
	elseif (y0 <= 1.56e+106)
		tmp = Float64(Float64(y0 * y2) * Float64(Float64(x * c) - Float64(k * y5)));
	else
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - 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)
	t_1 = (k * y1) * ((y2 * y4) - (z * i));
	tmp = 0.0;
	if (y0 <= -5.2e+34)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y0 <= -8.5e-186)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y0 <= 2e-307)
		tmp = (t * b) * ((j * y4) - (z * a));
	elseif (y0 <= 5e-191)
		tmp = t_1;
	elseif (y0 <= 9.5e-105)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y0 <= 1.65e-22)
		tmp = t_1;
	elseif (y0 <= 1.56e+106)
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	else
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(k * y1), $MachinePrecision] * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -5.2e+34], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -8.5e-186], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2e-307], N[(N[(t * b), $MachinePrecision] * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 5e-191], t$95$1, If[LessEqual[y0, 9.5e-105], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.65e-22], t$95$1, If[LessEqual[y0, 1.56e+106], N[(N[(y0 * y2), $MachinePrecision] * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y0 < -5.19999999999999995e34

   1. Initial program 24.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 66.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 66.9%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 66.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 66.9%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 66.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 66.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 66.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 66.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 66.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in b around inf 53.4%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if -5.19999999999999995e34 < y0 < -8.4999999999999994e-186

   1. Initial program 36.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 41.4%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around inf 34.4%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 34.4%

         \[\leadsto x \cdot \left(y \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right)\right) \]

   6. Simplified 34.4%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(b \cdot a - c \cdot i\right)\right)} \]

   if -8.4999999999999994e-186 < y0 < 1.99999999999999982e-307

   1. Initial program 37.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 37.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in t around inf 49.7%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 46.3%

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      2. +-commutative 46.3%

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)} \]

      3. mul-1-neg 46.3%

         \[\leadsto \left(b \cdot t\right) \cdot \left(j \cdot y4 + \color{blue}{\left(-a \cdot z\right)}\right) \]

      4. unsub-neg 46.3%

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)} \]

      5. *-commutative 46.3%

         \[\leadsto \left(b \cdot t\right) \cdot \left(j \cdot y4 - \color{blue}{z \cdot a}\right) \]

   6. Simplified 46.3%

      \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(j \cdot y4 - z \cdot a\right)} \]

   if 1.99999999999999982e-307 < y0 < 5.0000000000000001e-191 or 9.5000000000000002e-105 < y0 < 1.65e-22

   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 58.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 58.9%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 58.9%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 58.9%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 58.9%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in k around inf 52.2%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 50.0%

         \[\leadsto \color{blue}{\left(k \cdot y1\right) \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)} \]

      2. +-commutative 50.0%

         \[\leadsto \left(k \cdot y1\right) \cdot \color{blue}{\left(y2 \cdot y4 + -1 \cdot \left(i \cdot z\right)\right)} \]

      3. mul-1-neg 50.0%

         \[\leadsto \left(k \cdot y1\right) \cdot \left(y2 \cdot y4 + \color{blue}{\left(-i \cdot z\right)}\right) \]

      4. unsub-neg 50.0%

         \[\leadsto \left(k \cdot y1\right) \cdot \color{blue}{\left(y2 \cdot y4 - i \cdot z\right)} \]

      5. *-commutative 50.0%

         \[\leadsto \left(k \cdot y1\right) \cdot \left(y2 \cdot y4 - \color{blue}{z \cdot i}\right) \]

   8. Simplified 50.0%

      \[\leadsto \color{blue}{\left(k \cdot y1\right) \cdot \left(y2 \cdot y4 - z \cdot i\right)} \]

   if 5.0000000000000001e-191 < y0 < 9.5000000000000002e-105

   1. Initial program 13.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 53.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 66.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if 1.65e-22 < y0 < 1.55999999999999991e106

   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 40.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 40.7%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 40.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 40.7%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 40.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 40.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 40.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 40.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 40.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y2 around inf 51.3%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(c \cdot x - k \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 51.1%

         \[\leadsto \color{blue}{\left(y0 \cdot y2\right) \cdot \left(c \cdot x - k \cdot y5\right)} \]

   8. Simplified 51.1%

      \[\leadsto \color{blue}{\left(y0 \cdot y2\right) \cdot \left(c \cdot x - k \cdot y5\right)} \]

   if 1.55999999999999991e106 < y0

   1. Initial program 19.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 58.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 58.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 58.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 58.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 58.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 58.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 58.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 58.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 58.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 58.0%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -5.2 \cdot 10^{+34}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -8.5 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 2 \cdot 10^{-307}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)\\ \mathbf{elif}\;y0 \leq 5 \cdot 10^{-191}:\\ \;\;\;\;\left(k \cdot y1\right) \cdot \left(y2 \cdot y4 - z \cdot i\right)\\ \mathbf{elif}\;y0 \leq 9.5 \cdot 10^{-105}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 1.65 \cdot 10^{-22}:\\ \;\;\;\;\left(k \cdot y1\right) \cdot \left(y2 \cdot y4 - z \cdot i\right)\\ \mathbf{elif}\;y0 \leq 1.56 \cdot 10^{+106}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c - k \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 32.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y2 \cdot y4 - z \cdot i\\ \mathbf{if}\;y0 \leq -2.6 \cdot 10^{+34}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -7 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 4.9 \cdot 10^{-307}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)\\ \mathbf{elif}\;y0 \leq 5.4 \cdot 10^{-191}:\\ \;\;\;\;k \cdot \left(y1 \cdot t\_1\right)\\ \mathbf{elif}\;y0 \leq 2.6 \cdot 10^{-121}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 1.65 \cdot 10^{-22}:\\ \;\;\;\;\left(k \cdot y1\right) \cdot t\_1\\ \mathbf{elif}\;y0 \leq 2.6 \cdot 10^{+106}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c - k \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y2 y4) (* z i))))
   (if (<= y0 -2.6e+34)
     (* b (* y0 (- (* z k) (* x j))))
     (if (<= y0 -7e-186)
       (* x (* y (- (* a b) (* c i))))
       (if (<= y0 4.9e-307)
         (* (* t b) (- (* j y4) (* z a)))
         (if (<= y0 5.4e-191)
           (* k (* y1 t_1))
           (if (<= y0 2.6e-121)
             (* b (* y4 (- (* t j) (* y k))))
             (if (<= y0 1.65e-22)
               (* (* k y1) t_1)
               (if (<= y0 2.6e+106)
                 (* (* y0 y2) (- (* x c) (* k y5)))
                 (* c (* y0 (- (* x y2) (* z y3)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y2 * y4) - (z * i);
	double tmp;
	if (y0 <= -2.6e+34) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y0 <= -7e-186) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y0 <= 4.9e-307) {
		tmp = (t * b) * ((j * y4) - (z * a));
	} else if (y0 <= 5.4e-191) {
		tmp = k * (y1 * t_1);
	} else if (y0 <= 2.6e-121) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y0 <= 1.65e-22) {
		tmp = (k * y1) * t_1;
	} else if (y0 <= 2.6e+106) {
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	} else {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y2 * y4) - (z * i)
    if (y0 <= (-2.6d+34)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y0 <= (-7d-186)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y0 <= 4.9d-307) then
        tmp = (t * b) * ((j * y4) - (z * a))
    else if (y0 <= 5.4d-191) then
        tmp = k * (y1 * t_1)
    else if (y0 <= 2.6d-121) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y0 <= 1.65d-22) then
        tmp = (k * y1) * t_1
    else if (y0 <= 2.6d+106) then
        tmp = (y0 * y2) * ((x * c) - (k * y5))
    else
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y2 * y4) - (z * i);
	double tmp;
	if (y0 <= -2.6e+34) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y0 <= -7e-186) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y0 <= 4.9e-307) {
		tmp = (t * b) * ((j * y4) - (z * a));
	} else if (y0 <= 5.4e-191) {
		tmp = k * (y1 * t_1);
	} else if (y0 <= 2.6e-121) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y0 <= 1.65e-22) {
		tmp = (k * y1) * t_1;
	} else if (y0 <= 2.6e+106) {
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	} else {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y2 * y4) - (z * i)
	tmp = 0
	if y0 <= -2.6e+34:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y0 <= -7e-186:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y0 <= 4.9e-307:
		tmp = (t * b) * ((j * y4) - (z * a))
	elif y0 <= 5.4e-191:
		tmp = k * (y1 * t_1)
	elif y0 <= 2.6e-121:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y0 <= 1.65e-22:
		tmp = (k * y1) * t_1
	elif y0 <= 2.6e+106:
		tmp = (y0 * y2) * ((x * c) - (k * y5))
	else:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y2 * y4) - Float64(z * i))
	tmp = 0.0
	if (y0 <= -2.6e+34)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y0 <= -7e-186)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y0 <= 4.9e-307)
		tmp = Float64(Float64(t * b) * Float64(Float64(j * y4) - Float64(z * a)));
	elseif (y0 <= 5.4e-191)
		tmp = Float64(k * Float64(y1 * t_1));
	elseif (y0 <= 2.6e-121)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y0 <= 1.65e-22)
		tmp = Float64(Float64(k * y1) * t_1);
	elseif (y0 <= 2.6e+106)
		tmp = Float64(Float64(y0 * y2) * Float64(Float64(x * c) - Float64(k * y5)));
	else
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - 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)
	t_1 = (y2 * y4) - (z * i);
	tmp = 0.0;
	if (y0 <= -2.6e+34)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y0 <= -7e-186)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y0 <= 4.9e-307)
		tmp = (t * b) * ((j * y4) - (z * a));
	elseif (y0 <= 5.4e-191)
		tmp = k * (y1 * t_1);
	elseif (y0 <= 2.6e-121)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y0 <= 1.65e-22)
		tmp = (k * y1) * t_1;
	elseif (y0 <= 2.6e+106)
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	else
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -2.6e+34], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -7e-186], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.9e-307], N[(N[(t * b), $MachinePrecision] * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 5.4e-191], N[(k * N[(y1 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.6e-121], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.65e-22], N[(N[(k * y1), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[y0, 2.6e+106], N[(N[(y0 * y2), $MachinePrecision] * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y0 < -2.59999999999999997e34

   1. Initial program 24.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 66.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 66.9%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 66.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 66.9%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 66.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 66.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 66.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 66.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 66.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in b around inf 53.4%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if -2.59999999999999997e34 < y0 < -6.99999999999999978e-186

   1. Initial program 36.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 41.4%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around inf 34.4%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 34.4%

         \[\leadsto x \cdot \left(y \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right)\right) \]

   6. Simplified 34.4%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(b \cdot a - c \cdot i\right)\right)} \]

   if -6.99999999999999978e-186 < y0 < 4.9000000000000002e-307

   1. Initial program 37.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 37.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in t around inf 49.7%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 46.3%

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      2. +-commutative 46.3%

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)} \]

      3. mul-1-neg 46.3%

         \[\leadsto \left(b \cdot t\right) \cdot \left(j \cdot y4 + \color{blue}{\left(-a \cdot z\right)}\right) \]

      4. unsub-neg 46.3%

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)} \]

      5. *-commutative 46.3%

         \[\leadsto \left(b \cdot t\right) \cdot \left(j \cdot y4 - \color{blue}{z \cdot a}\right) \]

   6. Simplified 46.3%

      \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(j \cdot y4 - z \cdot a\right)} \]

   if 4.9000000000000002e-307 < y0 < 5.39999999999999998e-191

   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 59.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 59.8%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 59.8%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 59.8%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 59.8%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in k around -inf 52.6%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y1 \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 52.6%

         \[\leadsto \color{blue}{-k \cdot \left(y1 \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right)} \]

      2. *-commutative 52.6%

         \[\leadsto -\color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right) \cdot k} \]

      3. distribute-rgt-neg-in 52.6%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y2 \cdot y4\right) + i \cdot z\right)\right) \cdot \left(-k\right)} \]

      4. +-commutative 52.6%

         \[\leadsto \left(y1 \cdot \color{blue}{\left(i \cdot z + -1 \cdot \left(y2 \cdot y4\right)\right)}\right) \cdot \left(-k\right) \]

      5. mul-1-neg 52.6%

         \[\leadsto \left(y1 \cdot \left(i \cdot z + \color{blue}{\left(-y2 \cdot y4\right)}\right)\right) \cdot \left(-k\right) \]

      6. unsub-neg 52.6%

         \[\leadsto \left(y1 \cdot \color{blue}{\left(i \cdot z - y2 \cdot y4\right)}\right) \cdot \left(-k\right) \]

      7. *-commutative 52.6%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{z \cdot i} - y2 \cdot y4\right)\right) \cdot \left(-k\right) \]

   8. Simplified 52.6%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(z \cdot i - y2 \cdot y4\right)\right) \cdot \left(-k\right)} \]

   if 5.39999999999999998e-191 < y0 < 2.59999999999999986e-121

   1. Initial program 13.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 53.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 66.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if 2.59999999999999986e-121 < y0 < 1.65e-22

   1. Initial program 56.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 57.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 57.2%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 57.2%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 57.2%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 57.2%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in k around inf 51.6%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 51.6%

         \[\leadsto \color{blue}{\left(k \cdot y1\right) \cdot \left(-1 \cdot \left(i \cdot z\right) + y2 \cdot y4\right)} \]

      2. +-commutative 51.6%

         \[\leadsto \left(k \cdot y1\right) \cdot \color{blue}{\left(y2 \cdot y4 + -1 \cdot \left(i \cdot z\right)\right)} \]

      3. mul-1-neg 51.6%

         \[\leadsto \left(k \cdot y1\right) \cdot \left(y2 \cdot y4 + \color{blue}{\left(-i \cdot z\right)}\right) \]

      4. unsub-neg 51.6%

         \[\leadsto \left(k \cdot y1\right) \cdot \color{blue}{\left(y2 \cdot y4 - i \cdot z\right)} \]

      5. *-commutative 51.6%

         \[\leadsto \left(k \cdot y1\right) \cdot \left(y2 \cdot y4 - \color{blue}{z \cdot i}\right) \]

   8. Simplified 51.6%

      \[\leadsto \color{blue}{\left(k \cdot y1\right) \cdot \left(y2 \cdot y4 - z \cdot i\right)} \]

   if 1.65e-22 < y0 < 2.6000000000000002e106

   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 40.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 40.7%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 40.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 40.7%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 40.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 40.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 40.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 40.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 40.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y2 around inf 51.3%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(c \cdot x - k \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 51.1%

         \[\leadsto \color{blue}{\left(y0 \cdot y2\right) \cdot \left(c \cdot x - k \cdot y5\right)} \]

   8. Simplified 51.1%

      \[\leadsto \color{blue}{\left(y0 \cdot y2\right) \cdot \left(c \cdot x - k \cdot y5\right)} \]

   if 2.6000000000000002e106 < y0

   1. Initial program 19.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 58.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 58.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 58.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 58.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 58.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 58.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 58.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 58.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 58.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 58.0%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -2.6 \cdot 10^{+34}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -7 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 4.9 \cdot 10^{-307}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)\\ \mathbf{elif}\;y0 \leq 5.4 \cdot 10^{-191}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 2.6 \cdot 10^{-121}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 1.65 \cdot 10^{-22}:\\ \;\;\;\;\left(k \cdot y1\right) \cdot \left(y2 \cdot y4 - z \cdot i\right)\\ \mathbf{elif}\;y0 \leq 2.6 \cdot 10^{+106}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c - k \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 33.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -1.35 \cdot 10^{+34}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -8.5 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 8 \cdot 10^{-307}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)\\ \mathbf{elif}\;y0 \leq 6.5 \cdot 10^{-191}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.1 \cdot 10^{-50}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 8 \cdot 10^{+67}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -1.35e+34)
   (* b (* y0 (- (* z k) (* x j))))
   (if (<= y0 -8.5e-186)
     (* x (* y (- (* a b) (* c i))))
     (if (<= y0 8e-307)
       (* (* t b) (- (* j y4) (* z a)))
       (if (<= y0 6.5e-191)
         (* y1 (* y3 (- (* z a) (* j y4))))
         (if (<= y0 1.1e-50)
           (* b (* y4 (- (* t j) (* y k))))
           (if (<= y0 8e+67)
             (* y (* y3 (- (* c y4) (* a y5))))
             (* c (* y0 (- (* x y2) (* 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 (y0 <= -1.35e+34) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y0 <= -8.5e-186) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y0 <= 8e-307) {
		tmp = (t * b) * ((j * y4) - (z * a));
	} else if (y0 <= 6.5e-191) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (y0 <= 1.1e-50) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y0 <= 8e+67) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else {
		tmp = c * (y0 * ((x * y2) - (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 (y0 <= (-1.35d+34)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y0 <= (-8.5d-186)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y0 <= 8d-307) then
        tmp = (t * b) * ((j * y4) - (z * a))
    else if (y0 <= 6.5d-191) then
        tmp = y1 * (y3 * ((z * a) - (j * y4)))
    else if (y0 <= 1.1d-50) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y0 <= 8d+67) then
        tmp = y * (y3 * ((c * y4) - (a * y5)))
    else
        tmp = c * (y0 * ((x * y2) - (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 (y0 <= -1.35e+34) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y0 <= -8.5e-186) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y0 <= 8e-307) {
		tmp = (t * b) * ((j * y4) - (z * a));
	} else if (y0 <= 6.5e-191) {
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	} else if (y0 <= 1.1e-50) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y0 <= 8e+67) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else {
		tmp = c * (y0 * ((x * y2) - (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 y0 <= -1.35e+34:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y0 <= -8.5e-186:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y0 <= 8e-307:
		tmp = (t * b) * ((j * y4) - (z * a))
	elif y0 <= 6.5e-191:
		tmp = y1 * (y3 * ((z * a) - (j * y4)))
	elif y0 <= 1.1e-50:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y0 <= 8e+67:
		tmp = y * (y3 * ((c * y4) - (a * y5)))
	else:
		tmp = c * (y0 * ((x * y2) - (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 (y0 <= -1.35e+34)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y0 <= -8.5e-186)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y0 <= 8e-307)
		tmp = Float64(Float64(t * b) * Float64(Float64(j * y4) - Float64(z * a)));
	elseif (y0 <= 6.5e-191)
		tmp = Float64(y1 * Float64(y3 * Float64(Float64(z * a) - Float64(j * y4))));
	elseif (y0 <= 1.1e-50)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y0 <= 8e+67)
		tmp = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))));
	else
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - 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 (y0 <= -1.35e+34)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y0 <= -8.5e-186)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y0 <= 8e-307)
		tmp = (t * b) * ((j * y4) - (z * a));
	elseif (y0 <= 6.5e-191)
		tmp = y1 * (y3 * ((z * a) - (j * y4)));
	elseif (y0 <= 1.1e-50)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y0 <= 8e+67)
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	else
		tmp = c * (y0 * ((x * y2) - (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[LessEqual[y0, -1.35e+34], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -8.5e-186], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 8e-307], N[(N[(t * b), $MachinePrecision] * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 6.5e-191], N[(y1 * N[(y3 * N[(N[(z * a), $MachinePrecision] - N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.1e-50], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 8e+67], N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y0 < -1.35e34

   1. Initial program 24.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 66.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 66.9%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 66.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 66.9%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 66.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 66.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 66.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 66.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 66.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in b around inf 53.4%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if -1.35e34 < y0 < -8.4999999999999994e-186

   1. Initial program 36.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 41.4%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around inf 34.4%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 34.4%

         \[\leadsto x \cdot \left(y \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right)\right) \]

   6. Simplified 34.4%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(b \cdot a - c \cdot i\right)\right)} \]

   if -8.4999999999999994e-186 < y0 < 7.99999999999999927e-307

   1. Initial program 37.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 37.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in t around inf 49.7%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 46.3%

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      2. +-commutative 46.3%

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)} \]

      3. mul-1-neg 46.3%

         \[\leadsto \left(b \cdot t\right) \cdot \left(j \cdot y4 + \color{blue}{\left(-a \cdot z\right)}\right) \]

      4. unsub-neg 46.3%

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(j \cdot y4 - a \cdot z\right)} \]

      5. *-commutative 46.3%

         \[\leadsto \left(b \cdot t\right) \cdot \left(j \cdot y4 - \color{blue}{z \cdot a}\right) \]

   6. Simplified 46.3%

      \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(j \cdot y4 - z \cdot a\right)} \]

   if 7.99999999999999927e-307 < y0 < 6.4999999999999995e-191

   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 59.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 59.8%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 59.8%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 59.8%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 59.8%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in y3 around -inf 41.9%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]

   if 6.4999999999999995e-191 < y0 < 1.0999999999999999e-50

   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 b around inf 40.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in y4 around inf 45.3%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if 1.0999999999999999e-50 < y0 < 7.99999999999999986e67

   1. Initial program 36.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 16.7%

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   4. Taylor expanded in y3 around inf 48.8%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   if 7.99999999999999986e67 < y0

   1. Initial program 20.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 53.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 53.9%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 53.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 53.9%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 53.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 53.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 53.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 53.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 53.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 53.9%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.35 \cdot 10^{+34}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -8.5 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 8 \cdot 10^{-307}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)\\ \mathbf{elif}\;y0 \leq 6.5 \cdot 10^{-191}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a - j \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.1 \cdot 10^{-50}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 8 \cdot 10^{+67}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{if}\;y2 \leq -3.2 \cdot 10^{-177}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq -1.55 \cdot 10^{-291}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq 1.65 \cdot 10^{-228}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq 4.1 \cdot 10^{+54}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 3.8 \cdot 10^{+259}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y0 (- (* x y2) (* z y3))))))
   (if (<= y2 -3.2e-177)
     t_1
     (if (<= y2 -1.55e-291)
       (* x (* y (- (* a b) (* c i))))
       (if (<= y2 1.65e-228)
         (* b (* y4 (- (* t j) (* y k))))
         (if (<= y2 4.1e+54)
           (* b (* x (- (* y a) (* j y0))))
           (if (<= y2 3.8e+259) (* y1 (* y4 (- (* k y2) (* j 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 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (y2 <= -3.2e-177) {
		tmp = t_1;
	} else if (y2 <= -1.55e-291) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y2 <= 1.65e-228) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y2 <= 4.1e+54) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y2 <= 3.8e+259) {
		tmp = y1 * (y4 * ((k * y2) - (j * 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 = c * (y0 * ((x * y2) - (z * y3)))
    if (y2 <= (-3.2d-177)) then
        tmp = t_1
    else if (y2 <= (-1.55d-291)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y2 <= 1.65d-228) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y2 <= 4.1d+54) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y2 <= 3.8d+259) then
        tmp = y1 * (y4 * ((k * y2) - (j * 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 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (y2 <= -3.2e-177) {
		tmp = t_1;
	} else if (y2 <= -1.55e-291) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y2 <= 1.65e-228) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y2 <= 4.1e+54) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y2 <= 3.8e+259) {
		tmp = y1 * (y4 * ((k * y2) - (j * 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 = c * (y0 * ((x * y2) - (z * y3)))
	tmp = 0
	if y2 <= -3.2e-177:
		tmp = t_1
	elif y2 <= -1.55e-291:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y2 <= 1.65e-228:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y2 <= 4.1e+54:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y2 <= 3.8e+259:
		tmp = y1 * (y4 * ((k * y2) - (j * 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(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	tmp = 0.0
	if (y2 <= -3.2e-177)
		tmp = t_1;
	elseif (y2 <= -1.55e-291)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y2 <= 1.65e-228)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y2 <= 4.1e+54)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y2 <= 3.8e+259)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * 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 = c * (y0 * ((x * y2) - (z * y3)));
	tmp = 0.0;
	if (y2 <= -3.2e-177)
		tmp = t_1;
	elseif (y2 <= -1.55e-291)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y2 <= 1.65e-228)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y2 <= 4.1e+54)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y2 <= 3.8e+259)
		tmp = y1 * (y4 * ((k * y2) - (j * 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[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -3.2e-177], t$95$1, If[LessEqual[y2, -1.55e-291], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.65e-228], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.1e+54], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.8e+259], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -3.1999999999999998e-177 or 3.8e259 < 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 y0 around inf 52.4%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 52.4%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 52.4%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 52.4%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 52.4%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 52.4%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 52.4%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 52.4%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 52.4%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 51.1%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -3.1999999999999998e-177 < y2 < -1.55000000000000006e-291

   1. Initial program 33.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 36.6%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around inf 42.8%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 42.8%

         \[\leadsto x \cdot \left(y \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right)\right) \]

   6. Simplified 42.8%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(b \cdot a - c \cdot i\right)\right)} \]

   if -1.55000000000000006e-291 < y2 < 1.65000000000000003e-228

   1. Initial program 41.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 36.5%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if 1.65000000000000003e-228 < y2 < 4.09999999999999967e54

   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 b around inf 44.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 39.2%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if 4.09999999999999967e54 < y2 < 3.8e259

   1. Initial program 30.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 35.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 35.5%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 35.5%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 35.5%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 35.5%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in y4 around -inf 43.6%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 43.6%

         \[\leadsto y1 \cdot \left(y4 \cdot \left(\color{blue}{y2 \cdot k} - j \cdot y3\right)\right) \]

      2. *-commutative 43.6%

         \[\leadsto y1 \cdot \left(y4 \cdot \left(y2 \cdot k - \color{blue}{y3 \cdot j}\right)\right) \]

   8. Simplified 43.6%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(y2 \cdot k - y3 \cdot j\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -3.2 \cdot 10^{-177}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq -1.55 \cdot 10^{-291}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq 1.65 \cdot 10^{-228}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq 4.1 \cdot 10^{+54}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 3.8 \cdot 10^{+259}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 21.8% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{if}\;y2 \leq -8 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq -3.4 \cdot 10^{-128}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 5.2 \cdot 10^{-132}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;y2 \leq 8.5 \cdot 10^{-52}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 1.36 \cdot 10^{+35}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* y1 (* y2 y4)))))
   (if (<= y2 -8e+125)
     t_1
     (if (<= y2 -3.4e-128)
       (* c (* x (* y0 y2)))
       (if (<= y2 5.2e-132)
         (* b (* (* x y) a))
         (if (<= y2 8.5e-52)
           (* j (* y0 (* y3 y5)))
           (if (<= y2 1.36e+35) (* i (* j (* x y1))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y1 * (y2 * y4));
	double tmp;
	if (y2 <= -8e+125) {
		tmp = t_1;
	} else if (y2 <= -3.4e-128) {
		tmp = c * (x * (y0 * y2));
	} else if (y2 <= 5.2e-132) {
		tmp = b * ((x * y) * a);
	} else if (y2 <= 8.5e-52) {
		tmp = j * (y0 * (y3 * y5));
	} else if (y2 <= 1.36e+35) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (y1 * (y2 * y4))
    if (y2 <= (-8d+125)) then
        tmp = t_1
    else if (y2 <= (-3.4d-128)) then
        tmp = c * (x * (y0 * y2))
    else if (y2 <= 5.2d-132) then
        tmp = b * ((x * y) * a)
    else if (y2 <= 8.5d-52) then
        tmp = j * (y0 * (y3 * y5))
    else if (y2 <= 1.36d+35) then
        tmp = i * (j * (x * y1))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y1 * (y2 * y4));
	double tmp;
	if (y2 <= -8e+125) {
		tmp = t_1;
	} else if (y2 <= -3.4e-128) {
		tmp = c * (x * (y0 * y2));
	} else if (y2 <= 5.2e-132) {
		tmp = b * ((x * y) * a);
	} else if (y2 <= 8.5e-52) {
		tmp = j * (y0 * (y3 * y5));
	} else if (y2 <= 1.36e+35) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (y1 * (y2 * y4))
	tmp = 0
	if y2 <= -8e+125:
		tmp = t_1
	elif y2 <= -3.4e-128:
		tmp = c * (x * (y0 * y2))
	elif y2 <= 5.2e-132:
		tmp = b * ((x * y) * a)
	elif y2 <= 8.5e-52:
		tmp = j * (y0 * (y3 * y5))
	elif y2 <= 1.36e+35:
		tmp = i * (j * (x * y1))
	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(k * Float64(y1 * Float64(y2 * y4)))
	tmp = 0.0
	if (y2 <= -8e+125)
		tmp = t_1;
	elseif (y2 <= -3.4e-128)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (y2 <= 5.2e-132)
		tmp = Float64(b * Float64(Float64(x * y) * a));
	elseif (y2 <= 8.5e-52)
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	elseif (y2 <= 1.36e+35)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (y1 * (y2 * y4));
	tmp = 0.0;
	if (y2 <= -8e+125)
		tmp = t_1;
	elseif (y2 <= -3.4e-128)
		tmp = c * (x * (y0 * y2));
	elseif (y2 <= 5.2e-132)
		tmp = b * ((x * y) * a);
	elseif (y2 <= 8.5e-52)
		tmp = j * (y0 * (y3 * y5));
	elseif (y2 <= 1.36e+35)
		tmp = i * (j * (x * y1));
	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[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -8e+125], t$95$1, If[LessEqual[y2, -3.4e-128], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5.2e-132], N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 8.5e-52], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.36e+35], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -7.9999999999999994e125 or 1.36e35 < y2

   1. Initial program 31.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 38.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 38.2%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 38.2%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 38.2%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 38.2%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in y2 around inf 43.5%

      \[\leadsto \color{blue}{\left(y2 \cdot \left(a \cdot x - k \cdot y4\right)\right)} \cdot \left(-y1\right) \]
   7. Step-by-step derivation

      1. *-commutative 43.5%

         \[\leadsto \left(y2 \cdot \left(\color{blue}{x \cdot a} - k \cdot y4\right)\right) \cdot \left(-y1\right) \]

   8. Simplified 43.5%

      \[\leadsto \color{blue}{\left(y2 \cdot \left(x \cdot a - k \cdot y4\right)\right)} \cdot \left(-y1\right) \]

   9. Taylor expanded in x around 0 39.6%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 39.6%

          \[\leadsto k \cdot \left(y1 \cdot \color{blue}{\left(y4 \cdot y2\right)}\right) \]

   11. Simplified 39.6%

       \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y4 \cdot y2\right)\right)} \]

   if -7.9999999999999994e125 < y2 < -3.39999999999999975e-128

   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 y0 around inf 63.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 63.2%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 63.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 63.2%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 63.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 63.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 63.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 63.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 63.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 53.1%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 38.7%

      \[\leadsto c \cdot \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if -3.39999999999999975e-128 < y2 < 5.2000000000000002e-132

   1. Initial program 35.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 45.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 37.7%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   5. Taylor expanded in a around inf 32.6%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)} \]

   if 5.2000000000000002e-132 < y2 < 8.50000000000000006e-52

   1. Initial program 23.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 47.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 47.8%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 47.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 47.8%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 47.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 47.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 47.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 47.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 47.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in j around -inf 36.5%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 30.6%

         \[\leadsto \color{blue}{\left(j \cdot y0\right) \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)} \]

      2. *-commutative 30.6%

         \[\leadsto \color{blue}{\left(y0 \cdot j\right)} \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right) \]

      3. +-commutative 30.6%

         \[\leadsto \left(y0 \cdot j\right) \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)} \]

      4. mul-1-neg 30.6%

         \[\leadsto \left(y0 \cdot j\right) \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right) \]

      5. unsub-neg 30.6%

         \[\leadsto \left(y0 \cdot j\right) \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)} \]

      6. *-commutative 30.6%

         \[\leadsto \left(y0 \cdot j\right) \cdot \left(y3 \cdot y5 - \color{blue}{x \cdot b}\right) \]

   8. Simplified 30.6%

      \[\leadsto \color{blue}{\left(y0 \cdot j\right) \cdot \left(y3 \cdot y5 - x \cdot b\right)} \]

   9. Taylor expanded in y3 around inf 36.5%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]

   if 8.50000000000000006e-52 < y2 < 1.36e35

   1. Initial program 18.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 19.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 19.0%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 19.0%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 19.0%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 19.0%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in i around -inf 32.9%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 32.9%

         \[\leadsto \color{blue}{\left(i \cdot y1\right) \cdot \left(j \cdot x - k \cdot z\right)} \]

      2. *-commutative 32.9%

         \[\leadsto \color{blue}{\left(y1 \cdot i\right)} \cdot \left(j \cdot x - k \cdot z\right) \]

      3. *-commutative 32.9%

         \[\leadsto \left(y1 \cdot i\right) \cdot \left(\color{blue}{x \cdot j} - k \cdot z\right) \]

      4. *-commutative 32.9%

         \[\leadsto \left(y1 \cdot i\right) \cdot \left(x \cdot j - \color{blue}{z \cdot k}\right) \]

   8. Simplified 32.9%

      \[\leadsto \color{blue}{\left(y1 \cdot i\right) \cdot \left(x \cdot j - z \cdot k\right)} \]

   9. Taylor expanded in x around inf 20.6%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 36.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -8 \cdot 10^{+125}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -3.4 \cdot 10^{-128}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 5.2 \cdot 10^{-132}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;y2 \leq 8.5 \cdot 10^{-52}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 1.36 \cdot 10^{+35}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 21.7% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{if}\;y2 \leq -8.5 \cdot 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq -2.7 \cdot 10^{-128}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 4 \cdot 10^{-179}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq 1.9 \cdot 10^{-17}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq 3.3 \cdot 10^{+40}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* y1 (* y2 y4)))))
   (if (<= y2 -8.5e+128)
     t_1
     (if (<= y2 -2.7e-128)
       (* c (* x (* y0 y2)))
       (if (<= y2 4e-179)
         (* b (* x (* y a)))
         (if (<= y2 1.9e-17)
           (* y1 (* y3 (* z a)))
           (if (<= y2 3.3e+40) (* c (* y0 (* x y2))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y1 * (y2 * y4));
	double tmp;
	if (y2 <= -8.5e+128) {
		tmp = t_1;
	} else if (y2 <= -2.7e-128) {
		tmp = c * (x * (y0 * y2));
	} else if (y2 <= 4e-179) {
		tmp = b * (x * (y * a));
	} else if (y2 <= 1.9e-17) {
		tmp = y1 * (y3 * (z * a));
	} else if (y2 <= 3.3e+40) {
		tmp = c * (y0 * (x * y2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (y1 * (y2 * y4))
    if (y2 <= (-8.5d+128)) then
        tmp = t_1
    else if (y2 <= (-2.7d-128)) then
        tmp = c * (x * (y0 * y2))
    else if (y2 <= 4d-179) then
        tmp = b * (x * (y * a))
    else if (y2 <= 1.9d-17) then
        tmp = y1 * (y3 * (z * a))
    else if (y2 <= 3.3d+40) then
        tmp = c * (y0 * (x * y2))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y1 * (y2 * y4));
	double tmp;
	if (y2 <= -8.5e+128) {
		tmp = t_1;
	} else if (y2 <= -2.7e-128) {
		tmp = c * (x * (y0 * y2));
	} else if (y2 <= 4e-179) {
		tmp = b * (x * (y * a));
	} else if (y2 <= 1.9e-17) {
		tmp = y1 * (y3 * (z * a));
	} else if (y2 <= 3.3e+40) {
		tmp = c * (y0 * (x * y2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (y1 * (y2 * y4))
	tmp = 0
	if y2 <= -8.5e+128:
		tmp = t_1
	elif y2 <= -2.7e-128:
		tmp = c * (x * (y0 * y2))
	elif y2 <= 4e-179:
		tmp = b * (x * (y * a))
	elif y2 <= 1.9e-17:
		tmp = y1 * (y3 * (z * a))
	elif y2 <= 3.3e+40:
		tmp = c * (y0 * (x * y2))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(y1 * Float64(y2 * y4)))
	tmp = 0.0
	if (y2 <= -8.5e+128)
		tmp = t_1;
	elseif (y2 <= -2.7e-128)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (y2 <= 4e-179)
		tmp = Float64(b * Float64(x * Float64(y * a)));
	elseif (y2 <= 1.9e-17)
		tmp = Float64(y1 * Float64(y3 * Float64(z * a)));
	elseif (y2 <= 3.3e+40)
		tmp = Float64(c * Float64(y0 * Float64(x * y2)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (y1 * (y2 * y4));
	tmp = 0.0;
	if (y2 <= -8.5e+128)
		tmp = t_1;
	elseif (y2 <= -2.7e-128)
		tmp = c * (x * (y0 * y2));
	elseif (y2 <= 4e-179)
		tmp = b * (x * (y * a));
	elseif (y2 <= 1.9e-17)
		tmp = y1 * (y3 * (z * a));
	elseif (y2 <= 3.3e+40)
		tmp = c * (y0 * (x * y2));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -8.5e+128], t$95$1, If[LessEqual[y2, -2.7e-128], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4e-179], N[(b * N[(x * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.9e-17], N[(y1 * N[(y3 * N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.3e+40], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -8.50000000000000045e128 or 3.2999999999999998e40 < y2

   1. Initial program 32.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 39.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 39.0%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 39.0%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 39.0%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 39.0%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in y2 around inf 44.3%

      \[\leadsto \color{blue}{\left(y2 \cdot \left(a \cdot x - k \cdot y4\right)\right)} \cdot \left(-y1\right) \]
   7. Step-by-step derivation

      1. *-commutative 44.3%

         \[\leadsto \left(y2 \cdot \left(\color{blue}{x \cdot a} - k \cdot y4\right)\right) \cdot \left(-y1\right) \]

   8. Simplified 44.3%

      \[\leadsto \color{blue}{\left(y2 \cdot \left(x \cdot a - k \cdot y4\right)\right)} \cdot \left(-y1\right) \]

   9. Taylor expanded in x around 0 39.4%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 39.4%

          \[\leadsto k \cdot \left(y1 \cdot \color{blue}{\left(y4 \cdot y2\right)}\right) \]

   11. Simplified 39.4%

       \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y4 \cdot y2\right)\right)} \]

   if -8.50000000000000045e128 < y2 < -2.70000000000000006e-128

   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 y0 around inf 63.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 63.2%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 63.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 63.2%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 63.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 63.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 63.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 63.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 63.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 53.1%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 38.7%

      \[\leadsto c \cdot \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if -2.70000000000000006e-128 < y2 < 4.0000000000000001e-179

   1. Initial program 34.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 44.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 39.7%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   5. Taylor expanded in a around inf 33.9%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y\right)}\right) \]

   if 4.0000000000000001e-179 < y2 < 1.9000000000000001e-17

   1. Initial program 27.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 31.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 31.6%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 31.6%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 31.6%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 31.6%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in y3 around -inf 32.2%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]

   7. Taylor expanded in a around inf 32.4%

      \[\leadsto y1 \cdot \left(y3 \cdot \color{blue}{\left(a \cdot z\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative 32.4%

         \[\leadsto y1 \cdot \left(y3 \cdot \color{blue}{\left(z \cdot a\right)}\right) \]

   9. Simplified 32.4%

      \[\leadsto y1 \cdot \left(y3 \cdot \color{blue}{\left(z \cdot a\right)}\right) \]

   if 1.9000000000000001e-17 < y2 < 3.2999999999999998e40

   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 y0 around inf 40.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 40.0%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 40.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 40.0%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 40.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 40.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 40.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 40.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 40.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 27.4%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 27.5%

      \[\leadsto c \cdot \left(y0 \cdot \color{blue}{\left(x \cdot y2\right)}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -8.5 \cdot 10^{+128}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -2.7 \cdot 10^{-128}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 4 \cdot 10^{-179}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq 1.9 \cdot 10^{-17}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq 3.3 \cdot 10^{+40}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 22.6% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{if}\;y2 \leq -5.6 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq -2.9 \cdot 10^{-180}:\\ \;\;\;\;c \cdot \left(\left(z \cdot y3\right) \cdot \left(-y0\right)\right)\\ \mathbf{elif}\;y2 \leq 2.4 \cdot 10^{-183}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq 1.05 \cdot 10^{-18}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq 9.5 \cdot 10^{+40}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* y1 (* y2 y4)))))
   (if (<= y2 -5.6e+125)
     t_1
     (if (<= y2 -2.9e-180)
       (* c (* (* z y3) (- y0)))
       (if (<= y2 2.4e-183)
         (* b (* x (* y a)))
         (if (<= y2 1.05e-18)
           (* y1 (* y3 (* z a)))
           (if (<= y2 9.5e+40) (* c (* y0 (* x y2))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y1 * (y2 * y4));
	double tmp;
	if (y2 <= -5.6e+125) {
		tmp = t_1;
	} else if (y2 <= -2.9e-180) {
		tmp = c * ((z * y3) * -y0);
	} else if (y2 <= 2.4e-183) {
		tmp = b * (x * (y * a));
	} else if (y2 <= 1.05e-18) {
		tmp = y1 * (y3 * (z * a));
	} else if (y2 <= 9.5e+40) {
		tmp = c * (y0 * (x * y2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (y1 * (y2 * y4))
    if (y2 <= (-5.6d+125)) then
        tmp = t_1
    else if (y2 <= (-2.9d-180)) then
        tmp = c * ((z * y3) * -y0)
    else if (y2 <= 2.4d-183) then
        tmp = b * (x * (y * a))
    else if (y2 <= 1.05d-18) then
        tmp = y1 * (y3 * (z * a))
    else if (y2 <= 9.5d+40) then
        tmp = c * (y0 * (x * y2))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y1 * (y2 * y4));
	double tmp;
	if (y2 <= -5.6e+125) {
		tmp = t_1;
	} else if (y2 <= -2.9e-180) {
		tmp = c * ((z * y3) * -y0);
	} else if (y2 <= 2.4e-183) {
		tmp = b * (x * (y * a));
	} else if (y2 <= 1.05e-18) {
		tmp = y1 * (y3 * (z * a));
	} else if (y2 <= 9.5e+40) {
		tmp = c * (y0 * (x * y2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (y1 * (y2 * y4))
	tmp = 0
	if y2 <= -5.6e+125:
		tmp = t_1
	elif y2 <= -2.9e-180:
		tmp = c * ((z * y3) * -y0)
	elif y2 <= 2.4e-183:
		tmp = b * (x * (y * a))
	elif y2 <= 1.05e-18:
		tmp = y1 * (y3 * (z * a))
	elif y2 <= 9.5e+40:
		tmp = c * (y0 * (x * y2))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(y1 * Float64(y2 * y4)))
	tmp = 0.0
	if (y2 <= -5.6e+125)
		tmp = t_1;
	elseif (y2 <= -2.9e-180)
		tmp = Float64(c * Float64(Float64(z * y3) * Float64(-y0)));
	elseif (y2 <= 2.4e-183)
		tmp = Float64(b * Float64(x * Float64(y * a)));
	elseif (y2 <= 1.05e-18)
		tmp = Float64(y1 * Float64(y3 * Float64(z * a)));
	elseif (y2 <= 9.5e+40)
		tmp = Float64(c * Float64(y0 * Float64(x * y2)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (y1 * (y2 * y4));
	tmp = 0.0;
	if (y2 <= -5.6e+125)
		tmp = t_1;
	elseif (y2 <= -2.9e-180)
		tmp = c * ((z * y3) * -y0);
	elseif (y2 <= 2.4e-183)
		tmp = b * (x * (y * a));
	elseif (y2 <= 1.05e-18)
		tmp = y1 * (y3 * (z * a));
	elseif (y2 <= 9.5e+40)
		tmp = c * (y0 * (x * y2));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -5.6e+125], t$95$1, If[LessEqual[y2, -2.9e-180], N[(c * N[(N[(z * y3), $MachinePrecision] * (-y0)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.4e-183], N[(b * N[(x * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.05e-18], N[(y1 * N[(y3 * N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 9.5e+40], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -5.6000000000000002e125 or 9.5000000000000003e40 < y2

   1. Initial program 32.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 39.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 39.0%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 39.0%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 39.0%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 39.0%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in y2 around inf 44.3%

      \[\leadsto \color{blue}{\left(y2 \cdot \left(a \cdot x - k \cdot y4\right)\right)} \cdot \left(-y1\right) \]
   7. Step-by-step derivation

      1. *-commutative 44.3%

         \[\leadsto \left(y2 \cdot \left(\color{blue}{x \cdot a} - k \cdot y4\right)\right) \cdot \left(-y1\right) \]

   8. Simplified 44.3%

      \[\leadsto \color{blue}{\left(y2 \cdot \left(x \cdot a - k \cdot y4\right)\right)} \cdot \left(-y1\right) \]

   9. Taylor expanded in x around 0 39.4%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 39.4%

          \[\leadsto k \cdot \left(y1 \cdot \color{blue}{\left(y4 \cdot y2\right)}\right) \]

   11. Simplified 39.4%

       \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y4 \cdot y2\right)\right)} \]

   if -5.6000000000000002e125 < y2 < -2.8999999999999998e-180

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 61.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 61.7%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 61.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 61.7%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 61.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 61.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 61.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 61.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 61.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 52.8%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   7. Taylor expanded in x around 0 37.9%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 37.9%

         \[\leadsto c \cdot \color{blue}{\left(\left(-1 \cdot y0\right) \cdot \left(y3 \cdot z\right)\right)} \]

      2. neg-mul-1 37.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(-y0\right)} \cdot \left(y3 \cdot z\right)\right) \]

   9. Simplified 37.9%

      \[\leadsto c \cdot \color{blue}{\left(\left(-y0\right) \cdot \left(y3 \cdot z\right)\right)} \]

   if -2.8999999999999998e-180 < y2 < 2.39999999999999993e-183

   1. Initial program 38.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 45.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 40.3%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   5. Taylor expanded in a around inf 35.6%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y\right)}\right) \]

   if 2.39999999999999993e-183 < y2 < 1.05e-18

   1. Initial program 27.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 31.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 31.6%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 31.6%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 31.6%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 31.6%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in y3 around -inf 32.2%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]

   7. Taylor expanded in a around inf 32.4%

      \[\leadsto y1 \cdot \left(y3 \cdot \color{blue}{\left(a \cdot z\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative 32.4%

         \[\leadsto y1 \cdot \left(y3 \cdot \color{blue}{\left(z \cdot a\right)}\right) \]

   9. Simplified 32.4%

      \[\leadsto y1 \cdot \left(y3 \cdot \color{blue}{\left(z \cdot a\right)}\right) \]

   if 1.05e-18 < y2 < 9.5000000000000003e40

   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 y0 around inf 40.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 40.0%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 40.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 40.0%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 40.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 40.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 40.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 40.0%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 40.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 27.4%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 27.5%

      \[\leadsto c \cdot \left(y0 \cdot \color{blue}{\left(x \cdot y2\right)}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -5.6 \cdot 10^{+125}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -2.9 \cdot 10^{-180}:\\ \;\;\;\;c \cdot \left(\left(z \cdot y3\right) \cdot \left(-y0\right)\right)\\ \mathbf{elif}\;y2 \leq 2.4 \cdot 10^{-183}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq 1.05 \cdot 10^{-18}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq 9.5 \cdot 10^{+40}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 22.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -1.06 \cdot 10^{+127}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -8 \cdot 10^{-180}:\\ \;\;\;\;c \cdot \left(\left(z \cdot y3\right) \cdot \left(-y0\right)\right)\\ \mathbf{elif}\;y2 \leq 1.5 \cdot 10^{-184}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq 1.9 \cdot 10^{-18}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq 7.5 \cdot 10^{+136}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -1.06e+127)
   (* k (* y1 (* y2 y4)))
   (if (<= y2 -8e-180)
     (* c (* (* z y3) (- y0)))
     (if (<= y2 1.5e-184)
       (* b (* x (* y a)))
       (if (<= y2 1.9e-18)
         (* y1 (* y3 (* z a)))
         (if (<= y2 7.5e+136)
           (* c (* y0 (* x y2)))
           (* y1 (* y4 (* k y2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.06e+127) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y2 <= -8e-180) {
		tmp = c * ((z * y3) * -y0);
	} else if (y2 <= 1.5e-184) {
		tmp = b * (x * (y * a));
	} else if (y2 <= 1.9e-18) {
		tmp = y1 * (y3 * (z * a));
	} else if (y2 <= 7.5e+136) {
		tmp = c * (y0 * (x * y2));
	} else {
		tmp = y1 * (y4 * (k * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-1.06d+127)) then
        tmp = k * (y1 * (y2 * y4))
    else if (y2 <= (-8d-180)) then
        tmp = c * ((z * y3) * -y0)
    else if (y2 <= 1.5d-184) then
        tmp = b * (x * (y * a))
    else if (y2 <= 1.9d-18) then
        tmp = y1 * (y3 * (z * a))
    else if (y2 <= 7.5d+136) then
        tmp = c * (y0 * (x * y2))
    else
        tmp = y1 * (y4 * (k * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.06e+127) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y2 <= -8e-180) {
		tmp = c * ((z * y3) * -y0);
	} else if (y2 <= 1.5e-184) {
		tmp = b * (x * (y * a));
	} else if (y2 <= 1.9e-18) {
		tmp = y1 * (y3 * (z * a));
	} else if (y2 <= 7.5e+136) {
		tmp = c * (y0 * (x * y2));
	} else {
		tmp = y1 * (y4 * (k * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -1.06e+127:
		tmp = k * (y1 * (y2 * y4))
	elif y2 <= -8e-180:
		tmp = c * ((z * y3) * -y0)
	elif y2 <= 1.5e-184:
		tmp = b * (x * (y * a))
	elif y2 <= 1.9e-18:
		tmp = y1 * (y3 * (z * a))
	elif y2 <= 7.5e+136:
		tmp = c * (y0 * (x * y2))
	else:
		tmp = y1 * (y4 * (k * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -1.06e+127)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (y2 <= -8e-180)
		tmp = Float64(c * Float64(Float64(z * y3) * Float64(-y0)));
	elseif (y2 <= 1.5e-184)
		tmp = Float64(b * Float64(x * Float64(y * a)));
	elseif (y2 <= 1.9e-18)
		tmp = Float64(y1 * Float64(y3 * Float64(z * a)));
	elseif (y2 <= 7.5e+136)
		tmp = Float64(c * Float64(y0 * Float64(x * y2)));
	else
		tmp = Float64(y1 * Float64(y4 * Float64(k * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -1.06e+127)
		tmp = k * (y1 * (y2 * y4));
	elseif (y2 <= -8e-180)
		tmp = c * ((z * y3) * -y0);
	elseif (y2 <= 1.5e-184)
		tmp = b * (x * (y * a));
	elseif (y2 <= 1.9e-18)
		tmp = y1 * (y3 * (z * a));
	elseif (y2 <= 7.5e+136)
		tmp = c * (y0 * (x * y2));
	else
		tmp = y1 * (y4 * (k * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -1.06e+127], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -8e-180], N[(c * N[(N[(z * y3), $MachinePrecision] * (-y0)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.5e-184], N[(b * N[(x * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.9e-18], N[(y1 * N[(y3 * N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 7.5e+136], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(y4 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y2 < -1.06000000000000006e127

   1. Initial program 37.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 43.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 43.7%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 43.7%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 43.7%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 43.7%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in y2 around inf 55.3%

      \[\leadsto \color{blue}{\left(y2 \cdot \left(a \cdot x - k \cdot y4\right)\right)} \cdot \left(-y1\right) \]
   7. Step-by-step derivation

      1. *-commutative 55.3%

         \[\leadsto \left(y2 \cdot \left(\color{blue}{x \cdot a} - k \cdot y4\right)\right) \cdot \left(-y1\right) \]

   8. Simplified 55.3%

      \[\leadsto \color{blue}{\left(y2 \cdot \left(x \cdot a - k \cdot y4\right)\right)} \cdot \left(-y1\right) \]

   9. Taylor expanded in x around 0 47.0%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 47.0%

          \[\leadsto k \cdot \left(y1 \cdot \color{blue}{\left(y4 \cdot y2\right)}\right) \]

   11. Simplified 47.0%

       \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y4 \cdot y2\right)\right)} \]

   if -1.06000000000000006e127 < y2 < -8.0000000000000002e-180

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 61.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 61.7%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 61.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 61.7%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 61.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 61.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 61.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 61.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 61.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 52.8%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   7. Taylor expanded in x around 0 37.9%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 37.9%

         \[\leadsto c \cdot \color{blue}{\left(\left(-1 \cdot y0\right) \cdot \left(y3 \cdot z\right)\right)} \]

      2. neg-mul-1 37.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(-y0\right)} \cdot \left(y3 \cdot z\right)\right) \]

   9. Simplified 37.9%

      \[\leadsto c \cdot \color{blue}{\left(\left(-y0\right) \cdot \left(y3 \cdot z\right)\right)} \]

   if -8.0000000000000002e-180 < y2 < 1.49999999999999996e-184

   1. Initial program 38.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 45.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 40.3%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   5. Taylor expanded in a around inf 35.6%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y\right)}\right) \]

   if 1.49999999999999996e-184 < y2 < 1.8999999999999999e-18

   1. Initial program 27.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 31.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 31.6%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 31.6%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 31.6%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 31.6%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in y3 around -inf 32.2%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]

   7. Taylor expanded in a around inf 32.4%

      \[\leadsto y1 \cdot \left(y3 \cdot \color{blue}{\left(a \cdot z\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative 32.4%

         \[\leadsto y1 \cdot \left(y3 \cdot \color{blue}{\left(z \cdot a\right)}\right) \]

   9. Simplified 32.4%

      \[\leadsto y1 \cdot \left(y3 \cdot \color{blue}{\left(z \cdot a\right)}\right) \]

   if 1.8999999999999999e-18 < y2 < 7.5000000000000002e136

   1. Initial program 23.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 29.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 29.9%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 29.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 29.9%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 29.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 29.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 29.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 29.9%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 29.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 27.9%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 27.8%

      \[\leadsto c \cdot \left(y0 \cdot \color{blue}{\left(x \cdot y2\right)}\right) \]

   if 7.5000000000000002e136 < y2

   1. Initial program 32.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 36.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 36.7%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 36.7%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 36.7%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 36.7%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in y2 around inf 46.3%

      \[\leadsto \color{blue}{\left(y2 \cdot \left(a \cdot x - k \cdot y4\right)\right)} \cdot \left(-y1\right) \]
   7. Step-by-step derivation

      1. *-commutative 46.3%

         \[\leadsto \left(y2 \cdot \left(\color{blue}{x \cdot a} - k \cdot y4\right)\right) \cdot \left(-y1\right) \]

   8. Simplified 46.3%

      \[\leadsto \color{blue}{\left(y2 \cdot \left(x \cdot a - k \cdot y4\right)\right)} \cdot \left(-y1\right) \]

   9. Taylor expanded in x around 0 37.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot \left(y2 \cdot y4\right)\right)\right)} \cdot \left(-y1\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 37.5%

          \[\leadsto \color{blue}{\left(-k \cdot \left(y2 \cdot y4\right)\right)} \cdot \left(-y1\right) \]

       2. associate-*r* 39.7%

          \[\leadsto \left(-\color{blue}{\left(k \cdot y2\right) \cdot y4}\right) \cdot \left(-y1\right) \]

   11. Simplified 39.7%

       \[\leadsto \color{blue}{\left(-\left(k \cdot y2\right) \cdot y4\right)} \cdot \left(-y1\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.06 \cdot 10^{+127}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -8 \cdot 10^{-180}:\\ \;\;\;\;c \cdot \left(\left(z \cdot y3\right) \cdot \left(-y0\right)\right)\\ \mathbf{elif}\;y2 \leq 1.5 \cdot 10^{-184}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq 1.9 \cdot 10^{-18}:\\ \;\;\;\;y1 \cdot \left(y3 \cdot \left(z \cdot a\right)\right)\\ \mathbf{elif}\;y2 \leq 7.5 \cdot 10^{+136}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 29.3% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{if}\;y2 \leq -2.2 \cdot 10^{-178}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq -1.52 \cdot 10^{-292}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq 2.7 \cdot 10^{-228}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq 1.5 \cdot 10^{+27}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y0 (- (* x y2) (* z y3))))))
   (if (<= y2 -2.2e-178)
     t_1
     (if (<= y2 -1.52e-292)
       (* x (* y (- (* a b) (* c i))))
       (if (<= y2 2.7e-228)
         (* b (* y4 (- (* t j) (* y k))))
         (if (<= y2 1.5e+27) (* b (* x (- (* y a) (* j y0)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (y2 <= -2.2e-178) {
		tmp = t_1;
	} else if (y2 <= -1.52e-292) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y2 <= 2.7e-228) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y2 <= 1.5e+27) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (y0 * ((x * y2) - (z * y3)))
    if (y2 <= (-2.2d-178)) then
        tmp = t_1
    else if (y2 <= (-1.52d-292)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y2 <= 2.7d-228) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y2 <= 1.5d+27) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (y2 <= -2.2e-178) {
		tmp = t_1;
	} else if (y2 <= -1.52e-292) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y2 <= 2.7e-228) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y2 <= 1.5e+27) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y0 * ((x * y2) - (z * y3)))
	tmp = 0
	if y2 <= -2.2e-178:
		tmp = t_1
	elif y2 <= -1.52e-292:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y2 <= 2.7e-228:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y2 <= 1.5e+27:
		tmp = b * (x * ((y * a) - (j * y0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	tmp = 0.0
	if (y2 <= -2.2e-178)
		tmp = t_1;
	elseif (y2 <= -1.52e-292)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y2 <= 2.7e-228)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y2 <= 1.5e+27)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y0 * ((x * y2) - (z * y3)));
	tmp = 0.0;
	if (y2 <= -2.2e-178)
		tmp = t_1;
	elseif (y2 <= -1.52e-292)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y2 <= 2.7e-228)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y2 <= 1.5e+27)
		tmp = b * (x * ((y * a) - (j * y0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -2.2e-178], t$95$1, If[LessEqual[y2, -1.52e-292], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.7e-228], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.5e+27], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -2.2000000000000001e-178 or 1.49999999999999988e27 < y2

   1. Initial program 28.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 45.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 45.8%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 45.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 45.8%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 45.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 45.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 45.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 45.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 45.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 43.8%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -2.2000000000000001e-178 < y2 < -1.52e-292

   1. Initial program 33.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 36.6%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around inf 42.8%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 42.8%

         \[\leadsto x \cdot \left(y \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right)\right) \]

   6. Simplified 42.8%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(b \cdot a - c \cdot i\right)\right)} \]

   if -1.52e-292 < y2 < 2.69999999999999984e-228

   1. Initial program 41.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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 36.5%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if 2.69999999999999984e-228 < y2 < 1.49999999999999988e27

   1. Initial program 29.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 47.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 41.7%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2.2 \cdot 10^{-178}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq -1.52 \cdot 10^{-292}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq 2.7 \cdot 10^{-228}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq 1.5 \cdot 10^{+27}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 21.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{if}\;y2 \leq -1.45 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq 6.5 \cdot 10^{-132}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;y2 \leq 1.62 \cdot 10^{-54}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 7.2 \cdot 10^{-18}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y0 (* x y2)))))
   (if (<= y2 -1.45e-128)
     t_1
     (if (<= y2 6.5e-132)
       (* b (* (* x y) a))
       (if (<= y2 1.62e-54)
         (* j (* y0 (* y3 y5)))
         (if (<= y2 7.2e-18) (* 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 = c * (y0 * (x * y2));
	double tmp;
	if (y2 <= -1.45e-128) {
		tmp = t_1;
	} else if (y2 <= 6.5e-132) {
		tmp = b * ((x * y) * a);
	} else if (y2 <= 1.62e-54) {
		tmp = j * (y0 * (y3 * y5));
	} else if (y2 <= 7.2e-18) {
		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 = c * (y0 * (x * y2))
    if (y2 <= (-1.45d-128)) then
        tmp = t_1
    else if (y2 <= 6.5d-132) then
        tmp = b * ((x * y) * a)
    else if (y2 <= 1.62d-54) then
        tmp = j * (y0 * (y3 * y5))
    else if (y2 <= 7.2d-18) 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 = c * (y0 * (x * y2));
	double tmp;
	if (y2 <= -1.45e-128) {
		tmp = t_1;
	} else if (y2 <= 6.5e-132) {
		tmp = b * ((x * y) * a);
	} else if (y2 <= 1.62e-54) {
		tmp = j * (y0 * (y3 * y5));
	} else if (y2 <= 7.2e-18) {
		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 = c * (y0 * (x * y2))
	tmp = 0
	if y2 <= -1.45e-128:
		tmp = t_1
	elif y2 <= 6.5e-132:
		tmp = b * ((x * y) * a)
	elif y2 <= 1.62e-54:
		tmp = j * (y0 * (y3 * y5))
	elif y2 <= 7.2e-18:
		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(c * Float64(y0 * Float64(x * y2)))
	tmp = 0.0
	if (y2 <= -1.45e-128)
		tmp = t_1;
	elseif (y2 <= 6.5e-132)
		tmp = Float64(b * Float64(Float64(x * y) * a));
	elseif (y2 <= 1.62e-54)
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	elseif (y2 <= 7.2e-18)
		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 = c * (y0 * (x * y2));
	tmp = 0.0;
	if (y2 <= -1.45e-128)
		tmp = t_1;
	elseif (y2 <= 6.5e-132)
		tmp = b * ((x * y) * a);
	elseif (y2 <= 1.62e-54)
		tmp = j * (y0 * (y3 * y5));
	elseif (y2 <= 7.2e-18)
		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[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.45e-128], t$95$1, If[LessEqual[y2, 6.5e-132], N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.62e-54], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 7.2e-18], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -1.45e-128 or 7.20000000000000021e-18 < y2

   1. Initial program 29.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 44.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 44.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 44.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 44.1%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 44.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 44.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 44.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 44.1%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 44.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 41.6%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 31.7%

      \[\leadsto c \cdot \left(y0 \cdot \color{blue}{\left(x \cdot y2\right)}\right) \]

   if -1.45e-128 < y2 < 6.49999999999999991e-132

   1. Initial program 35.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 45.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 37.7%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   5. Taylor expanded in a around inf 32.6%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)} \]

   if 6.49999999999999991e-132 < y2 < 1.6200000000000001e-54

   1. Initial program 23.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 47.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 47.8%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 47.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 47.8%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 47.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 47.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 47.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 47.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 47.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in j around -inf 36.5%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 30.6%

         \[\leadsto \color{blue}{\left(j \cdot y0\right) \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right)} \]

      2. *-commutative 30.6%

         \[\leadsto \color{blue}{\left(y0 \cdot j\right)} \cdot \left(-1 \cdot \left(b \cdot x\right) + y3 \cdot y5\right) \]

      3. +-commutative 30.6%

         \[\leadsto \left(y0 \cdot j\right) \cdot \color{blue}{\left(y3 \cdot y5 + -1 \cdot \left(b \cdot x\right)\right)} \]

      4. mul-1-neg 30.6%

         \[\leadsto \left(y0 \cdot j\right) \cdot \left(y3 \cdot y5 + \color{blue}{\left(-b \cdot x\right)}\right) \]

      5. unsub-neg 30.6%

         \[\leadsto \left(y0 \cdot j\right) \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)} \]

      6. *-commutative 30.6%

         \[\leadsto \left(y0 \cdot j\right) \cdot \left(y3 \cdot y5 - \color{blue}{x \cdot b}\right) \]

   8. Simplified 30.6%

      \[\leadsto \color{blue}{\left(y0 \cdot j\right) \cdot \left(y3 \cdot y5 - x \cdot b\right)} \]

   9. Taylor expanded in y3 around inf 36.5%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]

   if 1.6200000000000001e-54 < y2 < 7.20000000000000021e-18

   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 y1 around -inf 33.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 33.4%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 33.4%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 33.4%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 33.4%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in y3 around -inf 67.5%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]

   7. Taylor expanded in a around inf 67.5%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 67.5%

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(z \cdot y3\right)}\right) \]

   9. Simplified 67.5%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.45 \cdot 10^{-128}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 6.5 \cdot 10^{-132}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{elif}\;y2 \leq 1.62 \cdot 10^{-54}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 7.2 \cdot 10^{-18}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 25.9% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -5.8 \cdot 10^{+128}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -3.4 \cdot 10^{-128}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 1.4 \cdot 10^{+59}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -5.8e+128)
   (* k (* y1 (* y2 y4)))
   (if (<= y2 -3.4e-128)
     (* c (* x (* y0 y2)))
     (if (<= y2 1.4e+59)
       (* b (* x (- (* y a) (* j y0))))
       (* y1 (* y4 (* k y2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -5.8e+128) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y2 <= -3.4e-128) {
		tmp = c * (x * (y0 * y2));
	} else if (y2 <= 1.4e+59) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else {
		tmp = y1 * (y4 * (k * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-5.8d+128)) then
        tmp = k * (y1 * (y2 * y4))
    else if (y2 <= (-3.4d-128)) then
        tmp = c * (x * (y0 * y2))
    else if (y2 <= 1.4d+59) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else
        tmp = y1 * (y4 * (k * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -5.8e+128) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y2 <= -3.4e-128) {
		tmp = c * (x * (y0 * y2));
	} else if (y2 <= 1.4e+59) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else {
		tmp = y1 * (y4 * (k * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -5.8e+128:
		tmp = k * (y1 * (y2 * y4))
	elif y2 <= -3.4e-128:
		tmp = c * (x * (y0 * y2))
	elif y2 <= 1.4e+59:
		tmp = b * (x * ((y * a) - (j * y0)))
	else:
		tmp = y1 * (y4 * (k * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -5.8e+128)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (y2 <= -3.4e-128)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (y2 <= 1.4e+59)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	else
		tmp = Float64(y1 * Float64(y4 * Float64(k * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -5.8e+128)
		tmp = k * (y1 * (y2 * y4));
	elseif (y2 <= -3.4e-128)
		tmp = c * (x * (y0 * y2));
	elseif (y2 <= 1.4e+59)
		tmp = b * (x * ((y * a) - (j * y0)));
	else
		tmp = y1 * (y4 * (k * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -5.8e+128], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -3.4e-128], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.4e+59], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(y4 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -5.8000000000000001e128

   1. Initial program 37.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 43.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 43.7%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 43.7%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 43.7%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 43.7%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in y2 around inf 55.3%

      \[\leadsto \color{blue}{\left(y2 \cdot \left(a \cdot x - k \cdot y4\right)\right)} \cdot \left(-y1\right) \]
   7. Step-by-step derivation

      1. *-commutative 55.3%

         \[\leadsto \left(y2 \cdot \left(\color{blue}{x \cdot a} - k \cdot y4\right)\right) \cdot \left(-y1\right) \]

   8. Simplified 55.3%

      \[\leadsto \color{blue}{\left(y2 \cdot \left(x \cdot a - k \cdot y4\right)\right)} \cdot \left(-y1\right) \]

   9. Taylor expanded in x around 0 47.0%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 47.0%

          \[\leadsto k \cdot \left(y1 \cdot \color{blue}{\left(y4 \cdot y2\right)}\right) \]

   11. Simplified 47.0%

       \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y4 \cdot y2\right)\right)} \]

   if -5.8000000000000001e128 < y2 < -3.39999999999999975e-128

   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 y0 around inf 63.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 63.2%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 63.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 63.2%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 63.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 63.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 63.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 63.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 63.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 53.1%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 38.7%

      \[\leadsto c \cdot \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if -3.39999999999999975e-128 < y2 < 1.3999999999999999e59

   1. Initial program 29.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 40.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 35.2%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if 1.3999999999999999e59 < y2

   1. Initial program 32.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 36.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 36.1%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 36.1%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 36.1%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 36.1%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in y2 around inf 41.5%

      \[\leadsto \color{blue}{\left(y2 \cdot \left(a \cdot x - k \cdot y4\right)\right)} \cdot \left(-y1\right) \]
   7. Step-by-step derivation

      1. *-commutative 41.5%

         \[\leadsto \left(y2 \cdot \left(\color{blue}{x \cdot a} - k \cdot y4\right)\right) \cdot \left(-y1\right) \]

   8. Simplified 41.5%

      \[\leadsto \color{blue}{\left(y2 \cdot \left(x \cdot a - k \cdot y4\right)\right)} \cdot \left(-y1\right) \]

   9. Taylor expanded in x around 0 38.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot \left(y2 \cdot y4\right)\right)\right)} \cdot \left(-y1\right) \]
   10. Step-by-step derivation

       1. mul-1-neg 38.3%

          \[\leadsto \color{blue}{\left(-k \cdot \left(y2 \cdot y4\right)\right)} \cdot \left(-y1\right) \]

       2. associate-*r* 38.3%

          \[\leadsto \left(-\color{blue}{\left(k \cdot y2\right) \cdot y4}\right) \cdot \left(-y1\right) \]

   11. Simplified 38.3%

       \[\leadsto \color{blue}{\left(-\left(k \cdot y2\right) \cdot y4\right)} \cdot \left(-y1\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -5.8 \cdot 10^{+128}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -3.4 \cdot 10^{-128}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 1.4 \cdot 10^{+59}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 29.1% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -1.55 \cdot 10^{-177} \lor \neg \left(y2 \leq 1.8 \cdot 10^{+29}\right):\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y2 -1.55e-177) (not (<= y2 1.8e+29)))
   (* c (* y0 (- (* x y2) (* z y3))))
   (* b (* x (- (* y a) (* j y0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y2 <= -1.55e-177) || !(y2 <= 1.8e+29)) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else {
		tmp = b * (x * ((y * a) - (j * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y2 <= (-1.55d-177)) .or. (.not. (y2 <= 1.8d+29))) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else
        tmp = b * (x * ((y * a) - (j * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y2 <= -1.55e-177) || !(y2 <= 1.8e+29)) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else {
		tmp = b * (x * ((y * a) - (j * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y2 <= -1.55e-177) or not (y2 <= 1.8e+29):
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	else:
		tmp = b * (x * ((y * a) - (j * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y2 <= -1.55e-177) || !(y2 <= 1.8e+29))
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	else
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y2 <= -1.55e-177) || ~((y2 <= 1.8e+29)))
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	else
		tmp = b * (x * ((y * a) - (j * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y2, -1.55e-177], N[Not[LessEqual[y2, 1.8e+29]], $MachinePrecision]], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y2 < -1.55000000000000009e-177 or 1.79999999999999988e29 < y2

   1. Initial program 28.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 45.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 45.8%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 45.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 45.8%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 45.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 45.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 45.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 45.8%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 45.8%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 43.8%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -1.55000000000000009e-177 < y2 < 1.79999999999999988e29

   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 b around inf 42.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 37.0%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.55 \cdot 10^{-177} \lor \neg \left(y2 \leq 1.8 \cdot 10^{+29}\right):\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 21.2% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -1.9 \cdot 10^{-128} \lor \neg \left(y2 \leq 8.2 \cdot 10^{+33}\right):\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y2 -1.9e-128) (not (<= y2 8.2e+33)))
   (* c (* x (* y0 y2)))
   (* b (* (* x y) a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y2 <= -1.9e-128) || !(y2 <= 8.2e+33)) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = b * ((x * y) * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y2 <= (-1.9d-128)) .or. (.not. (y2 <= 8.2d+33))) then
        tmp = c * (x * (y0 * y2))
    else
        tmp = b * ((x * y) * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y2 <= -1.9e-128) || !(y2 <= 8.2e+33)) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = b * ((x * y) * a);
	}
	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 <= -1.9e-128) or not (y2 <= 8.2e+33):
		tmp = c * (x * (y0 * y2))
	else:
		tmp = b * ((x * y) * a)
	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 <= -1.9e-128) || !(y2 <= 8.2e+33))
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	else
		tmp = Float64(b * Float64(Float64(x * y) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y2 <= -1.9e-128) || ~((y2 <= 8.2e+33)))
		tmp = c * (x * (y0 * y2));
	else
		tmp = b * ((x * y) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y2, -1.9e-128], N[Not[LessEqual[y2, 8.2e+33]], $MachinePrecision]], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y2 < -1.9000000000000001e-128 or 8.1999999999999999e33 < y2

   1. Initial program 29.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 45.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 45.2%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 45.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 45.2%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 45.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 45.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 45.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 45.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 45.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 43.8%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 32.4%

      \[\leadsto c \cdot \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if -1.9000000000000001e-128 < y2 < 8.1999999999999999e33

   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 b around inf 41.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 36.5%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   5. Taylor expanded in a around inf 27.5%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.9 \cdot 10^{-128} \lor \neg \left(y2 \leq 8.2 \cdot 10^{+33}\right):\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 21.2% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -5.8 \cdot 10^{-130} \lor \neg \left(y2 \leq 5 \cdot 10^{+34}\right):\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y2 -5.8e-130) (not (<= y2 5e+34)))
   (* c (* y0 (* x y2)))
   (* b (* (* x y) a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y2 <= -5.8e-130) || !(y2 <= 5e+34)) {
		tmp = c * (y0 * (x * y2));
	} else {
		tmp = b * ((x * y) * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y2 <= (-5.8d-130)) .or. (.not. (y2 <= 5d+34))) then
        tmp = c * (y0 * (x * y2))
    else
        tmp = b * ((x * y) * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y2 <= -5.8e-130) || !(y2 <= 5e+34)) {
		tmp = c * (y0 * (x * y2));
	} else {
		tmp = b * ((x * y) * a);
	}
	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 <= -5.8e-130) or not (y2 <= 5e+34):
		tmp = c * (y0 * (x * y2))
	else:
		tmp = b * ((x * y) * a)
	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 <= -5.8e-130) || !(y2 <= 5e+34))
		tmp = Float64(c * Float64(y0 * Float64(x * y2)));
	else
		tmp = Float64(b * Float64(Float64(x * y) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y2 <= -5.8e-130) || ~((y2 <= 5e+34)))
		tmp = c * (y0 * (x * y2));
	else
		tmp = b * ((x * y) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y2, -5.8e-130], N[Not[LessEqual[y2, 5e+34]], $MachinePrecision]], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y2 < -5.8e-130 or 4.9999999999999998e34 < y2

   1. Initial program 29.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 45.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 45.2%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 45.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 45.2%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 45.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 45.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 45.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 45.2%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 45.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 43.8%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 33.0%

      \[\leadsto c \cdot \left(y0 \cdot \color{blue}{\left(x \cdot y2\right)}\right) \]

   if -5.8e-130 < y2 < 4.9999999999999998e34

   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 b around inf 41.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 36.5%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   5. Taylor expanded in a around inf 27.5%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -5.8 \cdot 10^{-130} \lor \neg \left(y2 \leq 5 \cdot 10^{+34}\right):\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 22.2% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -3.3 \cdot 10^{-10} \lor \neg \left(y0 \leq 1.65 \cdot 10^{-22}\right):\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y0 -3.3e-10) (not (<= y0 1.65e-22)))
   (* c (* x (* y0 y2)))
   (* i (* j (* x y1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y0 <= -3.3e-10) || !(y0 <= 1.65e-22)) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = i * (j * (x * y1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y0 <= (-3.3d-10)) .or. (.not. (y0 <= 1.65d-22))) then
        tmp = c * (x * (y0 * y2))
    else
        tmp = i * (j * (x * y1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y0 <= -3.3e-10) || !(y0 <= 1.65e-22)) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = i * (j * (x * y1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y0 <= -3.3e-10) or not (y0 <= 1.65e-22):
		tmp = c * (x * (y0 * y2))
	else:
		tmp = i * (j * (x * y1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y0 <= -3.3e-10) || !(y0 <= 1.65e-22))
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	else
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y0 <= -3.3e-10) || ~((y0 <= 1.65e-22)))
		tmp = c * (x * (y0 * y2));
	else
		tmp = i * (j * (x * y1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y0, -3.3e-10], N[Not[LessEqual[y0, 1.65e-22]], $MachinePrecision]], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y0 < -3.3e-10 or 1.65e-22 < y0

   1. Initial program 25.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 56.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 56.7%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      2. mul-1-neg 56.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. unsub-neg 56.7%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. *-commutative 56.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. *-commutative 56.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 56.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 56.7%

         \[\leadsto y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 56.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(c \cdot \left(y2 \cdot x - z \cdot y3\right) - y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - b \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in c around inf 46.2%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 35.5%

      \[\leadsto c \cdot \color{blue}{\left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if -3.3e-10 < y0 < 1.65e-22

   1. Initial program 35.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 38.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 38.5%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 38.5%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 38.5%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 38.5%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in i around -inf 31.6%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 28.3%

         \[\leadsto \color{blue}{\left(i \cdot y1\right) \cdot \left(j \cdot x - k \cdot z\right)} \]

      2. *-commutative 28.3%

         \[\leadsto \color{blue}{\left(y1 \cdot i\right)} \cdot \left(j \cdot x - k \cdot z\right) \]

      3. *-commutative 28.3%

         \[\leadsto \left(y1 \cdot i\right) \cdot \left(\color{blue}{x \cdot j} - k \cdot z\right) \]

      4. *-commutative 28.3%

         \[\leadsto \left(y1 \cdot i\right) \cdot \left(x \cdot j - \color{blue}{z \cdot k}\right) \]

   8. Simplified 28.3%

      \[\leadsto \color{blue}{\left(y1 \cdot i\right) \cdot \left(x \cdot j - z \cdot k\right)} \]

   9. Taylor expanded in x around inf 22.5%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -3.3 \cdot 10^{-10} \lor \neg \left(y0 \leq 1.65 \cdot 10^{-22}\right):\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 18.8% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq 6 \cdot 10^{-210}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 6e-210) (* a (* (* x y) b)) (* 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 (y3 <= 6e-210) {
		tmp = a * ((x * y) * b);
	} 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 (y3 <= 6d-210) then
        tmp = a * ((x * y) * b)
    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 (y3 <= 6e-210) {
		tmp = a * ((x * y) * b);
	} 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 y3 <= 6e-210:
		tmp = a * ((x * y) * b)
	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 (y3 <= 6e-210)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	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 (y3 <= 6e-210)
		tmp = a * ((x * y) * b);
	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[LessEqual[y3, 6e-210], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y3 < 6.0000000000000003e-210

   1. Initial program 32.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 40.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 31.2%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   5. Taylor expanded in a around inf 21.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

   if 6.0000000000000003e-210 < y3

   1. Initial program 27.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. mul-1-neg 43.6%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 43.6%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 43.6%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 43.6%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in y3 around -inf 37.1%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]

   7. Taylor expanded in a around inf 24.2%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 24.2%

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(z \cdot y3\right)}\right) \]

   9. Simplified 24.2%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 22.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq 6 \cdot 10^{-210}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 18.6% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq 5.6 \cdot 10^{-210}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 5.6e-210) (* b (* (* x y) a)) (* 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 (y3 <= 5.6e-210) {
		tmp = b * ((x * y) * a);
	} 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 (y3 <= 5.6d-210) then
        tmp = b * ((x * y) * a)
    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 (y3 <= 5.6e-210) {
		tmp = b * ((x * y) * a);
	} 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 y3 <= 5.6e-210:
		tmp = b * ((x * y) * a)
	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 (y3 <= 5.6e-210)
		tmp = Float64(b * Float64(Float64(x * y) * a));
	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 (y3 <= 5.6e-210)
		tmp = b * ((x * y) * a);
	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[LessEqual[y3, 5.6e-210], N[(b * N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y3 < 5.6e-210

   1. Initial program 32.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 40.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in x around inf 31.2%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   5. Taylor expanded in a around inf 22.5%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y\right)\right)} \]

   if 5.6e-210 < y3

   1. Initial program 27.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. mul-1-neg 43.6%

         \[\leadsto \color{blue}{-y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. *-commutative 43.6%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot y1} \]

      3. distribute-rgt-neg-in 43.6%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-y1\right)} \]

   5. Simplified 43.6%

      \[\leadsto \color{blue}{\left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-y1\right)} \]

   6. Taylor expanded in y3 around -inf 37.1%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]

   7. Taylor expanded in a around inf 24.2%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 24.2%

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(z \cdot y3\right)}\right) \]

   9. Simplified 24.2%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 23.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq 5.6 \cdot 10^{-210}:\\ \;\;\;\;b \cdot \left(\left(x \cdot y\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 17.9% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(\left(x \cdot y\right) \cdot b\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* (* x y) b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * ((x * y) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * ((x * y) * b)

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(Float64(x * y) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * ((x * y) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 30.3%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Add Preprocessing

3. Taylor expanded in b around inf 36.5%

   \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

4. Taylor expanded in x around inf 27.2%

   \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

5. Taylor expanded in a around inf 18.0%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

6. Final simplification 18.0%

   \[\leadsto a \cdot \left(\left(x \cdot y\right) \cdot b\right) \]
7. 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 2024048 
(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)))))