Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 29.1% → 37.9%

Time: 59.7s

Alternatives: 38

Speedup: 3.1×

• 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: 29.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 37.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot y1 - b \cdot y0\\ t_2 := y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ t_3 := t \cdot y2 - y \cdot y3\\ t_4 := y \cdot \left(a \cdot b - c \cdot i\right)\\ \mathbf{if}\;y1 \leq -1.86 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y1 \leq -4.65 \cdot 10^{-113}:\\ \;\;\;\;x \cdot t\_4\\ \mathbf{elif}\;y1 \leq -4.3 \cdot 10^{-219}:\\ \;\;\;\;y5 \cdot \left(a \cdot t\_3 + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -1.9 \cdot 10^{-280}:\\ \;\;\;\;x \cdot \left(\left(t\_4 + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot t\_1\right)\\ \mathbf{elif}\;y1 \leq 5.5 \cdot 10^{-229}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(\left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right) + j \cdot \left(x \cdot t\_1\right)\right) + \left(c \cdot y4 - a \cdot y5\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 5.5 \cdot 10^{-165}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 2.9 \cdot 10^{-128}:\\ \;\;\;\;a \cdot \left(y5 \cdot t\_3\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* i y1) (* b y0)))
        (t_2 (* y1 (- (* i (- (* x j) (* z k))) (* a (- (* x y2) (* z y3))))))
        (t_3 (- (* t y2) (* y y3)))
        (t_4 (* y (- (* a b) (* c i)))))
   (if (<= y1 -1.86e+34)
     t_2
     (if (<= y1 -4.65e-113)
       (* x t_4)
       (if (<= y1 -4.3e-219)
         (*
          y5
          (+
           (* a t_3)
           (+ (* i (- (* y k) (* t j))) (* y0 (- (* j y3) (* k y2))))))
         (if (<= y1 -1.9e-280)
           (* x (+ (+ t_4 (* y2 (- (* c y0) (* a y1)))) (* j t_1)))
           (if (<= y1 5.5e-229)
             (+
              (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5)))
              (+
               (+
                (* (- (* t j) (* y k)) (- (* b y4) (* i y5)))
                (* j (* x t_1)))
               (* (- (* c y4) (* a y5)) (- (* y y3) (* t y2)))))
             (if (<= y1 5.5e-165)
               (* b (* k (- (* z y0) (* y y4))))
               (if (<= y1 2.9e-128) (* a (* y5 t_3)) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (i * y1) - (b * y0);
	double t_2 = y1 * ((i * ((x * j) - (z * k))) - (a * ((x * y2) - (z * y3))));
	double t_3 = (t * y2) - (y * y3);
	double t_4 = y * ((a * b) - (c * i));
	double tmp;
	if (y1 <= -1.86e+34) {
		tmp = t_2;
	} else if (y1 <= -4.65e-113) {
		tmp = x * t_4;
	} else if (y1 <= -4.3e-219) {
		tmp = y5 * ((a * t_3) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y1 <= -1.9e-280) {
		tmp = x * ((t_4 + (y2 * ((c * y0) - (a * y1)))) + (j * t_1));
	} else if (y1 <= 5.5e-229) {
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (((((t * j) - (y * k)) * ((b * y4) - (i * y5))) + (j * (x * t_1))) + (((c * y4) - (a * y5)) * ((y * y3) - (t * y2))));
	} else if (y1 <= 5.5e-165) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (y1 <= 2.9e-128) {
		tmp = a * (y5 * t_3);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (i * y1) - (b * y0)
    t_2 = y1 * ((i * ((x * j) - (z * k))) - (a * ((x * y2) - (z * y3))))
    t_3 = (t * y2) - (y * y3)
    t_4 = y * ((a * b) - (c * i))
    if (y1 <= (-1.86d+34)) then
        tmp = t_2
    else if (y1 <= (-4.65d-113)) then
        tmp = x * t_4
    else if (y1 <= (-4.3d-219)) then
        tmp = y5 * ((a * t_3) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
    else if (y1 <= (-1.9d-280)) then
        tmp = x * ((t_4 + (y2 * ((c * y0) - (a * y1)))) + (j * t_1))
    else if (y1 <= 5.5d-229) then
        tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (((((t * j) - (y * k)) * ((b * y4) - (i * y5))) + (j * (x * t_1))) + (((c * y4) - (a * y5)) * ((y * y3) - (t * y2))))
    else if (y1 <= 5.5d-165) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (y1 <= 2.9d-128) then
        tmp = a * (y5 * t_3)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (i * y1) - (b * y0);
	double t_2 = y1 * ((i * ((x * j) - (z * k))) - (a * ((x * y2) - (z * y3))));
	double t_3 = (t * y2) - (y * y3);
	double t_4 = y * ((a * b) - (c * i));
	double tmp;
	if (y1 <= -1.86e+34) {
		tmp = t_2;
	} else if (y1 <= -4.65e-113) {
		tmp = x * t_4;
	} else if (y1 <= -4.3e-219) {
		tmp = y5 * ((a * t_3) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (y1 <= -1.9e-280) {
		tmp = x * ((t_4 + (y2 * ((c * y0) - (a * y1)))) + (j * t_1));
	} else if (y1 <= 5.5e-229) {
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (((((t * j) - (y * k)) * ((b * y4) - (i * y5))) + (j * (x * t_1))) + (((c * y4) - (a * y5)) * ((y * y3) - (t * y2))));
	} else if (y1 <= 5.5e-165) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (y1 <= 2.9e-128) {
		tmp = a * (y5 * t_3);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (i * y1) - (b * y0)
	t_2 = y1 * ((i * ((x * j) - (z * k))) - (a * ((x * y2) - (z * y3))))
	t_3 = (t * y2) - (y * y3)
	t_4 = y * ((a * b) - (c * i))
	tmp = 0
	if y1 <= -1.86e+34:
		tmp = t_2
	elif y1 <= -4.65e-113:
		tmp = x * t_4
	elif y1 <= -4.3e-219:
		tmp = y5 * ((a * t_3) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
	elif y1 <= -1.9e-280:
		tmp = x * ((t_4 + (y2 * ((c * y0) - (a * y1)))) + (j * t_1))
	elif y1 <= 5.5e-229:
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (((((t * j) - (y * k)) * ((b * y4) - (i * y5))) + (j * (x * t_1))) + (((c * y4) - (a * y5)) * ((y * y3) - (t * y2))))
	elif y1 <= 5.5e-165:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif y1 <= 2.9e-128:
		tmp = a * (y5 * t_3)
	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(i * y1) - Float64(b * y0))
	t_2 = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) - Float64(a * Float64(Float64(x * y2) - Float64(z * y3)))))
	t_3 = Float64(Float64(t * y2) - Float64(y * y3))
	t_4 = Float64(y * Float64(Float64(a * b) - Float64(c * i)))
	tmp = 0.0
	if (y1 <= -1.86e+34)
		tmp = t_2;
	elseif (y1 <= -4.65e-113)
		tmp = Float64(x * t_4);
	elseif (y1 <= -4.3e-219)
		tmp = Float64(y5 * Float64(Float64(a * t_3) + Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))));
	elseif (y1 <= -1.9e-280)
		tmp = Float64(x * Float64(Float64(t_4 + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * t_1)));
	elseif (y1 <= 5.5e-229)
		tmp = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(Float64(Float64(Float64(Float64(t * j) - Float64(y * k)) * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(j * Float64(x * t_1))) + Float64(Float64(Float64(c * y4) - Float64(a * y5)) * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y1 <= 5.5e-165)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (y1 <= 2.9e-128)
		tmp = Float64(a * Float64(y5 * t_3));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (i * y1) - (b * y0);
	t_2 = y1 * ((i * ((x * j) - (z * k))) - (a * ((x * y2) - (z * y3))));
	t_3 = (t * y2) - (y * y3);
	t_4 = y * ((a * b) - (c * i));
	tmp = 0.0;
	if (y1 <= -1.86e+34)
		tmp = t_2;
	elseif (y1 <= -4.65e-113)
		tmp = x * t_4;
	elseif (y1 <= -4.3e-219)
		tmp = y5 * ((a * t_3) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	elseif (y1 <= -1.9e-280)
		tmp = x * ((t_4 + (y2 * ((c * y0) - (a * y1)))) + (j * t_1));
	elseif (y1 <= 5.5e-229)
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (((((t * j) - (y * k)) * ((b * y4) - (i * y5))) + (j * (x * t_1))) + (((c * y4) - (a * y5)) * ((y * y3) - (t * y2))));
	elseif (y1 <= 5.5e-165)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (y1 <= 2.9e-128)
		tmp = a * (y5 * t_3);
	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[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -1.86e+34], t$95$2, If[LessEqual[y1, -4.65e-113], N[(x * t$95$4), $MachinePrecision], If[LessEqual[y1, -4.3e-219], N[(y5 * N[(N[(a * t$95$3), $MachinePrecision] + N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.9e-280], N[(x * N[(N[(t$95$4 + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 5.5e-229], N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision] * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 5.5e-165], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.9e-128], N[(a * N[(y5 * t$95$3), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y1 < -1.86e34 or 2.9e-128 < y1

   1. Initial program 32.7%

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

   3. Taylor expanded in y1 around -inf 56.0%

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

      1. associate-*r* 56.0%

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

      2. neg-mul-1 56.0%

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

      3. +-commutative 56.0%

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

      4. mul-1-neg 56.0%

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

      5. unsub-neg 56.0%

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

      6. *-commutative 56.0%

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

      7. *-commutative 56.0%

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

      8. *-commutative 56.0%

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

      9. *-commutative 56.0%

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

   5. Simplified 56.0%

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

   6. Taylor expanded in y4 around 0 61.0%

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

   if -1.86e34 < y1 < -4.6499999999999999e-113

   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 x around inf 57.4%

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

   4. Taylor expanded in y around inf 62.7%

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

   if -4.6499999999999999e-113 < y1 < -4.3000000000000003e-219

   1. Initial program 47.0%

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

   3. Taylor expanded in y5 around -inf 63.5%

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

   if -4.3000000000000003e-219 < y1 < -1.9000000000000001e-280

   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 x around inf 77.8%

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

   if -1.9000000000000001e-280 < y1 < 5.5000000000000001e-229

   1. Initial program 45.3%

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

   3. Taylor expanded in j around inf 65.5%

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

      1. mul-1-neg 65.5%

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

      2. *-commutative 65.5%

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

   5. Simplified 65.5%

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

   if 5.5000000000000001e-229 < y1 < 5.49999999999999969e-165

   1. Initial program 30.0%

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

   3. Taylor expanded in b around inf 70.4%

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

   4. Taylor expanded in k around -inf 90.4%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 90.4%

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

      2. neg-mul-1 90.4%

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

   6. Simplified 90.4%

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

   if 5.49999999999999969e-165 < y1 < 2.9e-128

   1. Initial program 62.5%

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

   3. Taylor expanded in a around inf 75.0%

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

      1. +-commutative 75.0%

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

      2. mul-1-neg 75.0%

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

      3. unsub-neg 75.0%

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

      4. *-commutative 75.0%

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

      5. *-commutative 75.0%

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

      6. *-commutative 75.0%

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

      7. mul-1-neg 75.0%

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

      8. *-commutative 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in y5 around inf 75.1%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.86 \cdot 10^{+34}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq -4.65 \cdot 10^{-113}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -4.3 \cdot 10^{-219}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -1.9 \cdot 10^{-280}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 5.5 \cdot 10^{-229}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(\left(\left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right) + j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right) + \left(c \cdot y4 - a \cdot y5\right) \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 5.5 \cdot 10^{-165}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 2.9 \cdot 10^{-128}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 52.6% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y2) (* z y3)))
        (t_2 (- (* x j) (* z k)))
        (t_3
         (+
          (+
           (+
            (+
             (+
              (* (- (* a b) (* c i)) (- (* x y) (* z t)))
              (* t_2 (- (* i y1) (* b y0))))
             (* (- (* c y0) (* a y1)) t_1))
            (* (- (* t j) (* y k)) (- (* b y4) (* i y5))))
           (* (- (* c y4) (* a y5)) (- (* y y3) (* t y2))))
          (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5))))))
   (if (<= t_3 INFINITY) t_3 (* y1 (- (* i t_2) (* a 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 = (x * y2) - (z * y3);
	double t_2 = (x * j) - (z * k);
	double t_3 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (t_2 * ((i * y1) - (b * y0)))) + (((c * y0) - (a * y1)) * t_1)) + (((t * j) - (y * k)) * ((b * y4) - (i * y5)))) + (((c * y4) - (a * y5)) * ((y * y3) - (t * y2)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)));
	double tmp;
	if (t_3 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = y1 * ((i * t_2) - (a * 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 = (x * y2) - (z * y3);
	double t_2 = (x * j) - (z * k);
	double t_3 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (t_2 * ((i * y1) - (b * y0)))) + (((c * y0) - (a * y1)) * t_1)) + (((t * j) - (y * k)) * ((b * y4) - (i * y5)))) + (((c * y4) - (a * y5)) * ((y * y3) - (t * y2)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)));
	double tmp;
	if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = y1 * ((i * t_2) - (a * 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 = (x * y2) - (z * y3)
	t_2 = (x * j) - (z * k)
	t_3 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (t_2 * ((i * y1) - (b * y0)))) + (((c * y0) - (a * y1)) * t_1)) + (((t * j) - (y * k)) * ((b * y4) - (i * y5)))) + (((c * y4) - (a * y5)) * ((y * y3) - (t * y2)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)))
	tmp = 0
	if t_3 <= math.inf:
		tmp = t_3
	else:
		tmp = y1 * ((i * t_2) - (a * 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(x * y2) - Float64(z * y3))
	t_2 = Float64(Float64(x * j) - Float64(z * k))
	t_3 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(a * b) - Float64(c * i)) * Float64(Float64(x * y) - Float64(z * t))) + Float64(t_2 * Float64(Float64(i * y1) - Float64(b * y0)))) + Float64(Float64(Float64(c * y0) - Float64(a * y1)) * t_1)) + Float64(Float64(Float64(t * j) - Float64(y * k)) * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(Float64(Float64(c * y4) - Float64(a * y5)) * Float64(Float64(y * y3) - Float64(t * y2)))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))))
	tmp = 0.0
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(y1 * Float64(Float64(i * t_2) - Float64(a * 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 = (x * y2) - (z * y3);
	t_2 = (x * j) - (z * k);
	t_3 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (t_2 * ((i * y1) - (b * y0)))) + (((c * y0) - (a * y1)) * t_1)) + (((t * j) - (y * k)) * ((b * y4) - (i * y5)))) + (((c * y4) - (a * y5)) * ((y * y3) - (t * y2)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)));
	tmp = 0.0;
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = y1 * ((i * t_2) - (a * 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[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision] * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, Infinity], t$95$3, N[(y1 * N[(N[(i * t$95$2), $MachinePrecision] - N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.0%

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

   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 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. associate-*r* 39.0%

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

      2. neg-mul-1 39.0%

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

      3. +-commutative 39.0%

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

      4. mul-1-neg 39.0%

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

      5. unsub-neg 39.0%

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

      6. *-commutative 39.0%

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

      7. *-commutative 39.0%

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

      8. *-commutative 39.0%

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

      9. *-commutative 39.0%

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

   5. Simplified 39.0%

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

   6. Taylor expanded in y4 around 0 44.3%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.3%

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

Alternative 3: 33.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;y1 \leq -4.3 \cdot 10^{+172}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -3.3 \cdot 10^{+102}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -3 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -5.5 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -5.4 \cdot 10^{-218}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 4.8 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq 5 \cdot 10^{-163}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 1.8 \cdot 10^{-127}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 9 \cdot 10^{-112}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right) - a \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 2.3 \cdot 10^{+201}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (* x (+ (* y2 (- (* c y0) (* a y1))) (* j (- (* i y1) (* b y0)))))))
   (if (<= y1 -4.3e+172)
     (* a (* y1 (- (* z y3) (* x y2))))
     (if (<= y1 -3.3e+102)
       (* i (* z (- (* t c) (* k y1))))
       (if (<= y1 -3e+36)
         t_1
         (if (<= y1 -5.5e-137)
           (* x (* y (- (* a b) (* c i))))
           (if (<= y1 -5.4e-218)
             (* b (* a (- (* x y) (* z t))))
             (if (<= y1 4.8e-282)
               t_1
               (if (<= y1 5e-163)
                 (* b (* k (- (* z y0) (* y y4))))
                 (if (<= y1 1.8e-127)
                   (* a (* y5 (- (* t y2) (* y y3))))
                   (if (<= y1 9e-112)
                     (* y1 (- (* i (* x j)) (* a (* x y2))))
                     (if (<= y1 2.3e+201)
                       t_1
                       (* y1 (* z (- (* a y3) (* i k))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y1 <= -4.3e+172) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y1 <= -3.3e+102) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else if (y1 <= -3e+36) {
		tmp = t_1;
	} else if (y1 <= -5.5e-137) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y1 <= -5.4e-218) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y1 <= 4.8e-282) {
		tmp = t_1;
	} else if (y1 <= 5e-163) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (y1 <= 1.8e-127) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y1 <= 9e-112) {
		tmp = y1 * ((i * (x * j)) - (a * (x * y2)));
	} else if (y1 <= 2.3e+201) {
		tmp = t_1;
	} else {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))))
    if (y1 <= (-4.3d+172)) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (y1 <= (-3.3d+102)) then
        tmp = i * (z * ((t * c) - (k * y1)))
    else if (y1 <= (-3d+36)) then
        tmp = t_1
    else if (y1 <= (-5.5d-137)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y1 <= (-5.4d-218)) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (y1 <= 4.8d-282) then
        tmp = t_1
    else if (y1 <= 5d-163) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (y1 <= 1.8d-127) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (y1 <= 9d-112) then
        tmp = y1 * ((i * (x * j)) - (a * (x * y2)))
    else if (y1 <= 2.3d+201) then
        tmp = t_1
    else
        tmp = y1 * (z * ((a * y3) - (i * k)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y1 <= -4.3e+172) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y1 <= -3.3e+102) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else if (y1 <= -3e+36) {
		tmp = t_1;
	} else if (y1 <= -5.5e-137) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y1 <= -5.4e-218) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y1 <= 4.8e-282) {
		tmp = t_1;
	} else if (y1 <= 5e-163) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (y1 <= 1.8e-127) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y1 <= 9e-112) {
		tmp = y1 * ((i * (x * j)) - (a * (x * y2)));
	} else if (y1 <= 2.3e+201) {
		tmp = t_1;
	} else {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))))
	tmp = 0
	if y1 <= -4.3e+172:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif y1 <= -3.3e+102:
		tmp = i * (z * ((t * c) - (k * y1)))
	elif y1 <= -3e+36:
		tmp = t_1
	elif y1 <= -5.5e-137:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y1 <= -5.4e-218:
		tmp = b * (a * ((x * y) - (z * t)))
	elif y1 <= 4.8e-282:
		tmp = t_1
	elif y1 <= 5e-163:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif y1 <= 1.8e-127:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif y1 <= 9e-112:
		tmp = y1 * ((i * (x * j)) - (a * (x * y2)))
	elif y1 <= 2.3e+201:
		tmp = t_1
	else:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(x * Float64(Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (y1 <= -4.3e+172)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (y1 <= -3.3e+102)
		tmp = Float64(i * Float64(z * Float64(Float64(t * c) - Float64(k * y1))));
	elseif (y1 <= -3e+36)
		tmp = t_1;
	elseif (y1 <= -5.5e-137)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y1 <= -5.4e-218)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y1 <= 4.8e-282)
		tmp = t_1;
	elseif (y1 <= 5e-163)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (y1 <= 1.8e-127)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (y1 <= 9e-112)
		tmp = Float64(y1 * Float64(Float64(i * Float64(x * j)) - Float64(a * Float64(x * y2))));
	elseif (y1 <= 2.3e+201)
		tmp = t_1;
	else
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (y1 <= -4.3e+172)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (y1 <= -3.3e+102)
		tmp = i * (z * ((t * c) - (k * y1)));
	elseif (y1 <= -3e+36)
		tmp = t_1;
	elseif (y1 <= -5.5e-137)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y1 <= -5.4e-218)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (y1 <= 4.8e-282)
		tmp = t_1;
	elseif (y1 <= 5e-163)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (y1 <= 1.8e-127)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (y1 <= 9e-112)
		tmp = y1 * ((i * (x * j)) - (a * (x * y2)));
	elseif (y1 <= 2.3e+201)
		tmp = t_1;
	else
		tmp = y1 * (z * ((a * y3) - (i * k)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(x * N[(N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -4.3e+172], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3.3e+102], N[(i * N[(z * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3e+36], t$95$1, If[LessEqual[y1, -5.5e-137], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -5.4e-218], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 4.8e-282], t$95$1, If[LessEqual[y1, 5e-163], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.8e-127], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 9e-112], N[(y1 * N[(N[(i * N[(x * j), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.3e+201], t$95$1, N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y1 < -4.3000000000000003e172

   1. Initial program 39.2%

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

   3. Taylor expanded in a around inf 49.7%

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

      1. +-commutative 49.7%

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

      2. mul-1-neg 49.7%

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

      3. unsub-neg 49.7%

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

      4. *-commutative 49.7%

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

      5. *-commutative 49.7%

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

      6. *-commutative 49.7%

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

      7. mul-1-neg 49.7%

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

      8. *-commutative 49.7%

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

   5. Simplified 49.7%

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

   6. Taylor expanded in y1 around inf 64.1%

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

   if -4.3000000000000003e172 < y1 < -3.29999999999999999e102

   1. Initial program 30.0%

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

   3. Taylor expanded in z around -inf 30.1%

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

   4. Taylor expanded in i around -inf 60.9%

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

      1. associate-*r* 60.9%

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

      2. neg-mul-1 60.9%

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

   6. Simplified 60.9%

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

   if -3.29999999999999999e102 < y1 < -3e36 or -5.3999999999999999e-218 < y1 < 4.79999999999999994e-282 or 9.00000000000000024e-112 < y1 < 2.3000000000000001e201

   1. Initial program 33.7%

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

   3. Taylor expanded in x around inf 48.4%

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

   4. Taylor expanded in y around 0 55.8%

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

   if -3e36 < y1 < -5.5000000000000003e-137

   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 x around inf 58.1%

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

   4. Taylor expanded in y around inf 64.3%

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

   if -5.5000000000000003e-137 < y1 < -5.3999999999999999e-218

   1. Initial program 48.3%

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

   3. Taylor expanded in b around inf 49.8%

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

   4. Taylor expanded in a around inf 48.9%

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

   if 4.79999999999999994e-282 < y1 < 4.99999999999999977e-163

   1. Initial program 43.1%

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

   3. Taylor expanded in b around inf 48.0%

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

   4. Taylor expanded in k around -inf 67.2%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 67.2%

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

      2. neg-mul-1 67.2%

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

   6. Simplified 67.2%

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

   if 4.99999999999999977e-163 < y1 < 1.8e-127

   1. Initial program 62.5%

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

   3. Taylor expanded in a around inf 75.0%

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

      1. +-commutative 75.0%

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

      2. mul-1-neg 75.0%

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

      3. unsub-neg 75.0%

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

      4. *-commutative 75.0%

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

      5. *-commutative 75.0%

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

      6. *-commutative 75.0%

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

      7. mul-1-neg 75.0%

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

      8. *-commutative 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in y5 around inf 75.1%

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

   if 1.8e-127 < y1 < 9.00000000000000024e-112

   1. Initial program 33.3%

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

   3. Taylor expanded in y1 around -inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

      3. +-commutative 100.0%

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

      4. mul-1-neg 100.0%

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

      5. unsub-neg 100.0%

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

      6. *-commutative 100.0%

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

      7. *-commutative 100.0%

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

      8. *-commutative 100.0%

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

      9. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y4 around 0 100.0%

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

   7. Taylor expanded in z around 0 100.0%

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

   if 2.3000000000000001e201 < y1

   1. Initial program 22.7%

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

   3. Taylor expanded in y1 around -inf 59.0%

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

      1. associate-*r* 59.0%

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

      2. neg-mul-1 59.0%

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

      3. +-commutative 59.0%

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

      4. mul-1-neg 59.0%

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

      5. unsub-neg 59.0%

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

      6. *-commutative 59.0%

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

      7. *-commutative 59.0%

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

      8. *-commutative 59.0%

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

      9. *-commutative 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in z around -inf 73.7%

      \[\leadsto \color{blue}{y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -4.3 \cdot 10^{+172}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -3.3 \cdot 10^{+102}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -3 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq -5.5 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -5.4 \cdot 10^{-218}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 4.8 \cdot 10^{-282}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 5 \cdot 10^{-163}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 1.8 \cdot 10^{-127}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 9 \cdot 10^{-112}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right) - a \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 2.3 \cdot 10^{+201}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 40.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(\left(x \cdot \left(a \cdot b - c \cdot i\right) + k \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ t_2 := c \cdot y0 - a \cdot y1\\ t_3 := i \cdot \left(x \cdot j - z \cdot k\right)\\ t_4 := y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot t\_2\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \left(b \cdot \left(\frac{y2 \cdot t\_2}{b} + \left(\frac{i \cdot \left(j \cdot y1\right)}{b} - j \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+98}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq -160000:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-79}:\\ \;\;\;\;y1 \cdot \left(t\_3 + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-272}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+163}:\\ \;\;\;\;y1 \cdot \left(t\_3 - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y
          (+
           (+ (* x (- (* a b) (* c i))) (* k (- (* i y5) (* b y4))))
           (* y3 (- (* c y4) (* a y5))))))
        (t_2 (- (* c y0) (* a y1)))
        (t_3 (* i (- (* x j) (* z k))))
        (t_4
         (*
          y2
          (+
           (+ (* k (- (* y1 y4) (* y0 y5))) (* x t_2))
           (* t (- (* a y5) (* c y4)))))))
   (if (<= y -7.2e+193)
     t_1
     (if (<= y -6.5e+105)
       (* x (* b (+ (/ (* y2 t_2) b) (- (/ (* i (* j y1)) b) (* j y0)))))
       (if (<= y -2.7e+98)
         (* b (* j (- (* t y4) (* x y0))))
         (if (<= y -160000.0)
           t_4
           (if (<= y -1.5e-79)
             (*
              y1
              (+
               t_3
               (+ (* y4 (- (* k y2) (* j y3))) (* a (- (* z y3) (* x y2))))))
             (if (<= y -3.2e-272)
               t_4
               (if (<= y 4.5e+163)
                 (* y1 (- t_3 (* a (- (* x y2) (* 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 = y * (((x * ((a * b) - (c * i))) + (k * ((i * y5) - (b * y4)))) + (y3 * ((c * y4) - (a * y5))));
	double t_2 = (c * y0) - (a * y1);
	double t_3 = i * ((x * j) - (z * k));
	double t_4 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_2)) + (t * ((a * y5) - (c * y4))));
	double tmp;
	if (y <= -7.2e+193) {
		tmp = t_1;
	} else if (y <= -6.5e+105) {
		tmp = x * (b * (((y2 * t_2) / b) + (((i * (j * y1)) / b) - (j * y0))));
	} else if (y <= -2.7e+98) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y <= -160000.0) {
		tmp = t_4;
	} else if (y <= -1.5e-79) {
		tmp = y1 * (t_3 + ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2)))));
	} else if (y <= -3.2e-272) {
		tmp = t_4;
	} else if (y <= 4.5e+163) {
		tmp = y1 * (t_3 - (a * ((x * y2) - (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) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = y * (((x * ((a * b) - (c * i))) + (k * ((i * y5) - (b * y4)))) + (y3 * ((c * y4) - (a * y5))))
    t_2 = (c * y0) - (a * y1)
    t_3 = i * ((x * j) - (z * k))
    t_4 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_2)) + (t * ((a * y5) - (c * y4))))
    if (y <= (-7.2d+193)) then
        tmp = t_1
    else if (y <= (-6.5d+105)) then
        tmp = x * (b * (((y2 * t_2) / b) + (((i * (j * y1)) / b) - (j * y0))))
    else if (y <= (-2.7d+98)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y <= (-160000.0d0)) then
        tmp = t_4
    else if (y <= (-1.5d-79)) then
        tmp = y1 * (t_3 + ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2)))))
    else if (y <= (-3.2d-272)) then
        tmp = t_4
    else if (y <= 4.5d+163) then
        tmp = y1 * (t_3 - (a * ((x * y2) - (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 = y * (((x * ((a * b) - (c * i))) + (k * ((i * y5) - (b * y4)))) + (y3 * ((c * y4) - (a * y5))));
	double t_2 = (c * y0) - (a * y1);
	double t_3 = i * ((x * j) - (z * k));
	double t_4 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_2)) + (t * ((a * y5) - (c * y4))));
	double tmp;
	if (y <= -7.2e+193) {
		tmp = t_1;
	} else if (y <= -6.5e+105) {
		tmp = x * (b * (((y2 * t_2) / b) + (((i * (j * y1)) / b) - (j * y0))));
	} else if (y <= -2.7e+98) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y <= -160000.0) {
		tmp = t_4;
	} else if (y <= -1.5e-79) {
		tmp = y1 * (t_3 + ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2)))));
	} else if (y <= -3.2e-272) {
		tmp = t_4;
	} else if (y <= 4.5e+163) {
		tmp = y1 * (t_3 - (a * ((x * y2) - (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 = y * (((x * ((a * b) - (c * i))) + (k * ((i * y5) - (b * y4)))) + (y3 * ((c * y4) - (a * y5))))
	t_2 = (c * y0) - (a * y1)
	t_3 = i * ((x * j) - (z * k))
	t_4 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_2)) + (t * ((a * y5) - (c * y4))))
	tmp = 0
	if y <= -7.2e+193:
		tmp = t_1
	elif y <= -6.5e+105:
		tmp = x * (b * (((y2 * t_2) / b) + (((i * (j * y1)) / b) - (j * y0))))
	elif y <= -2.7e+98:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y <= -160000.0:
		tmp = t_4
	elif y <= -1.5e-79:
		tmp = y1 * (t_3 + ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2)))))
	elif y <= -3.2e-272:
		tmp = t_4
	elif y <= 4.5e+163:
		tmp = y1 * (t_3 - (a * ((x * y2) - (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(y * Float64(Float64(Float64(x * Float64(Float64(a * b) - Float64(c * i))) + Float64(k * Float64(Float64(i * y5) - Float64(b * y4)))) + Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5)))))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	t_3 = Float64(i * Float64(Float64(x * j) - Float64(z * k)))
	t_4 = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * t_2)) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))))
	tmp = 0.0
	if (y <= -7.2e+193)
		tmp = t_1;
	elseif (y <= -6.5e+105)
		tmp = Float64(x * Float64(b * Float64(Float64(Float64(y2 * t_2) / b) + Float64(Float64(Float64(i * Float64(j * y1)) / b) - Float64(j * y0)))));
	elseif (y <= -2.7e+98)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y <= -160000.0)
		tmp = t_4;
	elseif (y <= -1.5e-79)
		tmp = Float64(y1 * Float64(t_3 + Float64(Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2))))));
	elseif (y <= -3.2e-272)
		tmp = t_4;
	elseif (y <= 4.5e+163)
		tmp = Float64(y1 * Float64(t_3 - Float64(a * Float64(Float64(x * y2) - 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 = y * (((x * ((a * b) - (c * i))) + (k * ((i * y5) - (b * y4)))) + (y3 * ((c * y4) - (a * y5))));
	t_2 = (c * y0) - (a * y1);
	t_3 = i * ((x * j) - (z * k));
	t_4 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * t_2)) + (t * ((a * y5) - (c * y4))));
	tmp = 0.0;
	if (y <= -7.2e+193)
		tmp = t_1;
	elseif (y <= -6.5e+105)
		tmp = x * (b * (((y2 * t_2) / b) + (((i * (j * y1)) / b) - (j * y0))));
	elseif (y <= -2.7e+98)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y <= -160000.0)
		tmp = t_4;
	elseif (y <= -1.5e-79)
		tmp = y1 * (t_3 + ((y4 * ((k * y2) - (j * y3))) + (a * ((z * y3) - (x * y2)))));
	elseif (y <= -3.2e-272)
		tmp = t_4;
	elseif (y <= 4.5e+163)
		tmp = y1 * (t_3 - (a * ((x * y2) - (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[(y * N[(N[(N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.2e+193], t$95$1, If[LessEqual[y, -6.5e+105], N[(x * N[(b * N[(N[(N[(y2 * t$95$2), $MachinePrecision] / b), $MachinePrecision] + N[(N[(N[(i * N[(j * y1), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.7e+98], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -160000.0], t$95$4, If[LessEqual[y, -1.5e-79], N[(y1 * N[(t$95$3 + N[(N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.2e-272], t$95$4, If[LessEqual[y, 4.5e+163], N[(y1 * N[(t$95$3 - N[(a * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -7.2e193 or 4.49999999999999988e163 < y

   1. Initial program 25.4%

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

   3. Taylor expanded in y around inf 70.6%

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

      1. +-commutative 70.6%

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

      2. mul-1-neg 70.6%

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

      3. unsub-neg 70.6%

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

      4. *-commutative 70.6%

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

      5. *-commutative 70.6%

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

      6. mul-1-neg 70.6%

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

   5. Simplified 70.6%

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

   if -7.2e193 < y < -6.50000000000000049e105

   1. Initial program 37.5%

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

   3. Taylor expanded in x around inf 56.6%

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

   4. Taylor expanded in y around 0 56.8%

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

   5. Taylor expanded in b around inf 68.9%

      \[\leadsto x \cdot \color{blue}{\left(b \cdot \left(\frac{y2 \cdot \left(c \cdot y0 - a \cdot y1\right)}{b} - \left(-1 \cdot \frac{i \cdot \left(j \cdot y1\right)}{b} + j \cdot y0\right)\right)\right)} \]

   if -6.50000000000000049e105 < y < -2.7e98

   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 b around inf 26.7%

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

   4. Taylor expanded in j around inf 76.7%

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

   if -2.7e98 < y < -1.6e5 or -1.5e-79 < y < -3.2e-272

   1. Initial program 48.5%

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

   3. Taylor expanded in y2 around inf 55.8%

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

   if -1.6e5 < y < -1.5e-79

   1. Initial program 47.4%

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

   3. Taylor expanded in y1 around -inf 73.7%

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

      1. associate-*r* 73.7%

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

      2. neg-mul-1 73.7%

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

      3. +-commutative 73.7%

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

      4. mul-1-neg 73.7%

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

      5. unsub-neg 73.7%

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

      6. *-commutative 73.7%

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

      7. *-commutative 73.7%

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

      8. *-commutative 73.7%

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

      9. *-commutative 73.7%

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

   5. Simplified 73.7%

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

   if -3.2e-272 < y < 4.49999999999999988e163

   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 y1 around -inf 51.4%

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

      1. associate-*r* 51.4%

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

      2. neg-mul-1 51.4%

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

      3. +-commutative 51.4%

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

      4. mul-1-neg 51.4%

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

      5. unsub-neg 51.4%

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

      6. *-commutative 51.4%

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

      7. *-commutative 51.4%

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

      8. *-commutative 51.4%

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

      9. *-commutative 51.4%

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

   5. Simplified 51.4%

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

   6. Taylor expanded in y4 around 0 55.5%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+193}:\\ \;\;\;\;y \cdot \left(\left(x \cdot \left(a \cdot b - c \cdot i\right) + k \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \left(b \cdot \left(\frac{y2 \cdot \left(c \cdot y0 - a \cdot y1\right)}{b} + \left(\frac{i \cdot \left(j \cdot y1\right)}{b} - j \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+98}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq -160000:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-79}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-272}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+163}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(x \cdot \left(a \cdot b - c \cdot i\right) + k \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 41.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ t_2 := x \cdot j - z \cdot k\\ \mathbf{if}\;y2 \leq -2 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq -7.8 \cdot 10^{-50}:\\ \;\;\;\;y1 \cdot \left(x \cdot \left(i \cdot j - i \cdot \frac{z \cdot k}{x}\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -1.6 \cdot 10^{-275}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot \left(y1 - \frac{y \cdot y5}{z}\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 10^{-304}:\\ \;\;\;\;i \cdot \left(y1 \cdot t\_2\right)\\ \mathbf{elif}\;y2 \leq 3.8 \cdot 10^{-77}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 4.9 \cdot 10^{+29}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 2.6 \cdot 10^{+55}:\\ \;\;\;\;y1 \cdot \left(i \cdot t\_2 - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y2
          (+
           (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
           (* t (- (* a y5) (* c y4))))))
        (t_2 (- (* x j) (* z k))))
   (if (<= y2 -2e+29)
     t_1
     (if (<= y2 -7.8e-50)
       (*
        y1
        (+ (* x (- (* i j) (* i (/ (* z k) x)))) (* a (- (* z y3) (* x y2)))))
       (if (<= y2 -1.6e-275)
         (* a (* y3 (* z (- y1 (/ (* y y5) z)))))
         (if (<= y2 1e-304)
           (* i (* y1 t_2))
           (if (<= y2 3.8e-77)
             (*
              j
              (+
               (+ (* t (- (* b y4) (* i y5))) (* y3 (- (* y0 y5) (* y1 y4))))
               (* x (- (* i y1) (* b y0)))))
             (if (<= y2 4.9e+29)
               (*
                b
                (+
                 (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
                 (* y0 (- (* z k) (* x j)))))
               (if (<= y2 2.6e+55)
                 (* y1 (- (* i t_2) (* a (- (* x y2) (* 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 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	double t_2 = (x * j) - (z * k);
	double tmp;
	if (y2 <= -2e+29) {
		tmp = t_1;
	} else if (y2 <= -7.8e-50) {
		tmp = y1 * ((x * ((i * j) - (i * ((z * k) / x)))) + (a * ((z * y3) - (x * y2))));
	} else if (y2 <= -1.6e-275) {
		tmp = a * (y3 * (z * (y1 - ((y * y5) / z))));
	} else if (y2 <= 1e-304) {
		tmp = i * (y1 * t_2);
	} else if (y2 <= 3.8e-77) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	} else if (y2 <= 4.9e+29) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y2 <= 2.6e+55) {
		tmp = y1 * ((i * t_2) - (a * ((x * y2) - (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) :: t_2
    real(8) :: tmp
    t_1 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    t_2 = (x * j) - (z * k)
    if (y2 <= (-2d+29)) then
        tmp = t_1
    else if (y2 <= (-7.8d-50)) then
        tmp = y1 * ((x * ((i * j) - (i * ((z * k) / x)))) + (a * ((z * y3) - (x * y2))))
    else if (y2 <= (-1.6d-275)) then
        tmp = a * (y3 * (z * (y1 - ((y * y5) / z))))
    else if (y2 <= 1d-304) then
        tmp = i * (y1 * t_2)
    else if (y2 <= 3.8d-77) then
        tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
    else if (y2 <= 4.9d+29) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    else if (y2 <= 2.6d+55) then
        tmp = y1 * ((i * t_2) - (a * ((x * y2) - (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 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	double t_2 = (x * j) - (z * k);
	double tmp;
	if (y2 <= -2e+29) {
		tmp = t_1;
	} else if (y2 <= -7.8e-50) {
		tmp = y1 * ((x * ((i * j) - (i * ((z * k) / x)))) + (a * ((z * y3) - (x * y2))));
	} else if (y2 <= -1.6e-275) {
		tmp = a * (y3 * (z * (y1 - ((y * y5) / z))));
	} else if (y2 <= 1e-304) {
		tmp = i * (y1 * t_2);
	} else if (y2 <= 3.8e-77) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	} else if (y2 <= 4.9e+29) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y2 <= 2.6e+55) {
		tmp = y1 * ((i * t_2) - (a * ((x * y2) - (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 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	t_2 = (x * j) - (z * k)
	tmp = 0
	if y2 <= -2e+29:
		tmp = t_1
	elif y2 <= -7.8e-50:
		tmp = y1 * ((x * ((i * j) - (i * ((z * k) / x)))) + (a * ((z * y3) - (x * y2))))
	elif y2 <= -1.6e-275:
		tmp = a * (y3 * (z * (y1 - ((y * y5) / z))))
	elif y2 <= 1e-304:
		tmp = i * (y1 * t_2)
	elif y2 <= 3.8e-77:
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
	elif y2 <= 4.9e+29:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	elif y2 <= 2.6e+55:
		tmp = y1 * ((i * t_2) - (a * ((x * y2) - (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(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))))
	t_2 = Float64(Float64(x * j) - Float64(z * k))
	tmp = 0.0
	if (y2 <= -2e+29)
		tmp = t_1;
	elseif (y2 <= -7.8e-50)
		tmp = Float64(y1 * Float64(Float64(x * Float64(Float64(i * j) - Float64(i * Float64(Float64(z * k) / x)))) + Float64(a * Float64(Float64(z * y3) - Float64(x * y2)))));
	elseif (y2 <= -1.6e-275)
		tmp = Float64(a * Float64(y3 * Float64(z * Float64(y1 - Float64(Float64(y * y5) / z)))));
	elseif (y2 <= 1e-304)
		tmp = Float64(i * Float64(y1 * t_2));
	elseif (y2 <= 3.8e-77)
		tmp = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y2 <= 4.9e+29)
		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 (y2 <= 2.6e+55)
		tmp = Float64(y1 * Float64(Float64(i * t_2) - Float64(a * Float64(Float64(x * y2) - 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 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	t_2 = (x * j) - (z * k);
	tmp = 0.0;
	if (y2 <= -2e+29)
		tmp = t_1;
	elseif (y2 <= -7.8e-50)
		tmp = y1 * ((x * ((i * j) - (i * ((z * k) / x)))) + (a * ((z * y3) - (x * y2))));
	elseif (y2 <= -1.6e-275)
		tmp = a * (y3 * (z * (y1 - ((y * y5) / z))));
	elseif (y2 <= 1e-304)
		tmp = i * (y1 * t_2);
	elseif (y2 <= 3.8e-77)
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	elseif (y2 <= 4.9e+29)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	elseif (y2 <= 2.6e+55)
		tmp = y1 * ((i * t_2) - (a * ((x * y2) - (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[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -2e+29], t$95$1, If[LessEqual[y2, -7.8e-50], N[(y1 * N[(N[(x * N[(N[(i * j), $MachinePrecision] - N[(i * N[(N[(z * k), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.6e-275], N[(a * N[(y3 * N[(z * N[(y1 - N[(N[(y * y5), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1e-304], N[(i * N[(y1 * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.8e-77], N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.9e+29], 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[y2, 2.6e+55], N[(y1 * N[(N[(i * t$95$2), $MachinePrecision] - N[(a * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y2 < -1.99999999999999983e29 or 2.6e55 < y2

   1. Initial program 31.7%

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

   3. Taylor expanded in y2 around inf 66.9%

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

   if -1.99999999999999983e29 < y2 < -7.80000000000000042e-50

   1. Initial program 33.3%

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

   3. Taylor expanded in y1 around -inf 53.4%

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

      1. associate-*r* 53.4%

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

      2. neg-mul-1 53.4%

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

      3. +-commutative 53.4%

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

      4. mul-1-neg 53.4%

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

      5. unsub-neg 53.4%

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

      6. *-commutative 53.4%

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

      7. *-commutative 53.4%

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

      8. *-commutative 53.4%

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

      9. *-commutative 53.4%

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

   5. Simplified 53.4%

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

   6. Taylor expanded in y4 around 0 67.9%

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

   7. Taylor expanded in x around inf 68.2%

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

      1. +-commutative 68.2%

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

      2. mul-1-neg 68.2%

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

      3. unsub-neg 68.2%

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

      4. associate-/l* 68.2%

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

      5. *-commutative 68.2%

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

   9. Simplified 68.2%

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

   if -7.80000000000000042e-50 < y2 < -1.6e-275

   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 a around inf 47.7%

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

      1. +-commutative 47.7%

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

      2. mul-1-neg 47.7%

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

      3. unsub-neg 47.7%

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

      4. *-commutative 47.7%

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

      5. *-commutative 47.7%

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

      6. *-commutative 47.7%

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

      7. mul-1-neg 47.7%

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

      8. *-commutative 47.7%

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

   5. Simplified 47.7%

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

   6. Taylor expanded in y3 around -inf 43.4%

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

      1. associate-*r* 43.4%

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

      2. neg-mul-1 43.4%

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

   8. Simplified 43.4%

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

   9. Taylor expanded in z around inf 45.9%

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

   if -1.6e-275 < y2 < 9.99999999999999971e-305

   1. Initial program 23.0%

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

   3. Taylor expanded in y1 around -inf 55.5%

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

      1. associate-*r* 55.5%

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

      2. neg-mul-1 55.5%

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

      3. +-commutative 55.5%

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

      4. mul-1-neg 55.5%

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

      5. unsub-neg 55.5%

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

      6. *-commutative 55.5%

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

      7. *-commutative 55.5%

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

      8. *-commutative 55.5%

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

      9. *-commutative 55.5%

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

   5. Simplified 55.5%

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

   6. Taylor expanded in i around -inf 62.1%

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

   if 9.99999999999999971e-305 < y2 < 3.7999999999999999e-77

   1. Initial program 36.8%

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

   3. Taylor expanded in j around inf 55.4%

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

      1. +-commutative 55.4%

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

      2. mul-1-neg 55.4%

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

      3. unsub-neg 55.4%

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

      4. *-commutative 55.4%

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

   5. Simplified 55.4%

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

   if 3.7999999999999999e-77 < y2 < 4.9000000000000001e29

   1. Initial program 36.4%

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

   3. Taylor expanded in b around inf 65.5%

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

   if 4.9000000000000001e29 < y2 < 2.6e55

   1. Initial program 28.6%

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

   3. Taylor expanded in y1 around -inf 57.1%

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

      1. associate-*r* 57.1%

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

      2. neg-mul-1 57.1%

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

      3. +-commutative 57.1%

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

      4. mul-1-neg 57.1%

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

      5. unsub-neg 57.1%

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

      6. *-commutative 57.1%

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

      7. *-commutative 57.1%

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

      8. *-commutative 57.1%

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

      9. *-commutative 57.1%

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

   5. Simplified 57.1%

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

   6. Taylor expanded in y4 around 0 71.6%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2 \cdot 10^{+29}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -7.8 \cdot 10^{-50}:\\ \;\;\;\;y1 \cdot \left(x \cdot \left(i \cdot j - i \cdot \frac{z \cdot k}{x}\right) + a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -1.6 \cdot 10^{-275}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot \left(y1 - \frac{y \cdot y5}{z}\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 10^{-304}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y2 \leq 3.8 \cdot 10^{-77}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 4.9 \cdot 10^{+29}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 2.6 \cdot 10^{+55}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 31.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ t_2 := y1 \cdot \left(i \cdot \left(x \cdot j\right) - a \cdot \left(x \cdot y2\right)\right)\\ \mathbf{if}\;y1 \leq -4.3 \cdot 10^{+172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -1.36 \cdot 10^{+101}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -1.55 \cdot 10^{+32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y1 \leq -2.4 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -1.05 \cdot 10^{-271}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 1.9 \cdot 10^{-165}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 2.9 \cdot 10^{-127}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 2.65 \cdot 10^{+26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y1 \leq 4.5 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 10^{+224}:\\ \;\;\;\;\left(x \cdot y1\right) \cdot \left(i \cdot \left(j - k \cdot \frac{z}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y1 (- (* z y3) (* x y2)))))
        (t_2 (* y1 (- (* i (* x j)) (* a (* x y2))))))
   (if (<= y1 -4.3e+172)
     t_1
     (if (<= y1 -1.36e+101)
       (* i (* z (- (* t c) (* k y1))))
       (if (<= y1 -1.55e+32)
         t_2
         (if (<= y1 -2.4e-137)
           (* x (* y (- (* a b) (* c i))))
           (if (<= y1 -1.05e-271)
             (* b (* a (- (* x y) (* z t))))
             (if (<= y1 1.9e-165)
               (* b (* k (- (* z y0) (* y y4))))
               (if (<= y1 2.9e-127)
                 (* a (* y5 (- (* t y2) (* y y3))))
                 (if (<= y1 2.65e+26)
                   t_2
                   (if (<= y1 4.5e+62)
                     (* x (* y0 (- (* c y2) (* b j))))
                     (if (<= y1 1e+224)
                       (* (* x y1) (* i (- j (* k (/ z x)))))
                       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 * ((z * y3) - (x * y2)));
	double t_2 = y1 * ((i * (x * j)) - (a * (x * y2)));
	double tmp;
	if (y1 <= -4.3e+172) {
		tmp = t_1;
	} else if (y1 <= -1.36e+101) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else if (y1 <= -1.55e+32) {
		tmp = t_2;
	} else if (y1 <= -2.4e-137) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y1 <= -1.05e-271) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y1 <= 1.9e-165) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (y1 <= 2.9e-127) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y1 <= 2.65e+26) {
		tmp = t_2;
	} else if (y1 <= 4.5e+62) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (y1 <= 1e+224) {
		tmp = (x * y1) * (i * (j - (k * (z / x))));
	} 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 = a * (y1 * ((z * y3) - (x * y2)))
    t_2 = y1 * ((i * (x * j)) - (a * (x * y2)))
    if (y1 <= (-4.3d+172)) then
        tmp = t_1
    else if (y1 <= (-1.36d+101)) then
        tmp = i * (z * ((t * c) - (k * y1)))
    else if (y1 <= (-1.55d+32)) then
        tmp = t_2
    else if (y1 <= (-2.4d-137)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y1 <= (-1.05d-271)) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (y1 <= 1.9d-165) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (y1 <= 2.9d-127) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (y1 <= 2.65d+26) then
        tmp = t_2
    else if (y1 <= 4.5d+62) then
        tmp = x * (y0 * ((c * y2) - (b * j)))
    else if (y1 <= 1d+224) then
        tmp = (x * y1) * (i * (j - (k * (z / x))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y1 * ((z * y3) - (x * y2)));
	double t_2 = y1 * ((i * (x * j)) - (a * (x * y2)));
	double tmp;
	if (y1 <= -4.3e+172) {
		tmp = t_1;
	} else if (y1 <= -1.36e+101) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else if (y1 <= -1.55e+32) {
		tmp = t_2;
	} else if (y1 <= -2.4e-137) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y1 <= -1.05e-271) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y1 <= 1.9e-165) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (y1 <= 2.9e-127) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y1 <= 2.65e+26) {
		tmp = t_2;
	} else if (y1 <= 4.5e+62) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (y1 <= 1e+224) {
		tmp = (x * y1) * (i * (j - (k * (z / x))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y1 * ((z * y3) - (x * y2)))
	t_2 = y1 * ((i * (x * j)) - (a * (x * y2)))
	tmp = 0
	if y1 <= -4.3e+172:
		tmp = t_1
	elif y1 <= -1.36e+101:
		tmp = i * (z * ((t * c) - (k * y1)))
	elif y1 <= -1.55e+32:
		tmp = t_2
	elif y1 <= -2.4e-137:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y1 <= -1.05e-271:
		tmp = b * (a * ((x * y) - (z * t)))
	elif y1 <= 1.9e-165:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif y1 <= 2.9e-127:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif y1 <= 2.65e+26:
		tmp = t_2
	elif y1 <= 4.5e+62:
		tmp = x * (y0 * ((c * y2) - (b * j)))
	elif y1 <= 1e+224:
		tmp = (x * y1) * (i * (j - (k * (z / x))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))))
	t_2 = Float64(y1 * Float64(Float64(i * Float64(x * j)) - Float64(a * Float64(x * y2))))
	tmp = 0.0
	if (y1 <= -4.3e+172)
		tmp = t_1;
	elseif (y1 <= -1.36e+101)
		tmp = Float64(i * Float64(z * Float64(Float64(t * c) - Float64(k * y1))));
	elseif (y1 <= -1.55e+32)
		tmp = t_2;
	elseif (y1 <= -2.4e-137)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y1 <= -1.05e-271)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y1 <= 1.9e-165)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (y1 <= 2.9e-127)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (y1 <= 2.65e+26)
		tmp = t_2;
	elseif (y1 <= 4.5e+62)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (y1 <= 1e+224)
		tmp = Float64(Float64(x * y1) * Float64(i * Float64(j - Float64(k * Float64(z / x)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y1 * ((z * y3) - (x * y2)));
	t_2 = y1 * ((i * (x * j)) - (a * (x * y2)));
	tmp = 0.0;
	if (y1 <= -4.3e+172)
		tmp = t_1;
	elseif (y1 <= -1.36e+101)
		tmp = i * (z * ((t * c) - (k * y1)));
	elseif (y1 <= -1.55e+32)
		tmp = t_2;
	elseif (y1 <= -2.4e-137)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y1 <= -1.05e-271)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (y1 <= 1.9e-165)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (y1 <= 2.9e-127)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (y1 <= 2.65e+26)
		tmp = t_2;
	elseif (y1 <= 4.5e+62)
		tmp = x * (y0 * ((c * y2) - (b * j)));
	elseif (y1 <= 1e+224)
		tmp = (x * y1) * (i * (j - (k * (z / x))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y1 * N[(N[(i * N[(x * j), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -4.3e+172], t$95$1, If[LessEqual[y1, -1.36e+101], N[(i * N[(z * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.55e+32], t$95$2, If[LessEqual[y1, -2.4e-137], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.05e-271], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.9e-165], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.9e-127], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.65e+26], t$95$2, If[LessEqual[y1, 4.5e+62], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1e+224], N[(N[(x * y1), $MachinePrecision] * N[(i * N[(j - N[(k * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y1 < -4.3000000000000003e172 or 9.9999999999999997e223 < y1

   1. Initial program 30.4%

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

   3. Taylor expanded in a around inf 54.2%

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

      1. +-commutative 54.2%

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

      2. mul-1-neg 54.2%

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

      3. unsub-neg 54.2%

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

      4. *-commutative 54.2%

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

      5. *-commutative 54.2%

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

      6. *-commutative 54.2%

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

      7. mul-1-neg 54.2%

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

      8. *-commutative 54.2%

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

   5. Simplified 54.2%

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

   6. Taylor expanded in y1 around inf 67.5%

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

   if -4.3000000000000003e172 < y1 < -1.35999999999999998e101

   1. Initial program 30.0%

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

   3. Taylor expanded in z around -inf 30.1%

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

   4. Taylor expanded in i around -inf 60.9%

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

      1. associate-*r* 60.9%

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

      2. neg-mul-1 60.9%

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

   6. Simplified 60.9%

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

   if -1.35999999999999998e101 < y1 < -1.54999999999999997e32 or 2.9e-127 < y1 < 2.64999999999999984e26

   1. Initial program 28.7%

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

   3. Taylor expanded in y1 around -inf 58.1%

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

      1. associate-*r* 58.1%

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

      2. neg-mul-1 58.1%

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

      3. +-commutative 58.1%

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

      4. mul-1-neg 58.1%

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

      5. unsub-neg 58.1%

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

      6. *-commutative 58.1%

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

      7. *-commutative 58.1%

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

      8. *-commutative 58.1%

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

      9. *-commutative 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in y4 around 0 60.5%

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

   7. Taylor expanded in z around 0 58.2%

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

   if -1.54999999999999997e32 < y1 < -2.4e-137

   1. Initial program 31.1%

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

   3. Taylor expanded in x around inf 60.7%

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

   4. Taylor expanded in y around inf 64.9%

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

   if -2.4e-137 < y1 < -1.05e-271

   1. Initial program 45.1%

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

   3. Taylor expanded in b around inf 50.1%

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

   4. Taylor expanded in a around inf 45.8%

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

   if -1.05e-271 < y1 < 1.90000000000000009e-165

   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 b around inf 35.9%

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

   4. Taylor expanded in k around -inf 52.5%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 52.5%

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

      2. neg-mul-1 52.5%

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

   6. Simplified 52.5%

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

   if 1.90000000000000009e-165 < y1 < 2.9e-127

   1. Initial program 62.5%

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

   3. Taylor expanded in a around inf 75.0%

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

      1. +-commutative 75.0%

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

      2. mul-1-neg 75.0%

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

      3. unsub-neg 75.0%

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

      4. *-commutative 75.0%

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

      5. *-commutative 75.0%

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

      6. *-commutative 75.0%

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

      7. mul-1-neg 75.0%

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

      8. *-commutative 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in y5 around inf 75.1%

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

   if 2.64999999999999984e26 < y1 < 4.49999999999999999e62

   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 x around inf 34.1%

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

   4. Taylor expanded in y around 0 17.5%

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

   5. Taylor expanded in y0 around inf 50.9%

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

      1. *-commutative 50.9%

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

      2. *-commutative 50.9%

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

   7. Simplified 50.9%

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

   if 4.49999999999999999e62 < y1 < 9.9999999999999997e223

   1. Initial program 39.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. associate-*r* 58.9%

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

      2. neg-mul-1 58.9%

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

      3. +-commutative 58.9%

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

      4. mul-1-neg 58.9%

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

      5. unsub-neg 58.9%

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

      6. *-commutative 58.9%

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

      7. *-commutative 58.9%

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

      8. *-commutative 58.9%

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

      9. *-commutative 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in y4 around 0 59.0%

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

   7. Taylor expanded in x around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. mul-1-neg 61.4%

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

      3. unsub-neg 61.4%

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

      4. associate-/l* 61.4%

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

      5. *-commutative 61.4%

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

   9. Simplified 61.4%

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

   10. Taylor expanded in a around 0 56.8%

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

       1. associate-*r* 54.4%

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

       2. associate-/l* 59.1%

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

       3. *-commutative 59.1%

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

       4. associate-*r/ 54.5%

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

       5. distribute-lft-out-- 54.5%

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

       6. associate-*r/ 59.1%

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

       7. *-commutative 59.1%

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

       8. associate-/l* 59.1%

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

   12. Simplified 59.1%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -4.3 \cdot 10^{+172}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -1.36 \cdot 10^{+101}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -1.55 \cdot 10^{+32}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right) - a \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -2.4 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -1.05 \cdot 10^{-271}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 1.9 \cdot 10^{-165}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 2.9 \cdot 10^{-127}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 2.65 \cdot 10^{+26}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right) - a \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 4.5 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 10^{+224}:\\ \;\;\;\;\left(x \cdot y1\right) \cdot \left(i \cdot \left(j - k \cdot \frac{z}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 43.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{if}\;y2 \leq -2.9 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq 1.02 \cdot 10^{-304}:\\ \;\;\;\;y \cdot \left(\left(x \cdot \left(a \cdot b - c \cdot i\right) + k \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 3.9 \cdot 10^{-83}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 1.25 \cdot 10^{+28}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 3.1 \cdot 10^{+54}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y2
          (+
           (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
           (* t (- (* a y5) (* c y4)))))))
   (if (<= y2 -2.9e+63)
     t_1
     (if (<= y2 1.02e-304)
       (*
        y
        (+
         (+ (* x (- (* a b) (* c i))) (* k (- (* i y5) (* b y4))))
         (* y3 (- (* c y4) (* a y5)))))
       (if (<= y2 3.9e-83)
         (*
          j
          (+
           (+ (* t (- (* b y4) (* i y5))) (* y3 (- (* y0 y5) (* y1 y4))))
           (* x (- (* i y1) (* b y0)))))
         (if (<= y2 1.25e+28)
           (*
            b
            (+
             (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
             (* y0 (- (* z k) (* x j)))))
           (if (<= y2 3.1e+54)
             (* y1 (- (* i (- (* x j) (* z k))) (* a (- (* x y2) (* 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 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	double tmp;
	if (y2 <= -2.9e+63) {
		tmp = t_1;
	} else if (y2 <= 1.02e-304) {
		tmp = y * (((x * ((a * b) - (c * i))) + (k * ((i * y5) - (b * y4)))) + (y3 * ((c * y4) - (a * y5))));
	} else if (y2 <= 3.9e-83) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	} else if (y2 <= 1.25e+28) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y2 <= 3.1e+54) {
		tmp = y1 * ((i * ((x * j) - (z * k))) - (a * ((x * y2) - (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 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    if (y2 <= (-2.9d+63)) then
        tmp = t_1
    else if (y2 <= 1.02d-304) then
        tmp = y * (((x * ((a * b) - (c * i))) + (k * ((i * y5) - (b * y4)))) + (y3 * ((c * y4) - (a * y5))))
    else if (y2 <= 3.9d-83) then
        tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
    else if (y2 <= 1.25d+28) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    else if (y2 <= 3.1d+54) then
        tmp = y1 * ((i * ((x * j) - (z * k))) - (a * ((x * y2) - (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 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	double tmp;
	if (y2 <= -2.9e+63) {
		tmp = t_1;
	} else if (y2 <= 1.02e-304) {
		tmp = y * (((x * ((a * b) - (c * i))) + (k * ((i * y5) - (b * y4)))) + (y3 * ((c * y4) - (a * y5))));
	} else if (y2 <= 3.9e-83) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	} else if (y2 <= 1.25e+28) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y2 <= 3.1e+54) {
		tmp = y1 * ((i * ((x * j) - (z * k))) - (a * ((x * y2) - (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 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	tmp = 0
	if y2 <= -2.9e+63:
		tmp = t_1
	elif y2 <= 1.02e-304:
		tmp = y * (((x * ((a * b) - (c * i))) + (k * ((i * y5) - (b * y4)))) + (y3 * ((c * y4) - (a * y5))))
	elif y2 <= 3.9e-83:
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
	elif y2 <= 1.25e+28:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	elif y2 <= 3.1e+54:
		tmp = y1 * ((i * ((x * j) - (z * k))) - (a * ((x * y2) - (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(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))))
	tmp = 0.0
	if (y2 <= -2.9e+63)
		tmp = t_1;
	elseif (y2 <= 1.02e-304)
		tmp = Float64(y * Float64(Float64(Float64(x * Float64(Float64(a * b) - Float64(c * i))) + Float64(k * Float64(Float64(i * y5) - Float64(b * y4)))) + Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5)))));
	elseif (y2 <= 3.9e-83)
		tmp = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y2 <= 1.25e+28)
		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 (y2 <= 3.1e+54)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) - Float64(a * Float64(Float64(x * y2) - 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 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	tmp = 0.0;
	if (y2 <= -2.9e+63)
		tmp = t_1;
	elseif (y2 <= 1.02e-304)
		tmp = y * (((x * ((a * b) - (c * i))) + (k * ((i * y5) - (b * y4)))) + (y3 * ((c * y4) - (a * y5))));
	elseif (y2 <= 3.9e-83)
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	elseif (y2 <= 1.25e+28)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	elseif (y2 <= 3.1e+54)
		tmp = y1 * ((i * ((x * j) - (z * k))) - (a * ((x * y2) - (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[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -2.9e+63], t$95$1, If[LessEqual[y2, 1.02e-304], N[(y * N[(N[(N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.9e-83], N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.25e+28], 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[y2, 3.1e+54], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -2.8999999999999999e63 or 3.0999999999999999e54 < 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 y2 around inf 67.8%

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

   if -2.8999999999999999e63 < y2 < 1.01999999999999992e-304

   1. Initial program 38.5%

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

   3. Taylor expanded in y around inf 53.1%

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

      1. +-commutative 53.1%

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

      2. mul-1-neg 53.1%

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

      3. unsub-neg 53.1%

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

      4. *-commutative 53.1%

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

      5. *-commutative 53.1%

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

      6. mul-1-neg 53.1%

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

   5. Simplified 53.1%

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

   if 1.01999999999999992e-304 < y2 < 3.9e-83

   1. Initial program 36.8%

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

   3. Taylor expanded in j around inf 55.4%

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

      1. +-commutative 55.4%

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

      2. mul-1-neg 55.4%

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

      3. unsub-neg 55.4%

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

      4. *-commutative 55.4%

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

   5. Simplified 55.4%

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

   if 3.9e-83 < y2 < 1.24999999999999989e28

   1. Initial program 36.4%

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

   3. Taylor expanded in b around inf 65.5%

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

   if 1.24999999999999989e28 < y2 < 3.0999999999999999e54

   1. Initial program 28.6%

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

   3. Taylor expanded in y1 around -inf 57.1%

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

      1. associate-*r* 57.1%

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

      2. neg-mul-1 57.1%

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

      3. +-commutative 57.1%

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

      4. mul-1-neg 57.1%

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

      5. unsub-neg 57.1%

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

      6. *-commutative 57.1%

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

      7. *-commutative 57.1%

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

      8. *-commutative 57.1%

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

      9. *-commutative 57.1%

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

   5. Simplified 57.1%

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

   6. Taylor expanded in y4 around 0 71.6%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2.9 \cdot 10^{+63}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 1.02 \cdot 10^{-304}:\\ \;\;\;\;y \cdot \left(\left(x \cdot \left(a \cdot b - c \cdot i\right) + k \cdot \left(i \cdot y5 - b \cdot y4\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 3.9 \cdot 10^{-83}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 1.25 \cdot 10^{+28}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq 3.1 \cdot 10^{+54}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 37.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b - c \cdot i\\ t_2 := y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ t_3 := t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot t\_1\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{if}\;y1 \leq -3.3 \cdot 10^{+35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y1 \leq -1.9 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(y \cdot t\_1\right)\\ \mathbf{elif}\;y1 \leq -1.1 \cdot 10^{-216}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y1 \leq 2.1 \cdot 10^{-286}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 5.5 \cdot 10^{-229}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y1 \leq 7.5 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a b) (* c i)))
        (t_2 (* y1 (- (* i (- (* x j) (* z k))) (* a (- (* x y2) (* z y3))))))
        (t_3
         (*
          t
          (+
           (- (* j (- (* b y4) (* i y5))) (* z t_1))
           (* y2 (- (* a y5) (* c y4)))))))
   (if (<= y1 -3.3e+35)
     t_2
     (if (<= y1 -1.9e-137)
       (* x (* y t_1))
       (if (<= y1 -1.1e-216)
         t_3
         (if (<= y1 2.1e-286)
           (* x (+ (* y2 (- (* c y0) (* a y1))) (* j (- (* i y1) (* b y0)))))
           (if (<= y1 5.5e-229)
             t_3
             (if (<= y1 7.5e-140) (* b (* k (- (* z y0) (* y y4)))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * b) - (c * i);
	double t_2 = y1 * ((i * ((x * j) - (z * k))) - (a * ((x * y2) - (z * y3))));
	double t_3 = t * (((j * ((b * y4) - (i * y5))) - (z * t_1)) + (y2 * ((a * y5) - (c * y4))));
	double tmp;
	if (y1 <= -3.3e+35) {
		tmp = t_2;
	} else if (y1 <= -1.9e-137) {
		tmp = x * (y * t_1);
	} else if (y1 <= -1.1e-216) {
		tmp = t_3;
	} else if (y1 <= 2.1e-286) {
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	} else if (y1 <= 5.5e-229) {
		tmp = t_3;
	} else if (y1 <= 7.5e-140) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (a * b) - (c * i)
    t_2 = y1 * ((i * ((x * j) - (z * k))) - (a * ((x * y2) - (z * y3))))
    t_3 = t * (((j * ((b * y4) - (i * y5))) - (z * t_1)) + (y2 * ((a * y5) - (c * y4))))
    if (y1 <= (-3.3d+35)) then
        tmp = t_2
    else if (y1 <= (-1.9d-137)) then
        tmp = x * (y * t_1)
    else if (y1 <= (-1.1d-216)) then
        tmp = t_3
    else if (y1 <= 2.1d-286) then
        tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))))
    else if (y1 <= 5.5d-229) then
        tmp = t_3
    else if (y1 <= 7.5d-140) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * b) - (c * i);
	double t_2 = y1 * ((i * ((x * j) - (z * k))) - (a * ((x * y2) - (z * y3))));
	double t_3 = t * (((j * ((b * y4) - (i * y5))) - (z * t_1)) + (y2 * ((a * y5) - (c * y4))));
	double tmp;
	if (y1 <= -3.3e+35) {
		tmp = t_2;
	} else if (y1 <= -1.9e-137) {
		tmp = x * (y * t_1);
	} else if (y1 <= -1.1e-216) {
		tmp = t_3;
	} else if (y1 <= 2.1e-286) {
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	} else if (y1 <= 5.5e-229) {
		tmp = t_3;
	} else if (y1 <= 7.5e-140) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (a * b) - (c * i)
	t_2 = y1 * ((i * ((x * j) - (z * k))) - (a * ((x * y2) - (z * y3))))
	t_3 = t * (((j * ((b * y4) - (i * y5))) - (z * t_1)) + (y2 * ((a * y5) - (c * y4))))
	tmp = 0
	if y1 <= -3.3e+35:
		tmp = t_2
	elif y1 <= -1.9e-137:
		tmp = x * (y * t_1)
	elif y1 <= -1.1e-216:
		tmp = t_3
	elif y1 <= 2.1e-286:
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))))
	elif y1 <= 5.5e-229:
		tmp = t_3
	elif y1 <= 7.5e-140:
		tmp = b * (k * ((z * y0) - (y * y4)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(a * b) - Float64(c * i))
	t_2 = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) - Float64(a * Float64(Float64(x * y2) - Float64(z * y3)))))
	t_3 = Float64(t * Float64(Float64(Float64(j * Float64(Float64(b * y4) - Float64(i * y5))) - Float64(z * t_1)) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))))
	tmp = 0.0
	if (y1 <= -3.3e+35)
		tmp = t_2;
	elseif (y1 <= -1.9e-137)
		tmp = Float64(x * Float64(y * t_1));
	elseif (y1 <= -1.1e-216)
		tmp = t_3;
	elseif (y1 <= 2.1e-286)
		tmp = Float64(x * Float64(Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y1 <= 5.5e-229)
		tmp = t_3;
	elseif (y1 <= 7.5e-140)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (a * b) - (c * i);
	t_2 = y1 * ((i * ((x * j) - (z * k))) - (a * ((x * y2) - (z * y3))));
	t_3 = t * (((j * ((b * y4) - (i * y5))) - (z * t_1)) + (y2 * ((a * y5) - (c * y4))));
	tmp = 0.0;
	if (y1 <= -3.3e+35)
		tmp = t_2;
	elseif (y1 <= -1.9e-137)
		tmp = x * (y * t_1);
	elseif (y1 <= -1.1e-216)
		tmp = t_3;
	elseif (y1 <= 2.1e-286)
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	elseif (y1 <= 5.5e-229)
		tmp = t_3;
	elseif (y1 <= 7.5e-140)
		tmp = b * (k * ((z * y0) - (y * y4)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -3.3e+35], t$95$2, If[LessEqual[y1, -1.9e-137], N[(x * N[(y * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.1e-216], t$95$3, If[LessEqual[y1, 2.1e-286], N[(x * N[(N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 5.5e-229], t$95$3, If[LessEqual[y1, 7.5e-140], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y1 < -3.3000000000000002e35 or 7.4999999999999998e-140 < y1

   1. Initial program 33.4%

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

   3. Taylor expanded in y1 around -inf 56.2%

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

      1. associate-*r* 56.2%

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

      2. neg-mul-1 56.2%

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

      3. +-commutative 56.2%

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

      4. mul-1-neg 56.2%

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

      5. unsub-neg 56.2%

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

      6. *-commutative 56.2%

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

      7. *-commutative 56.2%

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

      8. *-commutative 56.2%

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

      9. *-commutative 56.2%

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

   5. Simplified 56.2%

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

   6. Taylor expanded in y4 around 0 61.1%

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

   if -3.3000000000000002e35 < y1 < -1.89999999999999999e-137

   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 x around inf 58.1%

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

   4. Taylor expanded in y around inf 62.2%

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

   if -1.89999999999999999e-137 < y1 < -1.09999999999999995e-216 or 2.09999999999999988e-286 < y1 < 5.5000000000000001e-229

   1. Initial program 49.1%

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

   3. Taylor expanded in t around inf 55.0%

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

      1. +-commutative 55.0%

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

      2. mul-1-neg 55.0%

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

      3. unsub-neg 55.0%

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

      4. *-commutative 55.0%

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

   5. Simplified 55.0%

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

   if -1.09999999999999995e-216 < y1 < 2.09999999999999988e-286

   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 x around inf 50.8%

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

   4. Taylor expanded in y around 0 56.2%

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

   if 5.5000000000000001e-229 < y1 < 7.4999999999999998e-140

   1. Initial program 40.0%

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

   3. Taylor expanded in 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 k around -inf 67.9%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 67.9%

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

      2. neg-mul-1 67.9%

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

   6. Simplified 67.9%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -3.3 \cdot 10^{+35}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq -1.9 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -1.1 \cdot 10^{-216}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 2.1 \cdot 10^{-286}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 5.5 \cdot 10^{-229}:\\ \;\;\;\;t \cdot \left(\left(j \cdot \left(b \cdot y4 - i \cdot y5\right) - z \cdot \left(a \cdot b - c \cdot i\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 7.5 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 32.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{if}\;y1 \leq -3.7 \cdot 10^{+172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -6.2 \cdot 10^{+101}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -6.6:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -3.8 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -3.1 \cdot 10^{-279}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 2.3 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 1.05 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 2.1 \cdot 10^{+223}:\\ \;\;\;\;\left(x \cdot y1\right) \cdot \left(i \cdot \left(j - k \cdot \frac{z}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y1 (- (* z y3) (* x y2))))))
   (if (<= y1 -3.7e+172)
     t_1
     (if (<= y1 -6.2e+101)
       (* i (* z (- (* t c) (* k y1))))
       (if (<= y1 -6.6)
         (* x (* y1 (- (* i j) (* a y2))))
         (if (<= y1 -3.8e-137)
           (* x (* y (- (* a b) (* c i))))
           (if (<= y1 -3.1e-279)
             (* b (* a (- (* x y) (* z t))))
             (if (<= y1 2.3e-140)
               (* b (* k (- (* z y0) (* y y4))))
               (if (<= y1 1.05e+55)
                 (* x (* y0 (- (* c y2) (* b j))))
                 (if (<= y1 2.1e+223)
                   (* (* x y1) (* i (- j (* k (/ z x)))))
                   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 * ((z * y3) - (x * y2)));
	double tmp;
	if (y1 <= -3.7e+172) {
		tmp = t_1;
	} else if (y1 <= -6.2e+101) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else if (y1 <= -6.6) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else if (y1 <= -3.8e-137) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y1 <= -3.1e-279) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y1 <= 2.3e-140) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (y1 <= 1.05e+55) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (y1 <= 2.1e+223) {
		tmp = (x * y1) * (i * (j - (k * (z / x))));
	} 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 = a * (y1 * ((z * y3) - (x * y2)))
    if (y1 <= (-3.7d+172)) then
        tmp = t_1
    else if (y1 <= (-6.2d+101)) then
        tmp = i * (z * ((t * c) - (k * y1)))
    else if (y1 <= (-6.6d0)) then
        tmp = x * (y1 * ((i * j) - (a * y2)))
    else if (y1 <= (-3.8d-137)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y1 <= (-3.1d-279)) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (y1 <= 2.3d-140) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (y1 <= 1.05d+55) then
        tmp = x * (y0 * ((c * y2) - (b * j)))
    else if (y1 <= 2.1d+223) then
        tmp = (x * y1) * (i * (j - (k * (z / x))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y1 * ((z * y3) - (x * y2)));
	double tmp;
	if (y1 <= -3.7e+172) {
		tmp = t_1;
	} else if (y1 <= -6.2e+101) {
		tmp = i * (z * ((t * c) - (k * y1)));
	} else if (y1 <= -6.6) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else if (y1 <= -3.8e-137) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y1 <= -3.1e-279) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y1 <= 2.3e-140) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (y1 <= 1.05e+55) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (y1 <= 2.1e+223) {
		tmp = (x * y1) * (i * (j - (k * (z / x))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y1 * ((z * y3) - (x * y2)))
	tmp = 0
	if y1 <= -3.7e+172:
		tmp = t_1
	elif y1 <= -6.2e+101:
		tmp = i * (z * ((t * c) - (k * y1)))
	elif y1 <= -6.6:
		tmp = x * (y1 * ((i * j) - (a * y2)))
	elif y1 <= -3.8e-137:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y1 <= -3.1e-279:
		tmp = b * (a * ((x * y) - (z * t)))
	elif y1 <= 2.3e-140:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif y1 <= 1.05e+55:
		tmp = x * (y0 * ((c * y2) - (b * j)))
	elif y1 <= 2.1e+223:
		tmp = (x * y1) * (i * (j - (k * (z / x))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))))
	tmp = 0.0
	if (y1 <= -3.7e+172)
		tmp = t_1;
	elseif (y1 <= -6.2e+101)
		tmp = Float64(i * Float64(z * Float64(Float64(t * c) - Float64(k * y1))));
	elseif (y1 <= -6.6)
		tmp = Float64(x * Float64(y1 * Float64(Float64(i * j) - Float64(a * y2))));
	elseif (y1 <= -3.8e-137)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y1 <= -3.1e-279)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y1 <= 2.3e-140)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (y1 <= 1.05e+55)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (y1 <= 2.1e+223)
		tmp = Float64(Float64(x * y1) * Float64(i * Float64(j - Float64(k * Float64(z / x)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y1 * ((z * y3) - (x * y2)));
	tmp = 0.0;
	if (y1 <= -3.7e+172)
		tmp = t_1;
	elseif (y1 <= -6.2e+101)
		tmp = i * (z * ((t * c) - (k * y1)));
	elseif (y1 <= -6.6)
		tmp = x * (y1 * ((i * j) - (a * y2)));
	elseif (y1 <= -3.8e-137)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y1 <= -3.1e-279)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (y1 <= 2.3e-140)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (y1 <= 1.05e+55)
		tmp = x * (y0 * ((c * y2) - (b * j)));
	elseif (y1 <= 2.1e+223)
		tmp = (x * y1) * (i * (j - (k * (z / x))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -3.7e+172], t$95$1, If[LessEqual[y1, -6.2e+101], N[(i * N[(z * N[(N[(t * c), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -6.6], N[(x * N[(y1 * N[(N[(i * j), $MachinePrecision] - N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3.8e-137], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3.1e-279], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.3e-140], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.05e+55], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.1e+223], N[(N[(x * y1), $MachinePrecision] * N[(i * N[(j - N[(k * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y1 < -3.69999999999999972e172 or 2.09999999999999991e223 < y1

   1. Initial program 30.4%

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

   3. Taylor expanded in a around inf 54.2%

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

      1. +-commutative 54.2%

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

      2. mul-1-neg 54.2%

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

      3. unsub-neg 54.2%

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

      4. *-commutative 54.2%

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

      5. *-commutative 54.2%

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

      6. *-commutative 54.2%

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

      7. mul-1-neg 54.2%

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

      8. *-commutative 54.2%

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

   5. Simplified 54.2%

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

   6. Taylor expanded in y1 around inf 67.5%

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

   if -3.69999999999999972e172 < y1 < -6.19999999999999998e101

   1. Initial program 30.0%

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

   3. Taylor expanded in z around -inf 30.1%

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

   4. Taylor expanded in i around -inf 60.9%

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

      1. associate-*r* 60.9%

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

      2. neg-mul-1 60.9%

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

   6. Simplified 60.9%

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

   if -6.19999999999999998e101 < y1 < -6.5999999999999996

   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 x around inf 45.4%

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

   4. Taylor expanded in y1 around -inf 51.7%

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

      1. associate-*r* 51.7%

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

      2. neg-mul-1 51.7%

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

   6. Simplified 51.7%

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

   if -6.5999999999999996 < y1 < -3.79999999999999999e-137

   1. Initial program 30.8%

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

   3. Taylor expanded in x around inf 62.2%

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

   4. Taylor expanded in y around inf 69.6%

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

   if -3.79999999999999999e-137 < y1 < -3.0999999999999999e-279

   1. Initial program 45.1%

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

   3. Taylor expanded in b around inf 50.1%

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

   4. Taylor expanded in a around inf 45.8%

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

   if -3.0999999999999999e-279 < y1 < 2.3000000000000001e-140

   1. Initial program 43.0%

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

   3. Taylor expanded in b around inf 34.9%

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

   4. Taylor expanded in k around -inf 49.6%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 49.6%

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

      2. neg-mul-1 49.6%

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

   6. Simplified 49.6%

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

   if 2.3000000000000001e-140 < y1 < 1.05e55

   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 x around inf 53.4%

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

   4. Taylor expanded in y around 0 48.3%

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

   5. Taylor expanded in y0 around inf 48.1%

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

      1. *-commutative 48.1%

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

      2. *-commutative 48.1%

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

   7. Simplified 48.1%

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

   if 1.05e55 < y1 < 2.09999999999999991e223

   1. Initial program 39.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. 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. associate-*r* 58.9%

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

      2. neg-mul-1 58.9%

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

      3. +-commutative 58.9%

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

      4. mul-1-neg 58.9%

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

      5. unsub-neg 58.9%

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

      6. *-commutative 58.9%

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

      7. *-commutative 58.9%

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

      8. *-commutative 58.9%

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

      9. *-commutative 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in y4 around 0 59.0%

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

   7. Taylor expanded in x around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. mul-1-neg 61.4%

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

      3. unsub-neg 61.4%

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

      4. associate-/l* 61.4%

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

      5. *-commutative 61.4%

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

   9. Simplified 61.4%

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

   10. Taylor expanded in a around 0 56.8%

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

       1. associate-*r* 54.4%

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

       2. associate-/l* 59.1%

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

       3. *-commutative 59.1%

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

       4. associate-*r/ 54.5%

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

       5. distribute-lft-out-- 54.5%

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

       6. associate-*r/ 59.1%

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

       7. *-commutative 59.1%

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

       8. associate-/l* 59.1%

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

   12. Simplified 59.1%

       \[\leadsto \color{blue}{\left(x \cdot y1\right) \cdot \left(i \cdot \left(j - k \cdot \frac{z}{x}\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -3.7 \cdot 10^{+172}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -6.2 \cdot 10^{+101}:\\ \;\;\;\;i \cdot \left(z \cdot \left(t \cdot c - k \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -6.6:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -3.8 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -3.1 \cdot 10^{-279}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 2.3 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 1.05 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 2.1 \cdot 10^{+223}:\\ \;\;\;\;\left(x \cdot y1\right) \cdot \left(i \cdot \left(j - k \cdot \frac{z}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 32.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y1\right) \cdot \left(i \cdot \left(j - k \cdot \frac{z}{x}\right)\right)\\ t_2 := a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{if}\;y1 \leq -2.1 \cdot 10^{+190}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y1 \leq -4.2 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -2.8:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -6.8 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -1.35 \cdot 10^{-270}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 5.8 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 10^{+52}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 1.8 \cdot 10^{+224}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* x y1) (* i (- j (* k (/ z x))))))
        (t_2 (* a (* y1 (- (* z y3) (* x y2))))))
   (if (<= y1 -2.1e+190)
     t_2
     (if (<= y1 -4.2e+97)
       t_1
       (if (<= y1 -2.8)
         (* x (* y1 (- (* i j) (* a y2))))
         (if (<= y1 -6.8e-137)
           (* x (* y (- (* a b) (* c i))))
           (if (<= y1 -1.35e-270)
             (* b (* a (- (* x y) (* z t))))
             (if (<= y1 5.8e-140)
               (* b (* k (- (* z y0) (* y y4))))
               (if (<= y1 1e+52)
                 (* x (* y0 (- (* c y2) (* b j))))
                 (if (<= y1 1.8e+224) t_1 t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y1) * (i * (j - (k * (z / x))));
	double t_2 = a * (y1 * ((z * y3) - (x * y2)));
	double tmp;
	if (y1 <= -2.1e+190) {
		tmp = t_2;
	} else if (y1 <= -4.2e+97) {
		tmp = t_1;
	} else if (y1 <= -2.8) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else if (y1 <= -6.8e-137) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y1 <= -1.35e-270) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y1 <= 5.8e-140) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (y1 <= 1e+52) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (y1 <= 1.8e+224) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * y1) * (i * (j - (k * (z / x))))
    t_2 = a * (y1 * ((z * y3) - (x * y2)))
    if (y1 <= (-2.1d+190)) then
        tmp = t_2
    else if (y1 <= (-4.2d+97)) then
        tmp = t_1
    else if (y1 <= (-2.8d0)) then
        tmp = x * (y1 * ((i * j) - (a * y2)))
    else if (y1 <= (-6.8d-137)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y1 <= (-1.35d-270)) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (y1 <= 5.8d-140) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (y1 <= 1d+52) then
        tmp = x * (y0 * ((c * y2) - (b * j)))
    else if (y1 <= 1.8d+224) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y1) * (i * (j - (k * (z / x))));
	double t_2 = a * (y1 * ((z * y3) - (x * y2)));
	double tmp;
	if (y1 <= -2.1e+190) {
		tmp = t_2;
	} else if (y1 <= -4.2e+97) {
		tmp = t_1;
	} else if (y1 <= -2.8) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else if (y1 <= -6.8e-137) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y1 <= -1.35e-270) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y1 <= 5.8e-140) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (y1 <= 1e+52) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (y1 <= 1.8e+224) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (x * y1) * (i * (j - (k * (z / x))))
	t_2 = a * (y1 * ((z * y3) - (x * y2)))
	tmp = 0
	if y1 <= -2.1e+190:
		tmp = t_2
	elif y1 <= -4.2e+97:
		tmp = t_1
	elif y1 <= -2.8:
		tmp = x * (y1 * ((i * j) - (a * y2)))
	elif y1 <= -6.8e-137:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y1 <= -1.35e-270:
		tmp = b * (a * ((x * y) - (z * t)))
	elif y1 <= 5.8e-140:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif y1 <= 1e+52:
		tmp = x * (y0 * ((c * y2) - (b * j)))
	elif y1 <= 1.8e+224:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(x * y1) * Float64(i * Float64(j - Float64(k * Float64(z / x)))))
	t_2 = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))))
	tmp = 0.0
	if (y1 <= -2.1e+190)
		tmp = t_2;
	elseif (y1 <= -4.2e+97)
		tmp = t_1;
	elseif (y1 <= -2.8)
		tmp = Float64(x * Float64(y1 * Float64(Float64(i * j) - Float64(a * y2))));
	elseif (y1 <= -6.8e-137)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y1 <= -1.35e-270)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y1 <= 5.8e-140)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (y1 <= 1e+52)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (y1 <= 1.8e+224)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (x * y1) * (i * (j - (k * (z / x))));
	t_2 = a * (y1 * ((z * y3) - (x * y2)));
	tmp = 0.0;
	if (y1 <= -2.1e+190)
		tmp = t_2;
	elseif (y1 <= -4.2e+97)
		tmp = t_1;
	elseif (y1 <= -2.8)
		tmp = x * (y1 * ((i * j) - (a * y2)));
	elseif (y1 <= -6.8e-137)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y1 <= -1.35e-270)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (y1 <= 5.8e-140)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (y1 <= 1e+52)
		tmp = x * (y0 * ((c * y2) - (b * j)));
	elseif (y1 <= 1.8e+224)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(x * y1), $MachinePrecision] * N[(i * N[(j - N[(k * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -2.1e+190], t$95$2, If[LessEqual[y1, -4.2e+97], t$95$1, If[LessEqual[y1, -2.8], N[(x * N[(y1 * N[(N[(i * j), $MachinePrecision] - N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -6.8e-137], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.35e-270], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 5.8e-140], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1e+52], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.8e+224], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y1 < -2.1000000000000001e190 or 1.8e224 < y1

   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 a around inf 54.6%

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

      1. +-commutative 54.6%

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

      2. mul-1-neg 54.6%

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

      3. unsub-neg 54.6%

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

      4. *-commutative 54.6%

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

      5. *-commutative 54.6%

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

      6. *-commutative 54.6%

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

      7. mul-1-neg 54.6%

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

      8. *-commutative 54.6%

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

   5. Simplified 54.6%

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

   6. Taylor expanded in y1 around inf 66.7%

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

   if -2.1000000000000001e190 < y1 < -4.20000000000000023e97 or 9.9999999999999999e51 < y1 < 1.8e224

   1. Initial program 37.6%

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

   3. Taylor expanded in y1 around -inf 57.4%

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

      1. associate-*r* 57.4%

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

      2. neg-mul-1 57.4%

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

      3. +-commutative 57.4%

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

      4. mul-1-neg 57.4%

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

      5. unsub-neg 57.4%

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

      6. *-commutative 57.4%

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

      7. *-commutative 57.4%

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

      8. *-commutative 57.4%

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

      9. *-commutative 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in y4 around 0 62.8%

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

   7. Taylor expanded in x around inf 62.8%

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

      1. +-commutative 62.8%

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

      2. mul-1-neg 62.8%

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

      3. unsub-neg 62.8%

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

      4. associate-/l* 62.8%

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

      5. *-commutative 62.8%

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

   9. Simplified 62.8%

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

   10. Taylor expanded in a around 0 59.5%

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

       1. associate-*r* 56.1%

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

       2. associate-/l* 59.5%

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

       3. *-commutative 59.5%

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

       4. associate-*r/ 56.1%

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

       5. distribute-lft-out-- 57.9%

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

       6. associate-*r/ 61.3%

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

       7. *-commutative 61.3%

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

       8. associate-/l* 61.3%

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

   12. Simplified 61.3%

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

   if -4.20000000000000023e97 < y1 < -2.7999999999999998

   1. Initial program 31.6%

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

   3. Taylor expanded in x around inf 42.5%

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

   4. Taylor expanded in y1 around -inf 49.2%

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

      1. associate-*r* 49.2%

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

      2. neg-mul-1 49.2%

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

   6. Simplified 49.2%

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

   if -2.7999999999999998 < y1 < -6.80000000000000028e-137

   1. Initial program 30.8%

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

   3. Taylor expanded in x around inf 62.2%

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

   4. Taylor expanded in y around inf 69.6%

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

   if -6.80000000000000028e-137 < y1 < -1.35000000000000004e-270

   1. Initial program 45.1%

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

   3. Taylor expanded in b around inf 50.1%

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

   4. Taylor expanded in a around inf 45.8%

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

   if -1.35000000000000004e-270 < y1 < 5.79999999999999995e-140

   1. Initial program 43.0%

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

   3. Taylor expanded in b around inf 34.9%

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

   4. Taylor expanded in k around -inf 49.6%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 49.6%

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

      2. neg-mul-1 49.6%

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

   6. Simplified 49.6%

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

   if 5.79999999999999995e-140 < y1 < 9.9999999999999999e51

   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 x around inf 53.4%

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

   4. Taylor expanded in y around 0 48.3%

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

   5. Taylor expanded in y0 around inf 48.1%

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

      1. *-commutative 48.1%

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

      2. *-commutative 48.1%

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

   7. Simplified 48.1%

      \[\leadsto x \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot c - j \cdot b\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -2.1 \cdot 10^{+190}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -4.2 \cdot 10^{+97}:\\ \;\;\;\;\left(x \cdot y1\right) \cdot \left(i \cdot \left(j - k \cdot \frac{z}{x}\right)\right)\\ \mathbf{elif}\;y1 \leq -2.8:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -6.8 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -1.35 \cdot 10^{-270}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 5.8 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 10^{+52}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 1.8 \cdot 10^{+224}:\\ \;\;\;\;\left(x \cdot y1\right) \cdot \left(i \cdot \left(j - k \cdot \frac{z}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 32.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ t_2 := a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{if}\;y1 \leq -4.2 \cdot 10^{+194}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y1 \leq -9 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -185:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -5.2 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -9.5 \cdot 10^{-274}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 3 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 6.5 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 6 \cdot 10^{+219}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* y1 (- (* x j) (* z k)))))
        (t_2 (* a (* y1 (- (* z y3) (* x y2))))))
   (if (<= y1 -4.2e+194)
     t_2
     (if (<= y1 -9e+98)
       t_1
       (if (<= y1 -185.0)
         (* x (* y1 (- (* i j) (* a y2))))
         (if (<= y1 -5.2e-137)
           (* x (* y (- (* a b) (* c i))))
           (if (<= y1 -9.5e-274)
             (* b (* a (- (* x y) (* z t))))
             (if (<= y1 3e-140)
               (* b (* k (- (* z y0) (* y y4))))
               (if (<= y1 6.5e+64)
                 (* x (* y0 (- (* c y2) (* b j))))
                 (if (<= y1 6e+219) t_1 t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y1 * ((x * j) - (z * k)));
	double t_2 = a * (y1 * ((z * y3) - (x * y2)));
	double tmp;
	if (y1 <= -4.2e+194) {
		tmp = t_2;
	} else if (y1 <= -9e+98) {
		tmp = t_1;
	} else if (y1 <= -185.0) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else if (y1 <= -5.2e-137) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y1 <= -9.5e-274) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y1 <= 3e-140) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (y1 <= 6.5e+64) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (y1 <= 6e+219) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * (y1 * ((x * j) - (z * k)))
    t_2 = a * (y1 * ((z * y3) - (x * y2)))
    if (y1 <= (-4.2d+194)) then
        tmp = t_2
    else if (y1 <= (-9d+98)) then
        tmp = t_1
    else if (y1 <= (-185.0d0)) then
        tmp = x * (y1 * ((i * j) - (a * y2)))
    else if (y1 <= (-5.2d-137)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y1 <= (-9.5d-274)) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (y1 <= 3d-140) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (y1 <= 6.5d+64) then
        tmp = x * (y0 * ((c * y2) - (b * j)))
    else if (y1 <= 6d+219) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y1 * ((x * j) - (z * k)));
	double t_2 = a * (y1 * ((z * y3) - (x * y2)));
	double tmp;
	if (y1 <= -4.2e+194) {
		tmp = t_2;
	} else if (y1 <= -9e+98) {
		tmp = t_1;
	} else if (y1 <= -185.0) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else if (y1 <= -5.2e-137) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y1 <= -9.5e-274) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y1 <= 3e-140) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (y1 <= 6.5e+64) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (y1 <= 6e+219) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (y1 * ((x * j) - (z * k)))
	t_2 = a * (y1 * ((z * y3) - (x * y2)))
	tmp = 0
	if y1 <= -4.2e+194:
		tmp = t_2
	elif y1 <= -9e+98:
		tmp = t_1
	elif y1 <= -185.0:
		tmp = x * (y1 * ((i * j) - (a * y2)))
	elif y1 <= -5.2e-137:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y1 <= -9.5e-274:
		tmp = b * (a * ((x * y) - (z * t)))
	elif y1 <= 3e-140:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif y1 <= 6.5e+64:
		tmp = x * (y0 * ((c * y2) - (b * j)))
	elif y1 <= 6e+219:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))))
	t_2 = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))))
	tmp = 0.0
	if (y1 <= -4.2e+194)
		tmp = t_2;
	elseif (y1 <= -9e+98)
		tmp = t_1;
	elseif (y1 <= -185.0)
		tmp = Float64(x * Float64(y1 * Float64(Float64(i * j) - Float64(a * y2))));
	elseif (y1 <= -5.2e-137)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y1 <= -9.5e-274)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y1 <= 3e-140)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (y1 <= 6.5e+64)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (y1 <= 6e+219)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (y1 * ((x * j) - (z * k)));
	t_2 = a * (y1 * ((z * y3) - (x * y2)));
	tmp = 0.0;
	if (y1 <= -4.2e+194)
		tmp = t_2;
	elseif (y1 <= -9e+98)
		tmp = t_1;
	elseif (y1 <= -185.0)
		tmp = x * (y1 * ((i * j) - (a * y2)));
	elseif (y1 <= -5.2e-137)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y1 <= -9.5e-274)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (y1 <= 3e-140)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (y1 <= 6.5e+64)
		tmp = x * (y0 * ((c * y2) - (b * j)));
	elseif (y1 <= 6e+219)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -4.2e+194], t$95$2, If[LessEqual[y1, -9e+98], t$95$1, If[LessEqual[y1, -185.0], N[(x * N[(y1 * N[(N[(i * j), $MachinePrecision] - N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -5.2e-137], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -9.5e-274], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3e-140], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 6.5e+64], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 6e+219], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y1 < -4.20000000000000032e194 or 5.9999999999999995e219 < y1

   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 a around inf 54.6%

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

      1. +-commutative 54.6%

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

      2. mul-1-neg 54.6%

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

      3. unsub-neg 54.6%

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

      4. *-commutative 54.6%

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

      5. *-commutative 54.6%

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

      6. *-commutative 54.6%

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

      7. mul-1-neg 54.6%

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

      8. *-commutative 54.6%

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

   5. Simplified 54.6%

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

   6. Taylor expanded in y1 around inf 66.7%

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

   if -4.20000000000000032e194 < y1 < -9.0000000000000004e98 or 6.50000000000000007e64 < y1 < 5.9999999999999995e219

   1. Initial program 37.6%

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

   3. Taylor expanded in y1 around -inf 57.4%

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

      1. associate-*r* 57.4%

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

      2. neg-mul-1 57.4%

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

      3. +-commutative 57.4%

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

      4. mul-1-neg 57.4%

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

      5. unsub-neg 57.4%

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

      6. *-commutative 57.4%

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

      7. *-commutative 57.4%

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

      8. *-commutative 57.4%

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

      9. *-commutative 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in i around -inf 59.6%

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

   if -9.0000000000000004e98 < y1 < -185

   1. Initial program 31.6%

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

   3. Taylor expanded in x around inf 42.5%

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

   4. Taylor expanded in y1 around -inf 49.2%

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

      1. associate-*r* 49.2%

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

      2. neg-mul-1 49.2%

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

   6. Simplified 49.2%

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

   if -185 < y1 < -5.1999999999999999e-137

   1. Initial program 30.8%

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

   3. Taylor expanded in x around inf 62.2%

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

   4. Taylor expanded in y around inf 69.6%

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

   if -5.1999999999999999e-137 < y1 < -9.5000000000000009e-274

   1. Initial program 45.1%

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

   3. Taylor expanded in b around inf 50.1%

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

   4. Taylor expanded in a around inf 45.8%

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

   if -9.5000000000000009e-274 < y1 < 3.00000000000000018e-140

   1. Initial program 43.0%

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

   3. Taylor expanded in b around inf 34.9%

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

   4. Taylor expanded in k around -inf 49.6%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 49.6%

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

      2. neg-mul-1 49.6%

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

   6. Simplified 49.6%

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

   if 3.00000000000000018e-140 < y1 < 6.50000000000000007e64

   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 x around inf 53.4%

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

   4. Taylor expanded in y around 0 48.3%

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

   5. Taylor expanded in y0 around inf 48.1%

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

      1. *-commutative 48.1%

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

      2. *-commutative 48.1%

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

   7. Simplified 48.1%

      \[\leadsto x \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot c - j \cdot b\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -4.2 \cdot 10^{+194}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -9 \cdot 10^{+98}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y1 \leq -185:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -5.2 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -9.5 \cdot 10^{-274}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 3 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 6.5 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 6 \cdot 10^{+219}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 32.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ t_2 := a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{if}\;y1 \leq -2.7 \cdot 10^{+188}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y1 \leq -5.5 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -2.5 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -1.2 \cdot 10^{-190}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 1.55 \cdot 10^{-164}:\\ \;\;\;\;\left(b \cdot y0\right) \cdot \left(z \cdot k - x \cdot j\right)\\ \mathbf{elif}\;y1 \leq 4.8 \cdot 10^{-140}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 1.4 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 1.75 \cdot 10^{+225}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* y1 (- (* x j) (* z k)))))
        (t_2 (* a (* y1 (- (* z y3) (* x y2))))))
   (if (<= y1 -2.7e+188)
     t_2
     (if (<= y1 -5.5e+42)
       t_1
       (if (<= y1 -2.5e-137)
         (* x (* y (- (* a b) (* c i))))
         (if (<= y1 -1.2e-190)
           (* b (* a (- (* x y) (* z t))))
           (if (<= y1 1.55e-164)
             (* (* b y0) (- (* z k) (* x j)))
             (if (<= y1 4.8e-140)
               (* a (* y5 (- (* t y2) (* y y3))))
               (if (<= y1 1.4e+49)
                 (* x (* y0 (- (* c y2) (* b j))))
                 (if (<= y1 1.75e+225) t_1 t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y1 * ((x * j) - (z * k)));
	double t_2 = a * (y1 * ((z * y3) - (x * y2)));
	double tmp;
	if (y1 <= -2.7e+188) {
		tmp = t_2;
	} else if (y1 <= -5.5e+42) {
		tmp = t_1;
	} else if (y1 <= -2.5e-137) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y1 <= -1.2e-190) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y1 <= 1.55e-164) {
		tmp = (b * y0) * ((z * k) - (x * j));
	} else if (y1 <= 4.8e-140) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y1 <= 1.4e+49) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (y1 <= 1.75e+225) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * (y1 * ((x * j) - (z * k)))
    t_2 = a * (y1 * ((z * y3) - (x * y2)))
    if (y1 <= (-2.7d+188)) then
        tmp = t_2
    else if (y1 <= (-5.5d+42)) then
        tmp = t_1
    else if (y1 <= (-2.5d-137)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y1 <= (-1.2d-190)) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (y1 <= 1.55d-164) then
        tmp = (b * y0) * ((z * k) - (x * j))
    else if (y1 <= 4.8d-140) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (y1 <= 1.4d+49) then
        tmp = x * (y0 * ((c * y2) - (b * j)))
    else if (y1 <= 1.75d+225) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y1 * ((x * j) - (z * k)));
	double t_2 = a * (y1 * ((z * y3) - (x * y2)));
	double tmp;
	if (y1 <= -2.7e+188) {
		tmp = t_2;
	} else if (y1 <= -5.5e+42) {
		tmp = t_1;
	} else if (y1 <= -2.5e-137) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y1 <= -1.2e-190) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y1 <= 1.55e-164) {
		tmp = (b * y0) * ((z * k) - (x * j));
	} else if (y1 <= 4.8e-140) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y1 <= 1.4e+49) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (y1 <= 1.75e+225) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (y1 * ((x * j) - (z * k)))
	t_2 = a * (y1 * ((z * y3) - (x * y2)))
	tmp = 0
	if y1 <= -2.7e+188:
		tmp = t_2
	elif y1 <= -5.5e+42:
		tmp = t_1
	elif y1 <= -2.5e-137:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y1 <= -1.2e-190:
		tmp = b * (a * ((x * y) - (z * t)))
	elif y1 <= 1.55e-164:
		tmp = (b * y0) * ((z * k) - (x * j))
	elif y1 <= 4.8e-140:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif y1 <= 1.4e+49:
		tmp = x * (y0 * ((c * y2) - (b * j)))
	elif y1 <= 1.75e+225:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))))
	t_2 = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))))
	tmp = 0.0
	if (y1 <= -2.7e+188)
		tmp = t_2;
	elseif (y1 <= -5.5e+42)
		tmp = t_1;
	elseif (y1 <= -2.5e-137)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y1 <= -1.2e-190)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y1 <= 1.55e-164)
		tmp = Float64(Float64(b * y0) * Float64(Float64(z * k) - Float64(x * j)));
	elseif (y1 <= 4.8e-140)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (y1 <= 1.4e+49)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (y1 <= 1.75e+225)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (y1 * ((x * j) - (z * k)));
	t_2 = a * (y1 * ((z * y3) - (x * y2)));
	tmp = 0.0;
	if (y1 <= -2.7e+188)
		tmp = t_2;
	elseif (y1 <= -5.5e+42)
		tmp = t_1;
	elseif (y1 <= -2.5e-137)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y1 <= -1.2e-190)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (y1 <= 1.55e-164)
		tmp = (b * y0) * ((z * k) - (x * j));
	elseif (y1 <= 4.8e-140)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (y1 <= 1.4e+49)
		tmp = x * (y0 * ((c * y2) - (b * j)));
	elseif (y1 <= 1.75e+225)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -2.7e+188], t$95$2, If[LessEqual[y1, -5.5e+42], t$95$1, If[LessEqual[y1, -2.5e-137], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.2e-190], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.55e-164], N[(N[(b * y0), $MachinePrecision] * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 4.8e-140], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.4e+49], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.75e+225], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y1 < -2.7e188 or 1.7500000000000002e225 < y1

   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 a around inf 54.6%

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

      1. +-commutative 54.6%

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

      2. mul-1-neg 54.6%

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

      3. unsub-neg 54.6%

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

      4. *-commutative 54.6%

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

      5. *-commutative 54.6%

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

      6. *-commutative 54.6%

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

      7. mul-1-neg 54.6%

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

      8. *-commutative 54.6%

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

   5. Simplified 54.6%

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

   6. Taylor expanded in y1 around inf 66.7%

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

   if -2.7e188 < y1 < -5.50000000000000001e42 or 1.3999999999999999e49 < y1 < 1.7500000000000002e225

   1. Initial program 36.4%

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

   3. Taylor expanded in y1 around -inf 59.3%

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

      1. associate-*r* 59.3%

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

      2. neg-mul-1 59.3%

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

      3. +-commutative 59.3%

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

      4. mul-1-neg 59.3%

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

      5. unsub-neg 59.3%

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

      6. *-commutative 59.3%

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

      7. *-commutative 59.3%

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

      8. *-commutative 59.3%

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

      9. *-commutative 59.3%

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

   5. Simplified 59.3%

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

   6. Taylor expanded in i around -inf 56.9%

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

   if -5.50000000000000001e42 < y1 < -2.5e-137

   1. Initial program 31.3%

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

   3. Taylor expanded in x around inf 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 63.0%

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

   if -2.5e-137 < y1 < -1.2e-190

   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 b around inf 57.9%

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

   4. Taylor expanded in a around inf 57.7%

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

   if -1.2e-190 < y1 < 1.55e-164

   1. Initial program 39.2%

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

   3. Taylor expanded in b around inf 37.6%

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

   4. Taylor expanded in y0 around inf 42.5%

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

      1. associate-*r* 40.2%

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

   6. Simplified 40.2%

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

   if 1.55e-164 < y1 < 4.79999999999999973e-140

   1. Initial program 75.0%

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

   3. Taylor expanded in a around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

      5. *-commutative 100.0%

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

      6. *-commutative 100.0%

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

      7. mul-1-neg 100.0%

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

      8. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y5 around inf 100.0%

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

   if 4.79999999999999973e-140 < y1 < 1.3999999999999999e49

   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 x around inf 53.4%

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

   4. Taylor expanded in y around 0 48.3%

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

   5. Taylor expanded in y0 around inf 48.1%

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

      1. *-commutative 48.1%

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

      2. *-commutative 48.1%

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

   7. Simplified 48.1%

      \[\leadsto x \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot c - j \cdot b\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -2.7 \cdot 10^{+188}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -5.5 \cdot 10^{+42}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y1 \leq -2.5 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -1.2 \cdot 10^{-190}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 1.55 \cdot 10^{-164}:\\ \;\;\;\;\left(b \cdot y0\right) \cdot \left(z \cdot k - x \cdot j\right)\\ \mathbf{elif}\;y1 \leq 4.8 \cdot 10^{-140}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 1.4 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 1.75 \cdot 10^{+225}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - a \cdot t\_2\right)\\ \mathbf{if}\;y1 \leq -9.6 \cdot 10^{+33}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y1 \leq -2.3 \cdot 10^{-5}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot t\_2 - i \cdot t\_1\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -3.7 \cdot 10^{-218}:\\ \;\;\;\;b \cdot \left(\left(a \cdot t\_1 + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 6.8 \cdot 10^{-289}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 6 \cdot 10^{-229}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 1.16 \cdot 10^{-139}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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) (* z t)))
        (t_2 (- (* x y2) (* z y3)))
        (t_3 (* y1 (- (* i (- (* x j) (* z k))) (* a t_2)))))
   (if (<= y1 -9.6e+33)
     t_3
     (if (<= y1 -2.3e-5)
       (* c (+ (- (* y0 t_2) (* i t_1)) (* y4 (- (* y y3) (* t y2)))))
       (if (<= y1 -3.7e-218)
         (*
          b
          (+
           (+ (* a t_1) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j)))))
         (if (<= y1 6.8e-289)
           (* x (+ (* y2 (- (* c y0) (* a y1))) (* j (- (* i y1) (* b y0)))))
           (if (<= y1 6e-229)
             (* a (* y5 (- (* t y2) (* y y3))))
             (if (<= y1 1.16e-139)
               (* b (* k (- (* z y0) (* y y4))))
               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 = (x * y) - (z * t);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = y1 * ((i * ((x * j) - (z * k))) - (a * t_2));
	double tmp;
	if (y1 <= -9.6e+33) {
		tmp = t_3;
	} else if (y1 <= -2.3e-5) {
		tmp = c * (((y0 * t_2) - (i * t_1)) + (y4 * ((y * y3) - (t * y2))));
	} else if (y1 <= -3.7e-218) {
		tmp = b * (((a * t_1) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y1 <= 6.8e-289) {
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	} else if (y1 <= 6e-229) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y1 <= 1.16e-139) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else {
		tmp = 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 = (x * y) - (z * t)
    t_2 = (x * y2) - (z * y3)
    t_3 = y1 * ((i * ((x * j) - (z * k))) - (a * t_2))
    if (y1 <= (-9.6d+33)) then
        tmp = t_3
    else if (y1 <= (-2.3d-5)) then
        tmp = c * (((y0 * t_2) - (i * t_1)) + (y4 * ((y * y3) - (t * y2))))
    else if (y1 <= (-3.7d-218)) then
        tmp = b * (((a * t_1) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    else if (y1 <= 6.8d-289) then
        tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))))
    else if (y1 <= 6d-229) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (y1 <= 1.16d-139) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else
        tmp = 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 = (x * y) - (z * t);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = y1 * ((i * ((x * j) - (z * k))) - (a * t_2));
	double tmp;
	if (y1 <= -9.6e+33) {
		tmp = t_3;
	} else if (y1 <= -2.3e-5) {
		tmp = c * (((y0 * t_2) - (i * t_1)) + (y4 * ((y * y3) - (t * y2))));
	} else if (y1 <= -3.7e-218) {
		tmp = b * (((a * t_1) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (y1 <= 6.8e-289) {
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	} else if (y1 <= 6e-229) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y1 <= 1.16e-139) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else {
		tmp = 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 = (x * y) - (z * t)
	t_2 = (x * y2) - (z * y3)
	t_3 = y1 * ((i * ((x * j) - (z * k))) - (a * t_2))
	tmp = 0
	if y1 <= -9.6e+33:
		tmp = t_3
	elif y1 <= -2.3e-5:
		tmp = c * (((y0 * t_2) - (i * t_1)) + (y4 * ((y * y3) - (t * y2))))
	elif y1 <= -3.7e-218:
		tmp = b * (((a * t_1) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	elif y1 <= 6.8e-289:
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))))
	elif y1 <= 6e-229:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif y1 <= 1.16e-139:
		tmp = b * (k * ((z * y0) - (y * y4)))
	else:
		tmp = 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(x * y) - Float64(z * t))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) - Float64(a * t_2)))
	tmp = 0.0
	if (y1 <= -9.6e+33)
		tmp = t_3;
	elseif (y1 <= -2.3e-5)
		tmp = Float64(c * Float64(Float64(Float64(y0 * t_2) - Float64(i * t_1)) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y1 <= -3.7e-218)
		tmp = Float64(b * Float64(Float64(Float64(a * t_1) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y1 <= 6.8e-289)
		tmp = Float64(x * Float64(Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y1 <= 6e-229)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (y1 <= 1.16e-139)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	else
		tmp = 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 = (x * y) - (z * t);
	t_2 = (x * y2) - (z * y3);
	t_3 = y1 * ((i * ((x * j) - (z * k))) - (a * t_2));
	tmp = 0.0;
	if (y1 <= -9.6e+33)
		tmp = t_3;
	elseif (y1 <= -2.3e-5)
		tmp = c * (((y0 * t_2) - (i * t_1)) + (y4 * ((y * y3) - (t * y2))));
	elseif (y1 <= -3.7e-218)
		tmp = b * (((a * t_1) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	elseif (y1 <= 6.8e-289)
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	elseif (y1 <= 6e-229)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (y1 <= 1.16e-139)
		tmp = b * (k * ((z * y0) - (y * y4)));
	else
		tmp = 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[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -9.6e+33], t$95$3, If[LessEqual[y1, -2.3e-5], N[(c * N[(N[(N[(y0 * t$95$2), $MachinePrecision] - N[(i * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3.7e-218], N[(b * N[(N[(N[(a * t$95$1), $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, 6.8e-289], N[(x * N[(N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 6e-229], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.16e-139], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y1 < -9.5999999999999999e33 or 1.15999999999999999e-139 < y1

   1. Initial program 33.4%

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

   3. Taylor expanded in y1 around -inf 56.2%

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

      1. associate-*r* 56.2%

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

      2. neg-mul-1 56.2%

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

      3. +-commutative 56.2%

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

      4. mul-1-neg 56.2%

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

      5. unsub-neg 56.2%

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

      6. *-commutative 56.2%

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

      7. *-commutative 56.2%

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

      8. *-commutative 56.2%

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

      9. *-commutative 56.2%

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

   5. Simplified 56.2%

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

   6. Taylor expanded in y4 around 0 61.1%

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

   if -9.5999999999999999e33 < y1 < -2.3e-5

   1. Initial program 37.5%

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

   3. Taylor expanded in c around inf 75.5%

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

      1. +-commutative 75.5%

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

      2. mul-1-neg 75.5%

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

      3. unsub-neg 75.5%

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

      4. *-commutative 75.5%

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

      5. *-commutative 75.5%

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

      6. *-commutative 75.5%

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

      7. *-commutative 75.5%

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

   5. Simplified 75.5%

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

   if -2.3e-5 < y1 < -3.7000000000000002e-218

   1. Initial program 35.4%

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

   3. Taylor expanded in b around inf 57.3%

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

   if -3.7000000000000002e-218 < y1 < 6.80000000000000036e-289

   1. Initial program 35.3%

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

   3. Taylor expanded in x around inf 53.6%

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

   4. Taylor expanded in y around 0 59.4%

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

   if 6.80000000000000036e-289 < y1 < 6.00000000000000005e-229

   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 a around inf 47.3%

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

      1. +-commutative 47.3%

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

      2. mul-1-neg 47.3%

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

      3. unsub-neg 47.3%

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

      4. *-commutative 47.3%

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

      5. *-commutative 47.3%

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

      6. *-commutative 47.3%

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

      7. mul-1-neg 47.3%

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

      8. *-commutative 47.3%

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

   5. Simplified 47.3%

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

   6. Taylor expanded in y5 around inf 47.5%

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

   if 6.00000000000000005e-229 < y1 < 1.15999999999999999e-139

   1. Initial program 42.9%

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

   3. Taylor expanded in b around inf 50.8%

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

   4. Taylor expanded in k around -inf 72.5%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 72.5%

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

      2. neg-mul-1 72.5%

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

   6. Simplified 72.5%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -9.6 \cdot 10^{+33}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq -2.3 \cdot 10^{-5}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - i \cdot \left(x \cdot y - z \cdot t\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -3.7 \cdot 10^{-218}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 6.8 \cdot 10^{-289}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 6 \cdot 10^{-229}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 1.16 \cdot 10^{-139}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ t_2 := y4 \cdot \left(t \cdot j - y \cdot k\right)\\ \mathbf{if}\;y1 \leq -7 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -1.1 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -8.6 \cdot 10^{-219}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + t\_2\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 6.6 \cdot 10^{-289}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 1.4 \cdot 10^{-260}:\\ \;\;\;\;b \cdot t\_2\\ \mathbf{elif}\;y1 \leq 1.16 \cdot 10^{-139}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (- (* i (- (* x j) (* z k))) (* a (- (* x y2) (* z y3))))))
        (t_2 (* y4 (- (* t j) (* y k)))))
   (if (<= y1 -7e+34)
     t_1
     (if (<= y1 -1.1e-137)
       (* x (* y (- (* a b) (* c i))))
       (if (<= y1 -8.6e-219)
         (* b (+ (+ (* a (- (* x y) (* z t))) t_2) (* y0 (- (* z k) (* x j)))))
         (if (<= y1 6.6e-289)
           (* x (+ (* y2 (- (* c y0) (* a y1))) (* j (- (* i y1) (* b y0)))))
           (if (<= y1 1.4e-260)
             (* b t_2)
             (if (<= y1 1.16e-139)
               (* b (* k (- (* z y0) (* y y4))))
               t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * ((i * ((x * j) - (z * k))) - (a * ((x * y2) - (z * y3))));
	double t_2 = y4 * ((t * j) - (y * k));
	double tmp;
	if (y1 <= -7e+34) {
		tmp = t_1;
	} else if (y1 <= -1.1e-137) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y1 <= -8.6e-219) {
		tmp = b * (((a * ((x * y) - (z * t))) + t_2) + (y0 * ((z * k) - (x * j))));
	} else if (y1 <= 6.6e-289) {
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	} else if (y1 <= 1.4e-260) {
		tmp = b * t_2;
	} else if (y1 <= 1.16e-139) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y1 * ((i * ((x * j) - (z * k))) - (a * ((x * y2) - (z * y3))))
    t_2 = y4 * ((t * j) - (y * k))
    if (y1 <= (-7d+34)) then
        tmp = t_1
    else if (y1 <= (-1.1d-137)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y1 <= (-8.6d-219)) then
        tmp = b * (((a * ((x * y) - (z * t))) + t_2) + (y0 * ((z * k) - (x * j))))
    else if (y1 <= 6.6d-289) then
        tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))))
    else if (y1 <= 1.4d-260) then
        tmp = b * t_2
    else if (y1 <= 1.16d-139) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * ((i * ((x * j) - (z * k))) - (a * ((x * y2) - (z * y3))));
	double t_2 = y4 * ((t * j) - (y * k));
	double tmp;
	if (y1 <= -7e+34) {
		tmp = t_1;
	} else if (y1 <= -1.1e-137) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y1 <= -8.6e-219) {
		tmp = b * (((a * ((x * y) - (z * t))) + t_2) + (y0 * ((z * k) - (x * j))));
	} else if (y1 <= 6.6e-289) {
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	} else if (y1 <= 1.4e-260) {
		tmp = b * t_2;
	} else if (y1 <= 1.16e-139) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y1 * ((i * ((x * j) - (z * k))) - (a * ((x * y2) - (z * y3))))
	t_2 = y4 * ((t * j) - (y * k))
	tmp = 0
	if y1 <= -7e+34:
		tmp = t_1
	elif y1 <= -1.1e-137:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y1 <= -8.6e-219:
		tmp = b * (((a * ((x * y) - (z * t))) + t_2) + (y0 * ((z * k) - (x * j))))
	elif y1 <= 6.6e-289:
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))))
	elif y1 <= 1.4e-260:
		tmp = b * t_2
	elif y1 <= 1.16e-139:
		tmp = b * (k * ((z * y0) - (y * y4)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) - Float64(a * Float64(Float64(x * y2) - Float64(z * y3)))))
	t_2 = Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))
	tmp = 0.0
	if (y1 <= -7e+34)
		tmp = t_1;
	elseif (y1 <= -1.1e-137)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y1 <= -8.6e-219)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + t_2) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y1 <= 6.6e-289)
		tmp = Float64(x * Float64(Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y1 <= 1.4e-260)
		tmp = Float64(b * t_2);
	elseif (y1 <= 1.16e-139)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y1 * ((i * ((x * j) - (z * k))) - (a * ((x * y2) - (z * y3))));
	t_2 = y4 * ((t * j) - (y * k));
	tmp = 0.0;
	if (y1 <= -7e+34)
		tmp = t_1;
	elseif (y1 <= -1.1e-137)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y1 <= -8.6e-219)
		tmp = b * (((a * ((x * y) - (z * t))) + t_2) + (y0 * ((z * k) - (x * j))));
	elseif (y1 <= 6.6e-289)
		tmp = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	elseif (y1 <= 1.4e-260)
		tmp = b * t_2;
	elseif (y1 <= 1.16e-139)
		tmp = b * (k * ((z * y0) - (y * y4)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -7e+34], t$95$1, If[LessEqual[y1, -1.1e-137], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -8.6e-219], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 6.6e-289], N[(x * N[(N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.4e-260], N[(b * t$95$2), $MachinePrecision], If[LessEqual[y1, 1.16e-139], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y1 < -6.99999999999999996e34 or 1.15999999999999999e-139 < y1

   1. Initial program 33.4%

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

   3. Taylor expanded in y1 around -inf 56.2%

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

      1. associate-*r* 56.2%

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

      2. neg-mul-1 56.2%

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

      3. +-commutative 56.2%

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

      4. mul-1-neg 56.2%

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

      5. unsub-neg 56.2%

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

      6. *-commutative 56.2%

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

      7. *-commutative 56.2%

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

      8. *-commutative 56.2%

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

      9. *-commutative 56.2%

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

   5. Simplified 56.2%

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

   6. Taylor expanded in y4 around 0 61.1%

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

   if -6.99999999999999996e34 < y1 < -1.1000000000000001e-137

   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 x around inf 58.1%

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

   4. Taylor expanded in y around inf 62.2%

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

   if -1.1000000000000001e-137 < y1 < -8.6000000000000005e-219

   1. Initial program 51.0%

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

   3. Taylor expanded in b around inf 52.5%

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

   if -8.6000000000000005e-219 < y1 < 6.59999999999999994e-289

   1. Initial program 35.3%

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

   3. Taylor expanded in x around inf 53.6%

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

   4. Taylor expanded in y around 0 59.4%

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

   if 6.59999999999999994e-289 < y1 < 1.3999999999999999e-260

   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 33.3%

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

   4. Taylor expanded in y4 around inf 67.4%

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

   if 1.3999999999999999e-260 < y1 < 1.15999999999999999e-139

   1. Initial program 46.1%

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

   3. Taylor expanded in b around inf 42.3%

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

   4. Taylor expanded in k around -inf 59.4%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 59.4%

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

      2. neg-mul-1 59.4%

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

   6. Simplified 59.4%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -7 \cdot 10^{+34}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq -1.1 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -8.6 \cdot 10^{-219}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 6.6 \cdot 10^{-289}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 1.4 \cdot 10^{-260}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y1 \leq 1.16 \cdot 10^{-139}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 31.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ t_2 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{if}\;y5 \leq -3.3 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq -4.2 \cdot 10^{-266}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.05 \cdot 10^{-183}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y5 \leq 5.3 \cdot 10^{-104}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y5 \leq 7.5 \cdot 10^{-32}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y5 \leq 3.3 \cdot 10^{+130} \lor \neg \left(y5 \leq 1.52 \cdot 10^{+259}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y5 (- (* t y2) (* y y3)))))
        (t_2 (* i (* y1 (- (* x j) (* z k))))))
   (if (<= y5 -3.3e+102)
     t_1
     (if (<= y5 -4.2e-266)
       (* a (* y1 (- (* z y3) (* x y2))))
       (if (<= y5 1.05e-183)
         t_2
         (if (<= y5 5.3e-104)
           (* b (* y4 (- (* t j) (* y k))))
           (if (<= y5 7.5e-32)
             (* b (* a (- (* x y) (* z t))))
             (if (or (<= y5 3.3e+130) (not (<= y5 1.52e+259))) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double t_2 = i * (y1 * ((x * j) - (z * k)));
	double tmp;
	if (y5 <= -3.3e+102) {
		tmp = t_1;
	} else if (y5 <= -4.2e-266) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y5 <= 1.05e-183) {
		tmp = t_2;
	} else if (y5 <= 5.3e-104) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y5 <= 7.5e-32) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if ((y5 <= 3.3e+130) || !(y5 <= 1.52e+259)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (y5 * ((t * y2) - (y * y3)))
    t_2 = i * (y1 * ((x * j) - (z * k)))
    if (y5 <= (-3.3d+102)) then
        tmp = t_1
    else if (y5 <= (-4.2d-266)) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (y5 <= 1.05d-183) then
        tmp = t_2
    else if (y5 <= 5.3d-104) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y5 <= 7.5d-32) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if ((y5 <= 3.3d+130) .or. (.not. (y5 <= 1.52d+259))) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double t_2 = i * (y1 * ((x * j) - (z * k)));
	double tmp;
	if (y5 <= -3.3e+102) {
		tmp = t_1;
	} else if (y5 <= -4.2e-266) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y5 <= 1.05e-183) {
		tmp = t_2;
	} else if (y5 <= 5.3e-104) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y5 <= 7.5e-32) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if ((y5 <= 3.3e+130) || !(y5 <= 1.52e+259)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y5 * ((t * y2) - (y * y3)))
	t_2 = i * (y1 * ((x * j) - (z * k)))
	tmp = 0
	if y5 <= -3.3e+102:
		tmp = t_1
	elif y5 <= -4.2e-266:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif y5 <= 1.05e-183:
		tmp = t_2
	elif y5 <= 5.3e-104:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y5 <= 7.5e-32:
		tmp = b * (a * ((x * y) - (z * t)))
	elif (y5 <= 3.3e+130) or not (y5 <= 1.52e+259):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	t_2 = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))))
	tmp = 0.0
	if (y5 <= -3.3e+102)
		tmp = t_1;
	elseif (y5 <= -4.2e-266)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (y5 <= 1.05e-183)
		tmp = t_2;
	elseif (y5 <= 5.3e-104)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y5 <= 7.5e-32)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif ((y5 <= 3.3e+130) || !(y5 <= 1.52e+259))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y5 * ((t * y2) - (y * y3)));
	t_2 = i * (y1 * ((x * j) - (z * k)));
	tmp = 0.0;
	if (y5 <= -3.3e+102)
		tmp = t_1;
	elseif (y5 <= -4.2e-266)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (y5 <= 1.05e-183)
		tmp = t_2;
	elseif (y5 <= 5.3e-104)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y5 <= 7.5e-32)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif ((y5 <= 3.3e+130) || ~((y5 <= 1.52e+259)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -3.3e+102], t$95$1, If[LessEqual[y5, -4.2e-266], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.05e-183], t$95$2, If[LessEqual[y5, 5.3e-104], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 7.5e-32], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y5, 3.3e+130], N[Not[LessEqual[y5, 1.52e+259]], $MachinePrecision]], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -3.29999999999999999e102 or 7.49999999999999953e-32 < y5 < 3.3e130 or 1.52000000000000004e259 < y5

   1. Initial program 28.4%

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

   3. Taylor expanded in a around inf 43.5%

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

      1. +-commutative 43.5%

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

      2. mul-1-neg 43.5%

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

      3. unsub-neg 43.5%

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

      4. *-commutative 43.5%

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

      5. *-commutative 43.5%

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

      6. *-commutative 43.5%

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

      7. mul-1-neg 43.5%

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

      8. *-commutative 43.5%

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

   5. Simplified 43.5%

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

   6. Taylor expanded in y5 around inf 47.6%

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

   if -3.29999999999999999e102 < y5 < -4.19999999999999994e-266

   1. Initial program 43.1%

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

   3. Taylor expanded in a around inf 44.9%

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

      1. +-commutative 44.9%

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

      2. mul-1-neg 44.9%

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

      3. unsub-neg 44.9%

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

      4. *-commutative 44.9%

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

      5. *-commutative 44.9%

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

      6. *-commutative 44.9%

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

      7. mul-1-neg 44.9%

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

      8. *-commutative 44.9%

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

   5. Simplified 44.9%

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

   6. Taylor expanded in y1 around inf 50.1%

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

   if -4.19999999999999994e-266 < y5 < 1.0500000000000001e-183 or 3.3e130 < y5 < 1.52000000000000004e259

   1. Initial program 34.9%

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

   3. Taylor expanded in y1 around -inf 42.1%

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

      1. associate-*r* 42.1%

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

      2. neg-mul-1 42.1%

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

      3. +-commutative 42.1%

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

      4. mul-1-neg 42.1%

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

      5. unsub-neg 42.1%

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

      6. *-commutative 42.1%

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

      7. *-commutative 42.1%

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

      8. *-commutative 42.1%

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

      9. *-commutative 42.1%

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

   5. Simplified 42.1%

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

   6. Taylor expanded in i around -inf 52.7%

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

   if 1.0500000000000001e-183 < y5 < 5.30000000000000018e-104

   1. Initial program 36.5%

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

   3. Taylor expanded in b around inf 42.2%

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

   4. Taylor expanded in y4 around inf 33.3%

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

   if 5.30000000000000018e-104 < y5 < 7.49999999999999953e-32

   1. Initial program 31.2%

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

   3. Taylor expanded in b around inf 50.3%

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

   4. Taylor expanded in a around inf 50.9%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -3.3 \cdot 10^{+102}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -4.2 \cdot 10^{-266}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.05 \cdot 10^{-183}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y5 \leq 5.3 \cdot 10^{-104}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y5 \leq 7.5 \cdot 10^{-32}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y5 \leq 3.3 \cdot 10^{+130} \lor \neg \left(y5 \leq 1.52 \cdot 10^{+259}\right):\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 32.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ t_2 := a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{if}\;y1 \leq -1.85 \cdot 10^{+189}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y1 \leq -3.2 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -5.8 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq 1.15 \cdot 10^{-125}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 1.25 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 4.4 \cdot 10^{+67}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y1 \leq 1.8 \cdot 10^{+220}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* y1 (- (* x j) (* z k)))))
        (t_2 (* a (* y1 (- (* z y3) (* x y2))))))
   (if (<= y1 -1.85e+189)
     t_2
     (if (<= y1 -3.2e+41)
       t_1
       (if (<= y1 -5.8e-137)
         (* x (* y (- (* a b) (* c i))))
         (if (<= y1 1.15e-125)
           (* a (* y5 (- (* t y2) (* y y3))))
           (if (<= y1 1.25e-18)
             (* x (* c (* y0 y2)))
             (if (<= y1 4.4e+67)
               (* b (* y4 (- (* t j) (* y k))))
               (if (<= y1 1.8e+220) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y1 * ((x * j) - (z * k)));
	double t_2 = a * (y1 * ((z * y3) - (x * y2)));
	double tmp;
	if (y1 <= -1.85e+189) {
		tmp = t_2;
	} else if (y1 <= -3.2e+41) {
		tmp = t_1;
	} else if (y1 <= -5.8e-137) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y1 <= 1.15e-125) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y1 <= 1.25e-18) {
		tmp = x * (c * (y0 * y2));
	} else if (y1 <= 4.4e+67) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y1 <= 1.8e+220) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * (y1 * ((x * j) - (z * k)))
    t_2 = a * (y1 * ((z * y3) - (x * y2)))
    if (y1 <= (-1.85d+189)) then
        tmp = t_2
    else if (y1 <= (-3.2d+41)) then
        tmp = t_1
    else if (y1 <= (-5.8d-137)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y1 <= 1.15d-125) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (y1 <= 1.25d-18) then
        tmp = x * (c * (y0 * y2))
    else if (y1 <= 4.4d+67) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y1 <= 1.8d+220) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y1 * ((x * j) - (z * k)));
	double t_2 = a * (y1 * ((z * y3) - (x * y2)));
	double tmp;
	if (y1 <= -1.85e+189) {
		tmp = t_2;
	} else if (y1 <= -3.2e+41) {
		tmp = t_1;
	} else if (y1 <= -5.8e-137) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y1 <= 1.15e-125) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y1 <= 1.25e-18) {
		tmp = x * (c * (y0 * y2));
	} else if (y1 <= 4.4e+67) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y1 <= 1.8e+220) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (y1 * ((x * j) - (z * k)))
	t_2 = a * (y1 * ((z * y3) - (x * y2)))
	tmp = 0
	if y1 <= -1.85e+189:
		tmp = t_2
	elif y1 <= -3.2e+41:
		tmp = t_1
	elif y1 <= -5.8e-137:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y1 <= 1.15e-125:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif y1 <= 1.25e-18:
		tmp = x * (c * (y0 * y2))
	elif y1 <= 4.4e+67:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y1 <= 1.8e+220:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))))
	t_2 = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))))
	tmp = 0.0
	if (y1 <= -1.85e+189)
		tmp = t_2;
	elseif (y1 <= -3.2e+41)
		tmp = t_1;
	elseif (y1 <= -5.8e-137)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y1 <= 1.15e-125)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (y1 <= 1.25e-18)
		tmp = Float64(x * Float64(c * Float64(y0 * y2)));
	elseif (y1 <= 4.4e+67)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y1 <= 1.8e+220)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (y1 * ((x * j) - (z * k)));
	t_2 = a * (y1 * ((z * y3) - (x * y2)));
	tmp = 0.0;
	if (y1 <= -1.85e+189)
		tmp = t_2;
	elseif (y1 <= -3.2e+41)
		tmp = t_1;
	elseif (y1 <= -5.8e-137)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y1 <= 1.15e-125)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (y1 <= 1.25e-18)
		tmp = x * (c * (y0 * y2));
	elseif (y1 <= 4.4e+67)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y1 <= 1.8e+220)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -1.85e+189], t$95$2, If[LessEqual[y1, -3.2e+41], t$95$1, If[LessEqual[y1, -5.8e-137], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.15e-125], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.25e-18], N[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 4.4e+67], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.8e+220], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y1 < -1.8500000000000001e189 or 1.80000000000000009e220 < y1

   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 a around inf 54.6%

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

      1. +-commutative 54.6%

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

      2. mul-1-neg 54.6%

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

      3. unsub-neg 54.6%

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

      4. *-commutative 54.6%

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

      5. *-commutative 54.6%

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

      6. *-commutative 54.6%

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

      7. mul-1-neg 54.6%

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

      8. *-commutative 54.6%

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

   5. Simplified 54.6%

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

   6. Taylor expanded in y1 around inf 66.7%

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

   if -1.8500000000000001e189 < y1 < -3.2000000000000001e41 or 4.4e67 < y1 < 1.80000000000000009e220

   1. Initial program 37.0%

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

   3. Taylor expanded in y1 around -inf 58.7%

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

      1. associate-*r* 58.7%

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

      2. neg-mul-1 58.7%

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

      3. +-commutative 58.7%

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

      4. mul-1-neg 58.7%

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

      5. unsub-neg 58.7%

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

      6. *-commutative 58.7%

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

      7. *-commutative 58.7%

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

      8. *-commutative 58.7%

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

      9. *-commutative 58.7%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in i around -inf 56.2%

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

   if -3.2000000000000001e41 < y1 < -5.7999999999999997e-137

   1. Initial program 31.3%

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

   3. Taylor expanded in x around inf 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 63.0%

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

   if -5.7999999999999997e-137 < y1 < 1.15e-125

   1. Initial program 45.1%

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

   3. Taylor expanded in a around inf 38.4%

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

      1. +-commutative 38.4%

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

      2. mul-1-neg 38.4%

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

      3. unsub-neg 38.4%

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

      4. *-commutative 38.4%

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

      5. *-commutative 38.4%

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

      6. *-commutative 38.4%

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

      7. mul-1-neg 38.4%

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

      8. *-commutative 38.4%

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

   5. Simplified 38.4%

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

   6. Taylor expanded in y5 around inf 37.3%

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

   if 1.15e-125 < y1 < 1.25000000000000009e-18

   1. Initial program 15.2%

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

   3. Taylor expanded in x around inf 65.6%

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

   4. Taylor expanded in y2 around inf 60.8%

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

   5. Taylor expanded in c around inf 55.7%

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

      1. *-commutative 55.7%

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

   7. Simplified 55.7%

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

   if 1.25000000000000009e-18 < y1 < 4.4e67

   1. Initial program 35.7%

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

   3. Taylor expanded in b around inf 35.7%

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

   4. Taylor expanded in y4 around inf 36.7%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.85 \cdot 10^{+189}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -3.2 \cdot 10^{+41}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y1 \leq -5.8 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq 1.15 \cdot 10^{-125}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 1.25 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 4.4 \cdot 10^{+67}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y1 \leq 1.8 \cdot 10^{+220}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 43.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{if}\;y2 \leq -2.05 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq 1.56 \cdot 10^{-299}:\\ \;\;\;\;a \cdot \left(\left(b \cdot \left(x \cdot y - z \cdot t\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 8.5 \cdot 10^{+42}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y2
          (+
           (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
           (* t (- (* a y5) (* c y4)))))))
   (if (<= y2 -2.05e+32)
     t_1
     (if (<= y2 1.56e-299)
       (*
        a
        (+
         (+ (* b (- (* x y) (* z t))) (* y1 (- (* z y3) (* x y2))))
         (* y5 (- (* t y2) (* y y3)))))
       (if (<= y2 8.5e+42)
         (*
          j
          (+
           (+ (* t (- (* b y4) (* i y5))) (* y3 (- (* y0 y5) (* y1 y4))))
           (* x (- (* i y1) (* b y0)))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	double tmp;
	if (y2 <= -2.05e+32) {
		tmp = t_1;
	} else if (y2 <= 1.56e-299) {
		tmp = a * (((b * ((x * y) - (z * t))) + (y1 * ((z * y3) - (x * y2)))) + (y5 * ((t * y2) - (y * y3))));
	} else if (y2 <= 8.5e+42) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    if (y2 <= (-2.05d+32)) then
        tmp = t_1
    else if (y2 <= 1.56d-299) then
        tmp = a * (((b * ((x * y) - (z * t))) + (y1 * ((z * y3) - (x * y2)))) + (y5 * ((t * y2) - (y * y3))))
    else if (y2 <= 8.5d+42) then
        tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	double tmp;
	if (y2 <= -2.05e+32) {
		tmp = t_1;
	} else if (y2 <= 1.56e-299) {
		tmp = a * (((b * ((x * y) - (z * t))) + (y1 * ((z * y3) - (x * y2)))) + (y5 * ((t * y2) - (y * y3))));
	} else if (y2 <= 8.5e+42) {
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	tmp = 0
	if y2 <= -2.05e+32:
		tmp = t_1
	elif y2 <= 1.56e-299:
		tmp = a * (((b * ((x * y) - (z * t))) + (y1 * ((z * y3) - (x * y2)))) + (y5 * ((t * y2) - (y * y3))))
	elif y2 <= 8.5e+42:
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))))
	tmp = 0.0
	if (y2 <= -2.05e+32)
		tmp = t_1;
	elseif (y2 <= 1.56e-299)
		tmp = Float64(a * Float64(Float64(Float64(b * Float64(Float64(x * y) - Float64(z * t))) + Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2)))) + Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3)))));
	elseif (y2 <= 8.5e+42)
		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 = 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 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	tmp = 0.0;
	if (y2 <= -2.05e+32)
		tmp = t_1;
	elseif (y2 <= 1.56e-299)
		tmp = a * (((b * ((x * y) - (z * t))) + (y1 * ((z * y3) - (x * y2)))) + (y5 * ((t * y2) - (y * y3))));
	elseif (y2 <= 8.5e+42)
		tmp = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -2.05e+32], t$95$1, If[LessEqual[y2, 1.56e-299], N[(a * N[(N[(N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 8.5e+42], 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], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y2 < -2.0499999999999999e32 or 8.5000000000000003e42 < y2

   1. Initial program 31.1%

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

   3. Taylor expanded in y2 around inf 66.6%

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

   if -2.0499999999999999e32 < y2 < 1.56e-299

   1. Initial program 40.2%

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

   3. Taylor expanded in a around inf 49.9%

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

      1. +-commutative 49.9%

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

      2. mul-1-neg 49.9%

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

      3. unsub-neg 49.9%

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

      4. *-commutative 49.9%

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

      5. *-commutative 49.9%

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

      6. *-commutative 49.9%

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

      7. mul-1-neg 49.9%

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

      8. *-commutative 49.9%

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

   5. Simplified 49.9%

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

   if 1.56e-299 < y2 < 8.5000000000000003e42

   1. Initial program 37.1%

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

   3. Taylor expanded in j around inf 50.8%

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

      1. +-commutative 50.8%

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

      2. mul-1-neg 50.8%

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

      3. unsub-neg 50.8%

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

      4. *-commutative 50.8%

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

   5. Simplified 50.8%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2.05 \cdot 10^{+32}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 1.56 \cdot 10^{-299}:\\ \;\;\;\;a \cdot \left(\left(b \cdot \left(x \cdot y - z \cdot t\right) + y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 8.5 \cdot 10^{+42}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 32.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{if}\;y1 \leq -1.55 \cdot 10^{+197}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -1.45 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -3.3 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -3.8 \cdot 10^{-258}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 1.7 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 1.5 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* y1 (- (* x j) (* z k))))))
   (if (<= y1 -1.55e+197)
     (* a (* y1 (- (* z y3) (* x y2))))
     (if (<= y1 -1.45e+43)
       t_1
       (if (<= y1 -3.3e-137)
         (* x (* y (- (* a b) (* c i))))
         (if (<= y1 -3.8e-258)
           (* b (* a (- (* x y) (* z t))))
           (if (<= y1 1.7e-140)
             (* b (* k (- (* z y0) (* y y4))))
             (if (<= y1 1.5e+49) (* x (* y0 (- (* c y2) (* b 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 = i * (y1 * ((x * j) - (z * k)));
	double tmp;
	if (y1 <= -1.55e+197) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y1 <= -1.45e+43) {
		tmp = t_1;
	} else if (y1 <= -3.3e-137) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y1 <= -3.8e-258) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y1 <= 1.7e-140) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (y1 <= 1.5e+49) {
		tmp = x * (y0 * ((c * y2) - (b * 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) :: tmp
    t_1 = i * (y1 * ((x * j) - (z * k)))
    if (y1 <= (-1.55d+197)) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (y1 <= (-1.45d+43)) then
        tmp = t_1
    else if (y1 <= (-3.3d-137)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y1 <= (-3.8d-258)) then
        tmp = b * (a * ((x * y) - (z * t)))
    else if (y1 <= 1.7d-140) then
        tmp = b * (k * ((z * y0) - (y * y4)))
    else if (y1 <= 1.5d+49) then
        tmp = x * (y0 * ((c * y2) - (b * 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 = i * (y1 * ((x * j) - (z * k)));
	double tmp;
	if (y1 <= -1.55e+197) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y1 <= -1.45e+43) {
		tmp = t_1;
	} else if (y1 <= -3.3e-137) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y1 <= -3.8e-258) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else if (y1 <= 1.7e-140) {
		tmp = b * (k * ((z * y0) - (y * y4)));
	} else if (y1 <= 1.5e+49) {
		tmp = x * (y0 * ((c * y2) - (b * 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 = i * (y1 * ((x * j) - (z * k)))
	tmp = 0
	if y1 <= -1.55e+197:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif y1 <= -1.45e+43:
		tmp = t_1
	elif y1 <= -3.3e-137:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y1 <= -3.8e-258:
		tmp = b * (a * ((x * y) - (z * t)))
	elif y1 <= 1.7e-140:
		tmp = b * (k * ((z * y0) - (y * y4)))
	elif y1 <= 1.5e+49:
		tmp = x * (y0 * ((c * y2) - (b * 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(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))))
	tmp = 0.0
	if (y1 <= -1.55e+197)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (y1 <= -1.45e+43)
		tmp = t_1;
	elseif (y1 <= -3.3e-137)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y1 <= -3.8e-258)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y1 <= 1.7e-140)
		tmp = Float64(b * Float64(k * Float64(Float64(z * y0) - Float64(y * y4))));
	elseif (y1 <= 1.5e+49)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * 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 = i * (y1 * ((x * j) - (z * k)));
	tmp = 0.0;
	if (y1 <= -1.55e+197)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (y1 <= -1.45e+43)
		tmp = t_1;
	elseif (y1 <= -3.3e-137)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y1 <= -3.8e-258)
		tmp = b * (a * ((x * y) - (z * t)));
	elseif (y1 <= 1.7e-140)
		tmp = b * (k * ((z * y0) - (y * y4)));
	elseif (y1 <= 1.5e+49)
		tmp = x * (y0 * ((c * y2) - (b * 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[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -1.55e+197], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.45e+43], t$95$1, If[LessEqual[y1, -3.3e-137], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3.8e-258], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.7e-140], N[(b * N[(k * N[(N[(z * y0), $MachinePrecision] - N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.5e+49], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y1 < -1.55e197

   1. Initial program 41.6%

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

   3. Taylor expanded in a around inf 49.6%

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

      1. +-commutative 49.6%

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

      2. mul-1-neg 49.6%

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

      3. unsub-neg 49.6%

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

      4. *-commutative 49.6%

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

      5. *-commutative 49.6%

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

      6. *-commutative 49.6%

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

      7. mul-1-neg 49.6%

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

      8. *-commutative 49.6%

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

   5. Simplified 49.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf 62.2%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   if -1.55e197 < y1 < -1.4500000000000001e43 or 1.5000000000000001e49 < y1

   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 y1 around -inf 58.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 58.5%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 58.5%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 58.5%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 58.5%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 58.5%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 58.5%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 58.5%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 58.5%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 58.5%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 58.5%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in i around -inf 55.4%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if -1.4500000000000001e43 < y1 < -3.3000000000000002e-137

   1. Initial program 31.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 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 63.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

   if -3.3000000000000002e-137 < y1 < -3.7999999999999998e-258

   1. Initial program 45.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 50.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 45.8%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -3.7999999999999998e-258 < y1 < 1.70000000000000004e-140

   1. Initial program 43.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 34.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in k around -inf 49.6%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 49.6%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

      2. neg-mul-1 49.6%

         \[\leadsto b \cdot \left(\color{blue}{\left(-k\right)} \cdot \left(y \cdot y4 - y0 \cdot z\right)\right) \]

   6. Simplified 49.6%

      \[\leadsto b \cdot \color{blue}{\left(\left(-k\right) \cdot \left(y \cdot y4 - y0 \cdot z\right)\right)} \]

   if 1.70000000000000004e-140 < y1 < 1.5000000000000001e49

   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 x around inf 53.4%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around 0 48.3%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in y0 around inf 48.1%

      \[\leadsto x \cdot \color{blue}{\left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 48.1%

         \[\leadsto x \cdot \left(y0 \cdot \left(\color{blue}{y2 \cdot c} - b \cdot j\right)\right) \]

      2. *-commutative 48.1%

         \[\leadsto x \cdot \left(y0 \cdot \left(y2 \cdot c - \color{blue}{j \cdot b}\right)\right) \]

   7. Simplified 48.1%

      \[\leadsto x \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot c - j \cdot b\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.55 \cdot 10^{+197}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -1.45 \cdot 10^{+43}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y1 \leq -3.3 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -3.8 \cdot 10^{-258}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 1.7 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \left(k \cdot \left(z \cdot y0 - y \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 1.5 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 32.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ t_2 := a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{if}\;y1 \leq -3.3 \cdot 10^{+196}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y1 \leq -1.08 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -5.2 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq 1.65 \cdot 10^{-140}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 1.25 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 3.6 \cdot 10^{+218}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* y1 (- (* x j) (* z k)))))
        (t_2 (* a (* y1 (- (* z y3) (* x y2))))))
   (if (<= y1 -3.3e+196)
     t_2
     (if (<= y1 -1.08e+43)
       t_1
       (if (<= y1 -5.2e-137)
         (* x (* y (- (* a b) (* c i))))
         (if (<= y1 1.65e-140)
           (* a (* y5 (- (* t y2) (* y y3))))
           (if (<= y1 1.25e+53)
             (* x (* y0 (- (* c y2) (* b j))))
             (if (<= y1 3.6e+218) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y1 * ((x * j) - (z * k)));
	double t_2 = a * (y1 * ((z * y3) - (x * y2)));
	double tmp;
	if (y1 <= -3.3e+196) {
		tmp = t_2;
	} else if (y1 <= -1.08e+43) {
		tmp = t_1;
	} else if (y1 <= -5.2e-137) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y1 <= 1.65e-140) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y1 <= 1.25e+53) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (y1 <= 3.6e+218) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * (y1 * ((x * j) - (z * k)))
    t_2 = a * (y1 * ((z * y3) - (x * y2)))
    if (y1 <= (-3.3d+196)) then
        tmp = t_2
    else if (y1 <= (-1.08d+43)) then
        tmp = t_1
    else if (y1 <= (-5.2d-137)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y1 <= 1.65d-140) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (y1 <= 1.25d+53) then
        tmp = x * (y0 * ((c * y2) - (b * j)))
    else if (y1 <= 3.6d+218) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y1 * ((x * j) - (z * k)));
	double t_2 = a * (y1 * ((z * y3) - (x * y2)));
	double tmp;
	if (y1 <= -3.3e+196) {
		tmp = t_2;
	} else if (y1 <= -1.08e+43) {
		tmp = t_1;
	} else if (y1 <= -5.2e-137) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y1 <= 1.65e-140) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y1 <= 1.25e+53) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (y1 <= 3.6e+218) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (y1 * ((x * j) - (z * k)))
	t_2 = a * (y1 * ((z * y3) - (x * y2)))
	tmp = 0
	if y1 <= -3.3e+196:
		tmp = t_2
	elif y1 <= -1.08e+43:
		tmp = t_1
	elif y1 <= -5.2e-137:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y1 <= 1.65e-140:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif y1 <= 1.25e+53:
		tmp = x * (y0 * ((c * y2) - (b * j)))
	elif y1 <= 3.6e+218:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))))
	t_2 = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))))
	tmp = 0.0
	if (y1 <= -3.3e+196)
		tmp = t_2;
	elseif (y1 <= -1.08e+43)
		tmp = t_1;
	elseif (y1 <= -5.2e-137)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y1 <= 1.65e-140)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (y1 <= 1.25e+53)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (y1 <= 3.6e+218)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (y1 * ((x * j) - (z * k)));
	t_2 = a * (y1 * ((z * y3) - (x * y2)));
	tmp = 0.0;
	if (y1 <= -3.3e+196)
		tmp = t_2;
	elseif (y1 <= -1.08e+43)
		tmp = t_1;
	elseif (y1 <= -5.2e-137)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y1 <= 1.65e-140)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (y1 <= 1.25e+53)
		tmp = x * (y0 * ((c * y2) - (b * j)));
	elseif (y1 <= 3.6e+218)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -3.3e+196], t$95$2, If[LessEqual[y1, -1.08e+43], t$95$1, If[LessEqual[y1, -5.2e-137], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.65e-140], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.25e+53], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.6e+218], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y1 < -3.3000000000000002e196 or 3.59999999999999991e218 < y1

   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 a around inf 54.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 54.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 54.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 54.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 54.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 54.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 54.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 54.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 54.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 54.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf 66.7%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   if -3.3000000000000002e196 < y1 < -1.08e43 or 1.2500000000000001e53 < y1 < 3.59999999999999991e218

   1. Initial program 36.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 59.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 59.3%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 59.3%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 59.3%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 59.3%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 59.3%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 59.3%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 59.3%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 59.3%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 59.3%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 59.3%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in i around -inf 56.9%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if -1.08e43 < y1 < -5.1999999999999999e-137

   1. Initial program 31.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 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 63.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

   if -5.1999999999999999e-137 < y1 < 1.64999999999999994e-140

   1. Initial program 43.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 38.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 38.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 38.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 38.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 38.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 38.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 38.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 38.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 38.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 38.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y5 around inf 37.0%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if 1.64999999999999994e-140 < y1 < 1.2500000000000001e53

   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 x around inf 53.4%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around 0 48.3%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in y0 around inf 48.1%

      \[\leadsto x \cdot \color{blue}{\left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 48.1%

         \[\leadsto x \cdot \left(y0 \cdot \left(\color{blue}{y2 \cdot c} - b \cdot j\right)\right) \]

      2. *-commutative 48.1%

         \[\leadsto x \cdot \left(y0 \cdot \left(y2 \cdot c - \color{blue}{j \cdot b}\right)\right) \]

   7. Simplified 48.1%

      \[\leadsto x \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot c - j \cdot b\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -3.3 \cdot 10^{+196}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -1.08 \cdot 10^{+43}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y1 \leq -5.2 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq 1.65 \cdot 10^{-140}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 1.25 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 3.6 \cdot 10^{+218}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 35.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{-153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{-194}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-287}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{+172}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (* x (+ (* y2 (- (* c y0) (* a y1))) (* j (- (* i y1) (* b y0)))))))
   (if (<= y -1.35e-153)
     t_1
     (if (<= y -7.4e-194)
       (* b (* z (- (* k y0) (* t a))))
       (if (<= y -1.85e-287)
         t_1
         (if (<= y 1.46e+172)
           (* y1 (- (* i (- (* x j) (* z k))) (* a (- (* x y2) (* z y3)))))
           (* x (* y (- (* a b) (* c i))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y <= -1.35e-153) {
		tmp = t_1;
	} else if (y <= -7.4e-194) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else if (y <= -1.85e-287) {
		tmp = t_1;
	} else if (y <= 1.46e+172) {
		tmp = y1 * ((i * ((x * j) - (z * k))) - (a * ((x * y2) - (z * y3))));
	} else {
		tmp = x * (y * ((a * b) - (c * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))))
    if (y <= (-1.35d-153)) then
        tmp = t_1
    else if (y <= (-7.4d-194)) then
        tmp = b * (z * ((k * y0) - (t * a)))
    else if (y <= (-1.85d-287)) then
        tmp = t_1
    else if (y <= 1.46d+172) then
        tmp = y1 * ((i * ((x * j) - (z * k))) - (a * ((x * y2) - (z * y3))))
    else
        tmp = x * (y * ((a * b) - (c * i)))
    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 * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y <= -1.35e-153) {
		tmp = t_1;
	} else if (y <= -7.4e-194) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else if (y <= -1.85e-287) {
		tmp = t_1;
	} else if (y <= 1.46e+172) {
		tmp = y1 * ((i * ((x * j) - (z * k))) - (a * ((x * y2) - (z * y3))));
	} else {
		tmp = x * (y * ((a * b) - (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))))
	tmp = 0
	if y <= -1.35e-153:
		tmp = t_1
	elif y <= -7.4e-194:
		tmp = b * (z * ((k * y0) - (t * a)))
	elif y <= -1.85e-287:
		tmp = t_1
	elif y <= 1.46e+172:
		tmp = y1 * ((i * ((x * j) - (z * k))) - (a * ((x * y2) - (z * y3))))
	else:
		tmp = x * (y * ((a * b) - (c * i)))
	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(Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (y <= -1.35e-153)
		tmp = t_1;
	elseif (y <= -7.4e-194)
		tmp = Float64(b * Float64(z * Float64(Float64(k * y0) - Float64(t * a))));
	elseif (y <= -1.85e-287)
		tmp = t_1;
	elseif (y <= 1.46e+172)
		tmp = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) - Float64(a * Float64(Float64(x * y2) - Float64(z * y3)))));
	else
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = x * ((y2 * ((c * y0) - (a * y1))) + (j * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (y <= -1.35e-153)
		tmp = t_1;
	elseif (y <= -7.4e-194)
		tmp = b * (z * ((k * y0) - (t * a)));
	elseif (y <= -1.85e-287)
		tmp = t_1;
	elseif (y <= 1.46e+172)
		tmp = y1 * ((i * ((x * j) - (z * k))) - (a * ((x * y2) - (z * y3))));
	else
		tmp = x * (y * ((a * b) - (c * i)));
	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[(N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.35e-153], t$95$1, If[LessEqual[y, -7.4e-194], N[(b * N[(z * N[(N[(k * y0), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.85e-287], t$95$1, If[LessEqual[y, 1.46e+172], N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.35000000000000005e-153 or -7.40000000000000016e-194 < y < -1.85000000000000013e-287

   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 x around inf 47.9%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around 0 50.4%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   if -1.35000000000000005e-153 < y < -7.40000000000000016e-194

   1. Initial program 37.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 75.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in z around -inf 76.0%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 76.0%

         \[\leadsto b \cdot \color{blue}{\left(-z \cdot \left(a \cdot t - k \cdot y0\right)\right)} \]

   6. Simplified 76.0%

      \[\leadsto b \cdot \color{blue}{\left(-z \cdot \left(a \cdot t - k \cdot y0\right)\right)} \]

   if -1.85000000000000013e-287 < y < 1.46e172

   1. Initial program 30.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 50.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 50.8%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 50.8%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 50.8%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 50.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 50.8%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 50.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 50.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 50.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 50.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 50.8%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around 0 55.0%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if 1.46e172 < y

   1. Initial program 27.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 36.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around inf 58.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-153}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{-194}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-287}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{+172}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 32.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{if}\;y1 \leq -1.25 \cdot 10^{+194}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -3.4 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -2.4 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq 9.4 \cdot 10^{-141}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 2.2 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* y1 (- (* x j) (* z k))))))
   (if (<= y1 -1.25e+194)
     (* a (* y1 (- (* z y3) (* x y2))))
     (if (<= y1 -3.4e+41)
       t_1
       (if (<= y1 -2.4e-137)
         (* x (* y (- (* a b) (* c i))))
         (if (<= y1 9.4e-141)
           (* a (* y5 (- (* t y2) (* y y3))))
           (if (<= y1 2.2e+49) (* x (* y0 (- (* c y2) (* b 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 = i * (y1 * ((x * j) - (z * k)));
	double tmp;
	if (y1 <= -1.25e+194) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y1 <= -3.4e+41) {
		tmp = t_1;
	} else if (y1 <= -2.4e-137) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y1 <= 9.4e-141) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y1 <= 2.2e+49) {
		tmp = x * (y0 * ((c * y2) - (b * 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) :: tmp
    t_1 = i * (y1 * ((x * j) - (z * k)))
    if (y1 <= (-1.25d+194)) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (y1 <= (-3.4d+41)) then
        tmp = t_1
    else if (y1 <= (-2.4d-137)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y1 <= 9.4d-141) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (y1 <= 2.2d+49) then
        tmp = x * (y0 * ((c * y2) - (b * 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 = i * (y1 * ((x * j) - (z * k)));
	double tmp;
	if (y1 <= -1.25e+194) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y1 <= -3.4e+41) {
		tmp = t_1;
	} else if (y1 <= -2.4e-137) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y1 <= 9.4e-141) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y1 <= 2.2e+49) {
		tmp = x * (y0 * ((c * y2) - (b * 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 = i * (y1 * ((x * j) - (z * k)))
	tmp = 0
	if y1 <= -1.25e+194:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif y1 <= -3.4e+41:
		tmp = t_1
	elif y1 <= -2.4e-137:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y1 <= 9.4e-141:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif y1 <= 2.2e+49:
		tmp = x * (y0 * ((c * y2) - (b * 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(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))))
	tmp = 0.0
	if (y1 <= -1.25e+194)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (y1 <= -3.4e+41)
		tmp = t_1;
	elseif (y1 <= -2.4e-137)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y1 <= 9.4e-141)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (y1 <= 2.2e+49)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * 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 = i * (y1 * ((x * j) - (z * k)));
	tmp = 0.0;
	if (y1 <= -1.25e+194)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (y1 <= -3.4e+41)
		tmp = t_1;
	elseif (y1 <= -2.4e-137)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y1 <= 9.4e-141)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (y1 <= 2.2e+49)
		tmp = x * (y0 * ((c * y2) - (b * 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[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -1.25e+194], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3.4e+41], t$95$1, If[LessEqual[y1, -2.4e-137], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 9.4e-141], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.2e+49], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y1 < -1.24999999999999997e194

   1. Initial program 41.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 49.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 49.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 49.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 49.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 49.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 49.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 49.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 49.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 49.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 49.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf 62.2%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   if -1.24999999999999997e194 < y1 < -3.39999999999999998e41 or 2.2000000000000001e49 < y1

   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 y1 around -inf 58.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 58.5%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 58.5%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 58.5%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 58.5%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 58.5%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 58.5%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 58.5%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 58.5%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 58.5%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 58.5%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in i around -inf 55.4%

      \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if -3.39999999999999998e41 < y1 < -2.4e-137

   1. Initial program 31.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 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 63.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

   if -2.4e-137 < y1 < 9.3999999999999995e-141

   1. Initial program 43.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 38.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 38.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 38.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 38.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 38.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 38.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 38.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 38.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 38.1%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 38.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y5 around inf 37.0%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if 9.3999999999999995e-141 < y1 < 2.2000000000000001e49

   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 x around inf 53.4%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y0 around inf 48.1%

      \[\leadsto \color{blue}{x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.25 \cdot 10^{+194}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -3.4 \cdot 10^{+41}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y1 \leq -2.4 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq 9.4 \cdot 10^{-141}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 2.2 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 22.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -3.2 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(\left(-a\right) \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -3 \cdot 10^{-179}:\\ \;\;\;\;a \cdot \left(\left(y \cdot y5\right) \cdot \left(-y3\right)\right)\\ \mathbf{elif}\;y1 \leq 4.6 \cdot 10^{-235}:\\ \;\;\;\;x \cdot \left(b \cdot \left(j \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 3 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 5.2 \cdot 10^{+189}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(z \cdot \left(-k \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -3.2e-13)
   (* x (* (- a) (* y1 y2)))
   (if (<= y1 -3e-179)
     (* a (* (* y y5) (- y3)))
     (if (<= y1 4.6e-235)
       (* x (* b (* j (- y0))))
       (if (<= y1 3e-15)
         (* x (* c (* y0 y2)))
         (if (<= y1 5.2e+189)
           (* i (* j (* x y1)))
           (* i (* z (- (* k 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 (y1 <= -3.2e-13) {
		tmp = x * (-a * (y1 * y2));
	} else if (y1 <= -3e-179) {
		tmp = a * ((y * y5) * -y3);
	} else if (y1 <= 4.6e-235) {
		tmp = x * (b * (j * -y0));
	} else if (y1 <= 3e-15) {
		tmp = x * (c * (y0 * y2));
	} else if (y1 <= 5.2e+189) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = i * (z * -(k * 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 (y1 <= (-3.2d-13)) then
        tmp = x * (-a * (y1 * y2))
    else if (y1 <= (-3d-179)) then
        tmp = a * ((y * y5) * -y3)
    else if (y1 <= 4.6d-235) then
        tmp = x * (b * (j * -y0))
    else if (y1 <= 3d-15) then
        tmp = x * (c * (y0 * y2))
    else if (y1 <= 5.2d+189) then
        tmp = i * (j * (x * y1))
    else
        tmp = i * (z * -(k * 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 (y1 <= -3.2e-13) {
		tmp = x * (-a * (y1 * y2));
	} else if (y1 <= -3e-179) {
		tmp = a * ((y * y5) * -y3);
	} else if (y1 <= 4.6e-235) {
		tmp = x * (b * (j * -y0));
	} else if (y1 <= 3e-15) {
		tmp = x * (c * (y0 * y2));
	} else if (y1 <= 5.2e+189) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = i * (z * -(k * 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 y1 <= -3.2e-13:
		tmp = x * (-a * (y1 * y2))
	elif y1 <= -3e-179:
		tmp = a * ((y * y5) * -y3)
	elif y1 <= 4.6e-235:
		tmp = x * (b * (j * -y0))
	elif y1 <= 3e-15:
		tmp = x * (c * (y0 * y2))
	elif y1 <= 5.2e+189:
		tmp = i * (j * (x * y1))
	else:
		tmp = i * (z * -(k * 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 (y1 <= -3.2e-13)
		tmp = Float64(x * Float64(Float64(-a) * Float64(y1 * y2)));
	elseif (y1 <= -3e-179)
		tmp = Float64(a * Float64(Float64(y * y5) * Float64(-y3)));
	elseif (y1 <= 4.6e-235)
		tmp = Float64(x * Float64(b * Float64(j * Float64(-y0))));
	elseif (y1 <= 3e-15)
		tmp = Float64(x * Float64(c * Float64(y0 * y2)));
	elseif (y1 <= 5.2e+189)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	else
		tmp = Float64(i * Float64(z * Float64(-Float64(k * 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 (y1 <= -3.2e-13)
		tmp = x * (-a * (y1 * y2));
	elseif (y1 <= -3e-179)
		tmp = a * ((y * y5) * -y3);
	elseif (y1 <= 4.6e-235)
		tmp = x * (b * (j * -y0));
	elseif (y1 <= 3e-15)
		tmp = x * (c * (y0 * y2));
	elseif (y1 <= 5.2e+189)
		tmp = i * (j * (x * y1));
	else
		tmp = i * (z * -(k * 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[LessEqual[y1, -3.2e-13], N[(x * N[((-a) * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3e-179], N[(a * N[(N[(y * y5), $MachinePrecision] * (-y3)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 4.6e-235], N[(x * N[(b * N[(j * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3e-15], N[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 5.2e+189], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(z * (-N[(k * y1), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y1 < -3.2e-13

   1. Initial program 36.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 42.0%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y2 around inf 42.2%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around 0 44.1%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(y1 \cdot y2\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 44.1%

         \[\leadsto x \cdot \color{blue}{\left(\left(-1 \cdot a\right) \cdot \left(y1 \cdot y2\right)\right)} \]

      2. neg-mul-1 44.1%

         \[\leadsto x \cdot \left(\color{blue}{\left(-a\right)} \cdot \left(y1 \cdot y2\right)\right) \]

   7. Simplified 44.1%

      \[\leadsto x \cdot \color{blue}{\left(\left(-a\right) \cdot \left(y1 \cdot y2\right)\right)} \]

   if -3.2e-13 < y1 < -3.00000000000000006e-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 a around inf 39.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 39.8%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 39.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 39.8%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 39.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 39.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 39.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 39.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 39.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 39.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around -inf 26.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 26.3%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

      2. neg-mul-1 26.3%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]

   8. Simplified 26.3%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf 26.0%

      \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \color{blue}{\left(y \cdot y5\right)}\right) \]

   if -3.00000000000000006e-179 < y1 < 4.59999999999999995e-235

   1. Initial program 41.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 36.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around 0 39.2%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf 30.8%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(j \cdot y0\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 30.8%

         \[\leadsto x \cdot \color{blue}{\left(-b \cdot \left(j \cdot y0\right)\right)} \]

      2. distribute-rgt-neg-in 30.8%

         \[\leadsto x \cdot \color{blue}{\left(b \cdot \left(-j \cdot y0\right)\right)} \]

      3. *-commutative 30.8%

         \[\leadsto x \cdot \left(b \cdot \left(-\color{blue}{y0 \cdot j}\right)\right) \]

      4. distribute-rgt-neg-in 30.8%

         \[\leadsto x \cdot \left(b \cdot \color{blue}{\left(y0 \cdot \left(-j\right)\right)}\right) \]

   7. Simplified 30.8%

      \[\leadsto x \cdot \color{blue}{\left(b \cdot \left(y0 \cdot \left(-j\right)\right)\right)} \]

   if 4.59999999999999995e-235 < y1 < 3e-15

   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 x around inf 47.5%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y2 around inf 40.2%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around inf 42.3%

      \[\leadsto x \cdot \color{blue}{\left(c \cdot \left(y0 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 42.3%

         \[\leadsto x \cdot \left(c \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

   7. Simplified 42.3%

      \[\leadsto x \cdot \color{blue}{\left(c \cdot \left(y2 \cdot y0\right)\right)} \]

   if 3e-15 < y1 < 5.19999999999999963e189

   1. Initial program 37.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 48.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 48.6%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 48.6%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 48.6%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 48.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 48.6%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 48.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 48.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 48.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 48.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 48.6%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around 0 50.7%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   7. Taylor expanded in j around inf 33.6%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]

   if 5.19999999999999963e189 < y1

   1. Initial program 26.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 57.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 57.6%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 57.6%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 57.6%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 57.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 57.6%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 57.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 57.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 57.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 57.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 57.6%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around 0 73.1%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 69.3%

      \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - \color{blue}{x \cdot \left(-1 \cdot \frac{i \cdot \left(k \cdot z\right)}{x} + i \cdot j\right)}\right) \]
   8. Step-by-step derivation

      1. +-commutative 69.3%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \color{blue}{\left(i \cdot j + -1 \cdot \frac{i \cdot \left(k \cdot z\right)}{x}\right)}\right) \]

      2. mul-1-neg 69.3%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \left(i \cdot j + \color{blue}{\left(-\frac{i \cdot \left(k \cdot z\right)}{x}\right)}\right)\right) \]

      3. unsub-neg 69.3%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \color{blue}{\left(i \cdot j - \frac{i \cdot \left(k \cdot z\right)}{x}\right)}\right) \]

      4. associate-/l* 69.3%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \left(i \cdot j - \color{blue}{i \cdot \frac{k \cdot z}{x}}\right)\right) \]

      5. *-commutative 69.3%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \left(i \cdot j - i \cdot \frac{\color{blue}{z \cdot k}}{x}\right)\right) \]

   9. Simplified 69.3%

      \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - \color{blue}{x \cdot \left(i \cdot j - i \cdot \frac{z \cdot k}{x}\right)}\right) \]

   10. Taylor expanded in k around inf 50.9%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 50.9%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. associate-*r* 54.9%

          \[\leadsto -i \cdot \color{blue}{\left(\left(k \cdot y1\right) \cdot z\right)} \]

   12. Simplified 54.9%

       \[\leadsto \color{blue}{-i \cdot \left(\left(k \cdot y1\right) \cdot z\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -3.2 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(\left(-a\right) \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -3 \cdot 10^{-179}:\\ \;\;\;\;a \cdot \left(\left(y \cdot y5\right) \cdot \left(-y3\right)\right)\\ \mathbf{elif}\;y1 \leq 4.6 \cdot 10^{-235}:\\ \;\;\;\;x \cdot \left(b \cdot \left(j \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 3 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 5.2 \cdot 10^{+189}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(z \cdot \left(-k \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 21.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\left(-a\right) \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{if}\;y2 \leq -1.35 \cdot 10^{+209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq -1.5 \cdot 10^{-51}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq -2.1 \cdot 10^{-217}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 1.72 \cdot 10^{-106}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(x \cdot y1\right)\\ \mathbf{elif}\;y2 \leq 3 \cdot 10^{+23}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \left(b \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* x (* (- a) (* y1 y2)))))
   (if (<= y2 -1.35e+209)
     t_1
     (if (<= y2 -1.5e-51)
       (* x (* i (* j y1)))
       (if (<= y2 -2.1e-217)
         (* y1 (* z (* a y3)))
         (if (<= y2 1.72e-106)
           (* (* i j) (* x y1))
           (if (<= y2 3e+23) (* (* x y0) (* b (- 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 = x * (-a * (y1 * y2));
	double tmp;
	if (y2 <= -1.35e+209) {
		tmp = t_1;
	} else if (y2 <= -1.5e-51) {
		tmp = x * (i * (j * y1));
	} else if (y2 <= -2.1e-217) {
		tmp = y1 * (z * (a * y3));
	} else if (y2 <= 1.72e-106) {
		tmp = (i * j) * (x * y1);
	} else if (y2 <= 3e+23) {
		tmp = (x * y0) * (b * -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) :: tmp
    t_1 = x * (-a * (y1 * y2))
    if (y2 <= (-1.35d+209)) then
        tmp = t_1
    else if (y2 <= (-1.5d-51)) then
        tmp = x * (i * (j * y1))
    else if (y2 <= (-2.1d-217)) then
        tmp = y1 * (z * (a * y3))
    else if (y2 <= 1.72d-106) then
        tmp = (i * j) * (x * y1)
    else if (y2 <= 3d+23) then
        tmp = (x * y0) * (b * -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 = x * (-a * (y1 * y2));
	double tmp;
	if (y2 <= -1.35e+209) {
		tmp = t_1;
	} else if (y2 <= -1.5e-51) {
		tmp = x * (i * (j * y1));
	} else if (y2 <= -2.1e-217) {
		tmp = y1 * (z * (a * y3));
	} else if (y2 <= 1.72e-106) {
		tmp = (i * j) * (x * y1);
	} else if (y2 <= 3e+23) {
		tmp = (x * y0) * (b * -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 = x * (-a * (y1 * y2))
	tmp = 0
	if y2 <= -1.35e+209:
		tmp = t_1
	elif y2 <= -1.5e-51:
		tmp = x * (i * (j * y1))
	elif y2 <= -2.1e-217:
		tmp = y1 * (z * (a * y3))
	elif y2 <= 1.72e-106:
		tmp = (i * j) * (x * y1)
	elif y2 <= 3e+23:
		tmp = (x * y0) * (b * -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(x * Float64(Float64(-a) * Float64(y1 * y2)))
	tmp = 0.0
	if (y2 <= -1.35e+209)
		tmp = t_1;
	elseif (y2 <= -1.5e-51)
		tmp = Float64(x * Float64(i * Float64(j * y1)));
	elseif (y2 <= -2.1e-217)
		tmp = Float64(y1 * Float64(z * Float64(a * y3)));
	elseif (y2 <= 1.72e-106)
		tmp = Float64(Float64(i * j) * Float64(x * y1));
	elseif (y2 <= 3e+23)
		tmp = Float64(Float64(x * y0) * Float64(b * Float64(-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 = x * (-a * (y1 * y2));
	tmp = 0.0;
	if (y2 <= -1.35e+209)
		tmp = t_1;
	elseif (y2 <= -1.5e-51)
		tmp = x * (i * (j * y1));
	elseif (y2 <= -2.1e-217)
		tmp = y1 * (z * (a * y3));
	elseif (y2 <= 1.72e-106)
		tmp = (i * j) * (x * y1);
	elseif (y2 <= 3e+23)
		tmp = (x * y0) * (b * -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[(x * N[((-a) * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.35e+209], t$95$1, If[LessEqual[y2, -1.5e-51], N[(x * N[(i * N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.1e-217], N[(y1 * N[(z * N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.72e-106], N[(N[(i * j), $MachinePrecision] * N[(x * y1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3e+23], N[(N[(x * y0), $MachinePrecision] * N[(b * (-j)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -1.35e209 or 3.0000000000000001e23 < y2

   1. Initial program 29.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 42.2%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y2 around inf 51.5%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around 0 45.3%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(y1 \cdot y2\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 45.3%

         \[\leadsto x \cdot \color{blue}{\left(\left(-1 \cdot a\right) \cdot \left(y1 \cdot y2\right)\right)} \]

      2. neg-mul-1 45.3%

         \[\leadsto x \cdot \left(\color{blue}{\left(-a\right)} \cdot \left(y1 \cdot y2\right)\right) \]

   7. Simplified 45.3%

      \[\leadsto x \cdot \color{blue}{\left(\left(-a\right) \cdot \left(y1 \cdot y2\right)\right)} \]

   if -1.35e209 < y2 < -1.50000000000000001e-51

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 52.7%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around 0 46.9%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in i around inf 33.9%

      \[\leadsto x \cdot \color{blue}{\left(i \cdot \left(j \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 33.9%

         \[\leadsto x \cdot \left(i \cdot \color{blue}{\left(y1 \cdot j\right)}\right) \]

   7. Simplified 33.9%

      \[\leadsto x \cdot \color{blue}{\left(i \cdot \left(y1 \cdot j\right)\right)} \]

   if -1.50000000000000001e-51 < y2 < -2.1e-217

   1. Initial program 50.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 12.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 12.5%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 12.5%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 12.5%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 12.5%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 12.5%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 12.5%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 12.5%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 12.5%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 12.5%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 12.5%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y3 around -inf 20.6%

      \[\leadsto \color{blue}{y1 \cdot \left(y3 \cdot \left(a \cdot z - j \cdot y4\right)\right)} \]

   7. Taylor expanded in a around inf 28.3%

      \[\leadsto y1 \cdot \color{blue}{\left(a \cdot \left(y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 35.7%

         \[\leadsto y1 \cdot \color{blue}{\left(\left(a \cdot y3\right) \cdot z\right)} \]

   9. Simplified 35.7%

      \[\leadsto y1 \cdot \color{blue}{\left(\left(a \cdot y3\right) \cdot z\right)} \]

   if -2.1e-217 < y2 < 1.7199999999999999e-106

   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 y1 around -inf 41.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 41.9%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 41.9%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 41.9%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 41.9%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 41.9%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 41.9%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 41.9%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 41.9%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 41.9%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 41.9%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around 0 39.8%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   7. Taylor expanded in j around inf 24.1%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 26.8%

         \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(x \cdot y1\right)} \]

      2. *-commutative 26.8%

         \[\leadsto \left(i \cdot j\right) \cdot \color{blue}{\left(y1 \cdot x\right)} \]

   9. Simplified 26.8%

      \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(y1 \cdot x\right)} \]

   if 1.7199999999999999e-106 < y2 < 3.0000000000000001e23

   1. Initial program 41.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 53.4%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around 0 42.1%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf 36.7%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot \left(x \cdot y0\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 36.7%

         \[\leadsto \color{blue}{-b \cdot \left(j \cdot \left(x \cdot y0\right)\right)} \]

      2. associate-*r* 42.3%

         \[\leadsto -\color{blue}{\left(b \cdot j\right) \cdot \left(x \cdot y0\right)} \]

      3. *-commutative 42.3%

         \[\leadsto -\color{blue}{\left(j \cdot b\right)} \cdot \left(x \cdot y0\right) \]

   7. Simplified 42.3%

      \[\leadsto \color{blue}{-\left(j \cdot b\right) \cdot \left(x \cdot y0\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.35 \cdot 10^{+209}:\\ \;\;\;\;x \cdot \left(\left(-a\right) \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -1.5 \cdot 10^{-51}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq -2.1 \cdot 10^{-217}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 1.72 \cdot 10^{-106}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(x \cdot y1\right)\\ \mathbf{elif}\;y2 \leq 3 \cdot 10^{+23}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \left(b \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(-a\right) \cdot \left(y1 \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 22.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -7.2 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \left(\left(-a\right) \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -1.2 \cdot 10^{-178}:\\ \;\;\;\;a \cdot \left(\left(y \cdot y5\right) \cdot \left(-y3\right)\right)\\ \mathbf{elif}\;y1 \leq 4.4 \cdot 10^{-236}:\\ \;\;\;\;x \cdot \left(b \cdot \left(j \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 3.5 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 4.5 \cdot 10^{+189}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -7.2e-14)
   (* x (* (- a) (* y1 y2)))
   (if (<= y1 -1.2e-178)
     (* a (* (* y y5) (- y3)))
     (if (<= y1 4.4e-236)
       (* x (* b (* j (- y0))))
       (if (<= y1 3.5e-15)
         (* x (* c (* y0 y2)))
         (if (<= y1 4.5e+189) (* i (* j (* x y1))) (* a (* y3 (* z 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 (y1 <= -7.2e-14) {
		tmp = x * (-a * (y1 * y2));
	} else if (y1 <= -1.2e-178) {
		tmp = a * ((y * y5) * -y3);
	} else if (y1 <= 4.4e-236) {
		tmp = x * (b * (j * -y0));
	} else if (y1 <= 3.5e-15) {
		tmp = x * (c * (y0 * y2));
	} else if (y1 <= 4.5e+189) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = a * (y3 * (z * 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 (y1 <= (-7.2d-14)) then
        tmp = x * (-a * (y1 * y2))
    else if (y1 <= (-1.2d-178)) then
        tmp = a * ((y * y5) * -y3)
    else if (y1 <= 4.4d-236) then
        tmp = x * (b * (j * -y0))
    else if (y1 <= 3.5d-15) then
        tmp = x * (c * (y0 * y2))
    else if (y1 <= 4.5d+189) then
        tmp = i * (j * (x * y1))
    else
        tmp = a * (y3 * (z * 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 (y1 <= -7.2e-14) {
		tmp = x * (-a * (y1 * y2));
	} else if (y1 <= -1.2e-178) {
		tmp = a * ((y * y5) * -y3);
	} else if (y1 <= 4.4e-236) {
		tmp = x * (b * (j * -y0));
	} else if (y1 <= 3.5e-15) {
		tmp = x * (c * (y0 * y2));
	} else if (y1 <= 4.5e+189) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = a * (y3 * (z * 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 y1 <= -7.2e-14:
		tmp = x * (-a * (y1 * y2))
	elif y1 <= -1.2e-178:
		tmp = a * ((y * y5) * -y3)
	elif y1 <= 4.4e-236:
		tmp = x * (b * (j * -y0))
	elif y1 <= 3.5e-15:
		tmp = x * (c * (y0 * y2))
	elif y1 <= 4.5e+189:
		tmp = i * (j * (x * y1))
	else:
		tmp = a * (y3 * (z * 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 (y1 <= -7.2e-14)
		tmp = Float64(x * Float64(Float64(-a) * Float64(y1 * y2)));
	elseif (y1 <= -1.2e-178)
		tmp = Float64(a * Float64(Float64(y * y5) * Float64(-y3)));
	elseif (y1 <= 4.4e-236)
		tmp = Float64(x * Float64(b * Float64(j * Float64(-y0))));
	elseif (y1 <= 3.5e-15)
		tmp = Float64(x * Float64(c * Float64(y0 * y2)));
	elseif (y1 <= 4.5e+189)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	else
		tmp = Float64(a * Float64(y3 * Float64(z * 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 (y1 <= -7.2e-14)
		tmp = x * (-a * (y1 * y2));
	elseif (y1 <= -1.2e-178)
		tmp = a * ((y * y5) * -y3);
	elseif (y1 <= 4.4e-236)
		tmp = x * (b * (j * -y0));
	elseif (y1 <= 3.5e-15)
		tmp = x * (c * (y0 * y2));
	elseif (y1 <= 4.5e+189)
		tmp = i * (j * (x * y1));
	else
		tmp = a * (y3 * (z * 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[LessEqual[y1, -7.2e-14], N[(x * N[((-a) * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.2e-178], N[(a * N[(N[(y * y5), $MachinePrecision] * (-y3)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 4.4e-236], N[(x * N[(b * N[(j * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.5e-15], N[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 4.5e+189], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y1 < -7.1999999999999996e-14

   1. Initial program 36.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 42.0%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y2 around inf 42.2%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around 0 44.1%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(y1 \cdot y2\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 44.1%

         \[\leadsto x \cdot \color{blue}{\left(\left(-1 \cdot a\right) \cdot \left(y1 \cdot y2\right)\right)} \]

      2. neg-mul-1 44.1%

         \[\leadsto x \cdot \left(\color{blue}{\left(-a\right)} \cdot \left(y1 \cdot y2\right)\right) \]

   7. Simplified 44.1%

      \[\leadsto x \cdot \color{blue}{\left(\left(-a\right) \cdot \left(y1 \cdot y2\right)\right)} \]

   if -7.1999999999999996e-14 < y1 < -1.20000000000000002e-178

   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 a around inf 39.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 39.8%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 39.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 39.8%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 39.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 39.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 39.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 39.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 39.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 39.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around -inf 26.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 26.3%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

      2. neg-mul-1 26.3%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]

   8. Simplified 26.3%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf 26.0%

      \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \color{blue}{\left(y \cdot y5\right)}\right) \]

   if -1.20000000000000002e-178 < y1 < 4.39999999999999985e-236

   1. Initial program 41.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 36.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around 0 39.2%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf 30.8%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(j \cdot y0\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 30.8%

         \[\leadsto x \cdot \color{blue}{\left(-b \cdot \left(j \cdot y0\right)\right)} \]

      2. distribute-rgt-neg-in 30.8%

         \[\leadsto x \cdot \color{blue}{\left(b \cdot \left(-j \cdot y0\right)\right)} \]

      3. *-commutative 30.8%

         \[\leadsto x \cdot \left(b \cdot \left(-\color{blue}{y0 \cdot j}\right)\right) \]

      4. distribute-rgt-neg-in 30.8%

         \[\leadsto x \cdot \left(b \cdot \color{blue}{\left(y0 \cdot \left(-j\right)\right)}\right) \]

   7. Simplified 30.8%

      \[\leadsto x \cdot \color{blue}{\left(b \cdot \left(y0 \cdot \left(-j\right)\right)\right)} \]

   if 4.39999999999999985e-236 < y1 < 3.5000000000000001e-15

   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 x around inf 47.5%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y2 around inf 40.2%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around inf 42.3%

      \[\leadsto x \cdot \color{blue}{\left(c \cdot \left(y0 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 42.3%

         \[\leadsto x \cdot \left(c \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

   7. Simplified 42.3%

      \[\leadsto x \cdot \color{blue}{\left(c \cdot \left(y2 \cdot y0\right)\right)} \]

   if 3.5000000000000001e-15 < y1 < 4.49999999999999973e189

   1. Initial program 37.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 48.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 48.6%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 48.6%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 48.6%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 48.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 48.6%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 48.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 48.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 48.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 48.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 48.6%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around 0 50.7%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   7. Taylor expanded in j around inf 33.6%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]

   if 4.49999999999999973e189 < y1

   1. Initial program 26.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 54.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 54.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 54.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 54.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 54.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 54.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 54.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 54.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 54.0%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 54.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around -inf 58.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 58.3%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

      2. neg-mul-1 58.3%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]

   8. Simplified 58.3%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

   9. Taylor expanded in y around 0 58.8%

      \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot z\right)\right)}\right) \]
   10. Step-by-step derivation

       1. neg-mul-1 58.8%

          \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \color{blue}{\left(-y1 \cdot z\right)}\right) \]

       2. distribute-lft-neg-in 58.8%

          \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \color{blue}{\left(\left(-y1\right) \cdot z\right)}\right) \]

       3. *-commutative 58.8%

          \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \color{blue}{\left(z \cdot \left(-y1\right)\right)}\right) \]

   11. Simplified 58.8%

       \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \color{blue}{\left(z \cdot \left(-y1\right)\right)}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -7.2 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \left(\left(-a\right) \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -1.2 \cdot 10^{-178}:\\ \;\;\;\;a \cdot \left(\left(y \cdot y5\right) \cdot \left(-y3\right)\right)\\ \mathbf{elif}\;y1 \leq 4.4 \cdot 10^{-236}:\\ \;\;\;\;x \cdot \left(b \cdot \left(j \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 3.5 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 4.5 \cdot 10^{+189}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 31.2% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;y5 \leq -2.9 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq -5.8 \cdot 10^{-270}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.4 \cdot 10^{-200}:\\ \;\;\;\;y1 \cdot \left(x \cdot \left(i \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 2.1 \cdot 10^{-33}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y5 (- (* t y2) (* y y3))))))
   (if (<= y5 -2.9e+102)
     t_1
     (if (<= y5 -5.8e-270)
       (* a (* y1 (- (* z y3) (* x y2))))
       (if (<= y5 1.4e-200)
         (* y1 (* x (* i j)))
         (if (<= y5 2.1e-33) (* b (* a (- (* x y) (* z t)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (y5 <= -2.9e+102) {
		tmp = t_1;
	} else if (y5 <= -5.8e-270) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y5 <= 1.4e-200) {
		tmp = y1 * (x * (i * j));
	} else if (y5 <= 2.1e-33) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y5 * ((t * y2) - (y * y3)))
    if (y5 <= (-2.9d+102)) then
        tmp = t_1
    else if (y5 <= (-5.8d-270)) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (y5 <= 1.4d-200) then
        tmp = y1 * (x * (i * j))
    else if (y5 <= 2.1d-33) then
        tmp = b * (a * ((x * y) - (z * t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (y5 <= -2.9e+102) {
		tmp = t_1;
	} else if (y5 <= -5.8e-270) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y5 <= 1.4e-200) {
		tmp = y1 * (x * (i * j));
	} else if (y5 <= 2.1e-33) {
		tmp = b * (a * ((x * y) - (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y5 * ((t * y2) - (y * y3)))
	tmp = 0
	if y5 <= -2.9e+102:
		tmp = t_1
	elif y5 <= -5.8e-270:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif y5 <= 1.4e-200:
		tmp = y1 * (x * (i * j))
	elif y5 <= 2.1e-33:
		tmp = b * (a * ((x * y) - (z * t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	tmp = 0.0
	if (y5 <= -2.9e+102)
		tmp = t_1;
	elseif (y5 <= -5.8e-270)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (y5 <= 1.4e-200)
		tmp = Float64(y1 * Float64(x * Float64(i * j)));
	elseif (y5 <= 2.1e-33)
		tmp = Float64(b * Float64(a * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y5 * ((t * y2) - (y * y3)));
	tmp = 0.0;
	if (y5 <= -2.9e+102)
		tmp = t_1;
	elseif (y5 <= -5.8e-270)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (y5 <= 1.4e-200)
		tmp = y1 * (x * (i * j));
	elseif (y5 <= 2.1e-33)
		tmp = b * (a * ((x * y) - (z * t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -2.9e+102], t$95$1, If[LessEqual[y5, -5.8e-270], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.4e-200], N[(y1 * N[(x * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.1e-33], N[(b * N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y5 < -2.9000000000000002e102 or 2.1e-33 < y5

   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 a around inf 40.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 40.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 40.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 40.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 40.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 40.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 40.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 40.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 40.6%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 40.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y5 around inf 44.6%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -2.9000000000000002e102 < y5 < -5.79999999999999965e-270

   1. Initial program 43.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 44.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 44.9%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 44.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 44.9%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 44.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 44.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 44.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 44.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 44.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 44.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf 50.1%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   if -5.79999999999999965e-270 < y5 < 1.40000000000000003e-200

   1. Initial program 45.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 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. associate-*r* 52.3%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 52.3%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 52.3%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 52.3%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 52.3%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 52.3%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 52.3%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 52.3%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 52.3%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 52.3%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around 0 52.4%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   7. Taylor expanded in j around inf 42.9%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 42.9%

         \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(-i \cdot \left(j \cdot x\right)\right)} \]

      2. associate-*r* 46.0%

         \[\leadsto \left(-y1\right) \cdot \left(-\color{blue}{\left(i \cdot j\right) \cdot x}\right) \]

      3. distribute-lft-neg-in 46.0%

         \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(\left(-i \cdot j\right) \cdot x\right)} \]

      4. distribute-rgt-neg-in 46.0%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(i \cdot \left(-j\right)\right)} \cdot x\right) \]

   9. Simplified 46.0%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(\left(i \cdot \left(-j\right)\right) \cdot x\right)} \]

   if 1.40000000000000003e-200 < y5 < 2.1e-33

   1. Initial program 33.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 44.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in a around inf 32.3%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2.9 \cdot 10^{+102}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -5.8 \cdot 10^{-270}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 1.4 \cdot 10^{-200}:\\ \;\;\;\;y1 \cdot \left(x \cdot \left(i \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 2.1 \cdot 10^{-33}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 29.8% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;y5 \leq -3.3 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq -1.12 \cdot 10^{-269}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 2.8 \cdot 10^{-181}:\\ \;\;\;\;y1 \cdot \left(x \cdot \left(i \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 10^{-100}:\\ \;\;\;\;b \cdot \left(j \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y5 (- (* t y2) (* y y3))))))
   (if (<= y5 -3.3e+102)
     t_1
     (if (<= y5 -1.12e-269)
       (* a (* y1 (- (* z y3) (* x y2))))
       (if (<= y5 2.8e-181)
         (* y1 (* x (* i j)))
         (if (<= y5 1e-100) (* b (* j (* x (- 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 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (y5 <= -3.3e+102) {
		tmp = t_1;
	} else if (y5 <= -1.12e-269) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y5 <= 2.8e-181) {
		tmp = y1 * (x * (i * j));
	} else if (y5 <= 1e-100) {
		tmp = b * (j * (x * -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 = a * (y5 * ((t * y2) - (y * y3)))
    if (y5 <= (-3.3d+102)) then
        tmp = t_1
    else if (y5 <= (-1.12d-269)) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (y5 <= 2.8d-181) then
        tmp = y1 * (x * (i * j))
    else if (y5 <= 1d-100) then
        tmp = b * (j * (x * -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 = a * (y5 * ((t * y2) - (y * y3)));
	double tmp;
	if (y5 <= -3.3e+102) {
		tmp = t_1;
	} else if (y5 <= -1.12e-269) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y5 <= 2.8e-181) {
		tmp = y1 * (x * (i * j));
	} else if (y5 <= 1e-100) {
		tmp = b * (j * (x * -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 = a * (y5 * ((t * y2) - (y * y3)))
	tmp = 0
	if y5 <= -3.3e+102:
		tmp = t_1
	elif y5 <= -1.12e-269:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif y5 <= 2.8e-181:
		tmp = y1 * (x * (i * j))
	elif y5 <= 1e-100:
		tmp = b * (j * (x * -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(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))
	tmp = 0.0
	if (y5 <= -3.3e+102)
		tmp = t_1;
	elseif (y5 <= -1.12e-269)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (y5 <= 2.8e-181)
		tmp = Float64(y1 * Float64(x * Float64(i * j)));
	elseif (y5 <= 1e-100)
		tmp = Float64(b * Float64(j * Float64(x * Float64(-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 = a * (y5 * ((t * y2) - (y * y3)));
	tmp = 0.0;
	if (y5 <= -3.3e+102)
		tmp = t_1;
	elseif (y5 <= -1.12e-269)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (y5 <= 2.8e-181)
		tmp = y1 * (x * (i * j));
	elseif (y5 <= 1e-100)
		tmp = b * (j * (x * -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[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -3.3e+102], t$95$1, If[LessEqual[y5, -1.12e-269], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.8e-181], N[(y1 * N[(x * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1e-100], N[(b * N[(j * N[(x * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y5 < -3.29999999999999999e102 or 1e-100 < y5

   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 a around inf 39.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 39.8%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 39.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 39.8%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 39.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 39.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 39.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 39.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 39.8%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 39.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y5 around inf 43.3%

      \[\leadsto \color{blue}{a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -3.29999999999999999e102 < y5 < -1.12e-269

   1. Initial program 43.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 44.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 44.9%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 44.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 44.9%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 44.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 44.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 44.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 44.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 44.9%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 44.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf 50.1%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   if -1.12e-269 < y5 < 2.79999999999999986e-181

   1. Initial program 45.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 49.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 49.1%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 49.1%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 49.1%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 49.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 49.1%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 49.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 49.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 49.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 49.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 49.1%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around 0 49.3%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   7. Taylor expanded in j around inf 40.5%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 40.5%

         \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(-i \cdot \left(j \cdot x\right)\right)} \]

      2. associate-*r* 43.4%

         \[\leadsto \left(-y1\right) \cdot \left(-\color{blue}{\left(i \cdot j\right) \cdot x}\right) \]

      3. distribute-lft-neg-in 43.4%

         \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(\left(-i \cdot j\right) \cdot x\right)} \]

      4. distribute-rgt-neg-in 43.4%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(i \cdot \left(-j\right)\right)} \cdot x\right) \]

   9. Simplified 43.4%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(\left(i \cdot \left(-j\right)\right) \cdot x\right)} \]

   if 2.79999999999999986e-181 < y5 < 1e-100

   1. Initial program 36.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 51.0%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around 0 46.6%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf 33.6%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot \left(x \cdot y0\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 33.6%

         \[\leadsto \color{blue}{-b \cdot \left(j \cdot \left(x \cdot y0\right)\right)} \]

      2. distribute-rgt-neg-in 33.6%

         \[\leadsto \color{blue}{b \cdot \left(-j \cdot \left(x \cdot y0\right)\right)} \]

      3. *-commutative 33.6%

         \[\leadsto b \cdot \left(-\color{blue}{\left(x \cdot y0\right) \cdot j}\right) \]

      4. distribute-rgt-neg-in 33.6%

         \[\leadsto b \cdot \color{blue}{\left(\left(x \cdot y0\right) \cdot \left(-j\right)\right)} \]

   7. Simplified 33.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(x \cdot y0\right) \cdot \left(-j\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -3.3 \cdot 10^{+102}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq -1.12 \cdot 10^{-269}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 2.8 \cdot 10^{-181}:\\ \;\;\;\;y1 \cdot \left(x \cdot \left(i \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 10^{-100}:\\ \;\;\;\;b \cdot \left(j \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 26.3% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{if}\;j \leq -3.2 \cdot 10^{+253}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -3.3 \cdot 10^{-104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -4.7 \cdot 10^{-240}:\\ \;\;\;\;a \cdot \left(\left(y \cdot y5\right) \cdot \left(-y3\right)\right)\\ \mathbf{elif}\;j \leq 330000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(x \cdot \left(i \cdot j\right)\right)\\ \end{array} \end{array} \]

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 (- (* z y3) (* x y2))))))
   (if (<= j -3.2e+253)
     (* x (* i (* j y1)))
     (if (<= j -3.3e-104)
       t_1
       (if (<= j -4.7e-240)
         (* a (* (* y y5) (- y3)))
         (if (<= j 330000000.0) t_1 (* y1 (* x (* i j)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y1 * ((z * y3) - (x * y2)));
	double tmp;
	if (j <= -3.2e+253) {
		tmp = x * (i * (j * y1));
	} else if (j <= -3.3e-104) {
		tmp = t_1;
	} else if (j <= -4.7e-240) {
		tmp = a * ((y * y5) * -y3);
	} else if (j <= 330000000.0) {
		tmp = t_1;
	} else {
		tmp = y1 * (x * (i * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y1 * ((z * y3) - (x * y2)))
    if (j <= (-3.2d+253)) then
        tmp = x * (i * (j * y1))
    else if (j <= (-3.3d-104)) then
        tmp = t_1
    else if (j <= (-4.7d-240)) then
        tmp = a * ((y * y5) * -y3)
    else if (j <= 330000000.0d0) then
        tmp = t_1
    else
        tmp = y1 * (x * (i * j))
    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 * ((z * y3) - (x * y2)));
	double tmp;
	if (j <= -3.2e+253) {
		tmp = x * (i * (j * y1));
	} else if (j <= -3.3e-104) {
		tmp = t_1;
	} else if (j <= -4.7e-240) {
		tmp = a * ((y * y5) * -y3);
	} else if (j <= 330000000.0) {
		tmp = t_1;
	} else {
		tmp = y1 * (x * (i * j));
	}
	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 * ((z * y3) - (x * y2)))
	tmp = 0
	if j <= -3.2e+253:
		tmp = x * (i * (j * y1))
	elif j <= -3.3e-104:
		tmp = t_1
	elif j <= -4.7e-240:
		tmp = a * ((y * y5) * -y3)
	elif j <= 330000000.0:
		tmp = t_1
	else:
		tmp = y1 * (x * (i * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))))
	tmp = 0.0
	if (j <= -3.2e+253)
		tmp = Float64(x * Float64(i * Float64(j * y1)));
	elseif (j <= -3.3e-104)
		tmp = t_1;
	elseif (j <= -4.7e-240)
		tmp = Float64(a * Float64(Float64(y * y5) * Float64(-y3)));
	elseif (j <= 330000000.0)
		tmp = t_1;
	else
		tmp = Float64(y1 * Float64(x * Float64(i * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y1 * ((z * y3) - (x * y2)));
	tmp = 0.0;
	if (j <= -3.2e+253)
		tmp = x * (i * (j * y1));
	elseif (j <= -3.3e-104)
		tmp = t_1;
	elseif (j <= -4.7e-240)
		tmp = a * ((y * y5) * -y3);
	elseif (j <= 330000000.0)
		tmp = t_1;
	else
		tmp = y1 * (x * (i * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.2e+253], N[(x * N[(i * N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.3e-104], t$95$1, If[LessEqual[j, -4.7e-240], N[(a * N[(N[(y * y5), $MachinePrecision] * (-y3)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 330000000.0], t$95$1, N[(y1 * N[(x * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.2000000000000003e253

   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 x around inf 60.2%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around 0 67.3%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in i around inf 54.0%

      \[\leadsto x \cdot \color{blue}{\left(i \cdot \left(j \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 54.0%

         \[\leadsto x \cdot \left(i \cdot \color{blue}{\left(y1 \cdot j\right)}\right) \]

   7. Simplified 54.0%

      \[\leadsto x \cdot \color{blue}{\left(i \cdot \left(y1 \cdot j\right)\right)} \]

   if -3.2000000000000003e253 < j < -3.30000000000000002e-104 or -4.70000000000000012e-240 < j < 3.3e8

   1. Initial program 42.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 41.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 41.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 41.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 41.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 41.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 41.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 41.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 41.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 41.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 41.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf 35.7%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   if -3.30000000000000002e-104 < j < -4.70000000000000012e-240

   1. Initial program 24.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 38.4%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 38.4%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 38.4%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 38.4%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 38.4%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 38.4%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 38.4%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 38.4%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 38.4%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 38.4%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around -inf 48.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 48.5%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

      2. neg-mul-1 48.5%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]

   8. Simplified 48.5%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf 38.7%

      \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \color{blue}{\left(y \cdot y5\right)}\right) \]

   if 3.3e8 < j

   1. Initial program 27.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 45.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 45.8%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 45.8%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 45.8%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 45.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 45.8%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 45.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 45.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 45.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 45.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 45.8%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around 0 54.6%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   7. Taylor expanded in j around inf 47.9%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 47.9%

         \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(-i \cdot \left(j \cdot x\right)\right)} \]

      2. associate-*r* 49.2%

         \[\leadsto \left(-y1\right) \cdot \left(-\color{blue}{\left(i \cdot j\right) \cdot x}\right) \]

      3. distribute-lft-neg-in 49.2%

         \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(\left(-i \cdot j\right) \cdot x\right)} \]

      4. distribute-rgt-neg-in 49.2%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(i \cdot \left(-j\right)\right)} \cdot x\right) \]

   9. Simplified 49.2%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(\left(i \cdot \left(-j\right)\right) \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.2 \cdot 10^{+253}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -3.3 \cdot 10^{-104}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq -4.7 \cdot 10^{-240}:\\ \;\;\;\;a \cdot \left(\left(y \cdot y5\right) \cdot \left(-y3\right)\right)\\ \mathbf{elif}\;j \leq 330000000:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(x \cdot \left(i \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 21.5% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -9 \cdot 10^{+155}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -2.6 \cdot 10^{+64}:\\ \;\;\;\;i \cdot \left(z \cdot \left(-k \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -6.8 \cdot 10^{-241}:\\ \;\;\;\;a \cdot \left(\left(y \cdot y5\right) \cdot \left(-y3\right)\right)\\ \mathbf{elif}\;j \leq 12500000:\\ \;\;\;\;x \cdot \left(\left(-a\right) \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(x \cdot \left(i \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -9e+155)
   (* y1 (* i (* x j)))
   (if (<= j -2.6e+64)
     (* i (* z (- (* k y1))))
     (if (<= j -6.8e-241)
       (* a (* (* y y5) (- y3)))
       (if (<= j 12500000.0)
         (* x (* (- a) (* y1 y2)))
         (* y1 (* x (* i j))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -9e+155) {
		tmp = y1 * (i * (x * j));
	} else if (j <= -2.6e+64) {
		tmp = i * (z * -(k * y1));
	} else if (j <= -6.8e-241) {
		tmp = a * ((y * y5) * -y3);
	} else if (j <= 12500000.0) {
		tmp = x * (-a * (y1 * y2));
	} else {
		tmp = y1 * (x * (i * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (j <= (-9d+155)) then
        tmp = y1 * (i * (x * j))
    else if (j <= (-2.6d+64)) then
        tmp = i * (z * -(k * y1))
    else if (j <= (-6.8d-241)) then
        tmp = a * ((y * y5) * -y3)
    else if (j <= 12500000.0d0) then
        tmp = x * (-a * (y1 * y2))
    else
        tmp = y1 * (x * (i * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -9e+155) {
		tmp = y1 * (i * (x * j));
	} else if (j <= -2.6e+64) {
		tmp = i * (z * -(k * y1));
	} else if (j <= -6.8e-241) {
		tmp = a * ((y * y5) * -y3);
	} else if (j <= 12500000.0) {
		tmp = x * (-a * (y1 * y2));
	} else {
		tmp = y1 * (x * (i * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if j <= -9e+155:
		tmp = y1 * (i * (x * j))
	elif j <= -2.6e+64:
		tmp = i * (z * -(k * y1))
	elif j <= -6.8e-241:
		tmp = a * ((y * y5) * -y3)
	elif j <= 12500000.0:
		tmp = x * (-a * (y1 * y2))
	else:
		tmp = y1 * (x * (i * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -9e+155)
		tmp = Float64(y1 * Float64(i * Float64(x * j)));
	elseif (j <= -2.6e+64)
		tmp = Float64(i * Float64(z * Float64(-Float64(k * y1))));
	elseif (j <= -6.8e-241)
		tmp = Float64(a * Float64(Float64(y * y5) * Float64(-y3)));
	elseif (j <= 12500000.0)
		tmp = Float64(x * Float64(Float64(-a) * Float64(y1 * y2)));
	else
		tmp = Float64(y1 * Float64(x * Float64(i * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (j <= -9e+155)
		tmp = y1 * (i * (x * j));
	elseif (j <= -2.6e+64)
		tmp = i * (z * -(k * y1));
	elseif (j <= -6.8e-241)
		tmp = a * ((y * y5) * -y3);
	elseif (j <= 12500000.0)
		tmp = x * (-a * (y1 * y2));
	else
		tmp = y1 * (x * (i * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -9e+155], N[(y1 * N[(i * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.6e+64], N[(i * N[(z * (-N[(k * y1), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6.8e-241], N[(a * N[(N[(y * y5), $MachinePrecision] * (-y3)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 12500000.0], N[(x * N[((-a) * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(x * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -8.99999999999999947e155

   1. Initial program 23.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 29.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 29.0%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 29.0%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 29.0%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 29.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 29.0%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 29.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 29.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 29.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 29.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 29.0%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around 0 37.7%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   7. Taylor expanded in j around inf 40.7%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 40.7%

         \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(\left(-1 \cdot i\right) \cdot \left(j \cdot x\right)\right)} \]

      2. neg-mul-1 40.7%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(-i\right)} \cdot \left(j \cdot x\right)\right) \]

      3. *-commutative 40.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(-i\right) \cdot \color{blue}{\left(x \cdot j\right)}\right) \]

   9. Simplified 40.7%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(\left(-i\right) \cdot \left(x \cdot j\right)\right)} \]

   if -8.99999999999999947e155 < j < -2.59999999999999997e64

   1. Initial program 36.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 55.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 55.7%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 55.7%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 55.7%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 55.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 55.7%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 55.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 55.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 55.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 55.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 55.7%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around 0 53.5%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 48.3%

      \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - \color{blue}{x \cdot \left(-1 \cdot \frac{i \cdot \left(k \cdot z\right)}{x} + i \cdot j\right)}\right) \]
   8. Step-by-step derivation

      1. +-commutative 48.3%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \color{blue}{\left(i \cdot j + -1 \cdot \frac{i \cdot \left(k \cdot z\right)}{x}\right)}\right) \]

      2. mul-1-neg 48.3%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \left(i \cdot j + \color{blue}{\left(-\frac{i \cdot \left(k \cdot z\right)}{x}\right)}\right)\right) \]

      3. unsub-neg 48.3%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \color{blue}{\left(i \cdot j - \frac{i \cdot \left(k \cdot z\right)}{x}\right)}\right) \]

      4. associate-/l* 48.3%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \left(i \cdot j - \color{blue}{i \cdot \frac{k \cdot z}{x}}\right)\right) \]

      5. *-commutative 48.3%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \left(i \cdot j - i \cdot \frac{\color{blue}{z \cdot k}}{x}\right)\right) \]

   9. Simplified 48.3%

      \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - \color{blue}{x \cdot \left(i \cdot j - i \cdot \frac{z \cdot k}{x}\right)}\right) \]

   10. Taylor expanded in k around inf 33.1%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 33.1%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. associate-*r* 43.3%

          \[\leadsto -i \cdot \color{blue}{\left(\left(k \cdot y1\right) \cdot z\right)} \]

   12. Simplified 43.3%

       \[\leadsto \color{blue}{-i \cdot \left(\left(k \cdot y1\right) \cdot z\right)} \]

   if -2.59999999999999997e64 < j < -6.7999999999999998e-241

   1. Initial program 32.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 38.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 38.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 38.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 38.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 38.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 38.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 38.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 38.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 38.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 38.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around -inf 38.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 38.9%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

      2. neg-mul-1 38.9%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]

   8. Simplified 38.9%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf 29.6%

      \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \color{blue}{\left(y \cdot y5\right)}\right) \]

   if -6.7999999999999998e-241 < j < 1.25e7

   1. Initial program 49.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 51.4%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y2 around inf 40.1%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around 0 31.7%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(y1 \cdot y2\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 31.7%

         \[\leadsto x \cdot \color{blue}{\left(\left(-1 \cdot a\right) \cdot \left(y1 \cdot y2\right)\right)} \]

      2. neg-mul-1 31.7%

         \[\leadsto x \cdot \left(\color{blue}{\left(-a\right)} \cdot \left(y1 \cdot y2\right)\right) \]

   7. Simplified 31.7%

      \[\leadsto x \cdot \color{blue}{\left(\left(-a\right) \cdot \left(y1 \cdot y2\right)\right)} \]

   if 1.25e7 < j

   1. Initial program 27.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 45.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 45.8%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 45.8%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 45.8%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 45.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 45.8%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 45.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 45.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 45.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 45.8%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 45.8%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around 0 54.6%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   7. Taylor expanded in j around inf 47.9%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 47.9%

         \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(-i \cdot \left(j \cdot x\right)\right)} \]

      2. associate-*r* 49.2%

         \[\leadsto \left(-y1\right) \cdot \left(-\color{blue}{\left(i \cdot j\right) \cdot x}\right) \]

      3. distribute-lft-neg-in 49.2%

         \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(\left(-i \cdot j\right) \cdot x\right)} \]

      4. distribute-rgt-neg-in 49.2%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(i \cdot \left(-j\right)\right)} \cdot x\right) \]

   9. Simplified 49.2%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(\left(i \cdot \left(-j\right)\right) \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9 \cdot 10^{+155}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -2.6 \cdot 10^{+64}:\\ \;\;\;\;i \cdot \left(z \cdot \left(-k \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -6.8 \cdot 10^{-241}:\\ \;\;\;\;a \cdot \left(\left(y \cdot y5\right) \cdot \left(-y3\right)\right)\\ \mathbf{elif}\;j \leq 12500000:\\ \;\;\;\;x \cdot \left(\left(-a\right) \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(x \cdot \left(i \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 21.5% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \mathbf{if}\;j \leq -1.56 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1 \cdot 10^{+58}:\\ \;\;\;\;i \cdot \left(z \cdot \left(-k \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -6.6 \cdot 10^{-242}:\\ \;\;\;\;a \cdot \left(\left(y \cdot y5\right) \cdot \left(-y3\right)\right)\\ \mathbf{elif}\;j \leq 400000000:\\ \;\;\;\;x \cdot \left(\left(-a\right) \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* i (* x j)))))
   (if (<= j -1.56e+156)
     t_1
     (if (<= j -1e+58)
       (* i (* z (- (* k y1))))
       (if (<= j -6.6e-242)
         (* a (* (* y y5) (- y3)))
         (if (<= j 400000000.0) (* x (* (- a) (* y1 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 = y1 * (i * (x * j));
	double tmp;
	if (j <= -1.56e+156) {
		tmp = t_1;
	} else if (j <= -1e+58) {
		tmp = i * (z * -(k * y1));
	} else if (j <= -6.6e-242) {
		tmp = a * ((y * y5) * -y3);
	} else if (j <= 400000000.0) {
		tmp = x * (-a * (y1 * 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 = y1 * (i * (x * j))
    if (j <= (-1.56d+156)) then
        tmp = t_1
    else if (j <= (-1d+58)) then
        tmp = i * (z * -(k * y1))
    else if (j <= (-6.6d-242)) then
        tmp = a * ((y * y5) * -y3)
    else if (j <= 400000000.0d0) then
        tmp = x * (-a * (y1 * 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 = y1 * (i * (x * j));
	double tmp;
	if (j <= -1.56e+156) {
		tmp = t_1;
	} else if (j <= -1e+58) {
		tmp = i * (z * -(k * y1));
	} else if (j <= -6.6e-242) {
		tmp = a * ((y * y5) * -y3);
	} else if (j <= 400000000.0) {
		tmp = x * (-a * (y1 * 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 = y1 * (i * (x * j))
	tmp = 0
	if j <= -1.56e+156:
		tmp = t_1
	elif j <= -1e+58:
		tmp = i * (z * -(k * y1))
	elif j <= -6.6e-242:
		tmp = a * ((y * y5) * -y3)
	elif j <= 400000000.0:
		tmp = x * (-a * (y1 * 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(y1 * Float64(i * Float64(x * j)))
	tmp = 0.0
	if (j <= -1.56e+156)
		tmp = t_1;
	elseif (j <= -1e+58)
		tmp = Float64(i * Float64(z * Float64(-Float64(k * y1))));
	elseif (j <= -6.6e-242)
		tmp = Float64(a * Float64(Float64(y * y5) * Float64(-y3)));
	elseif (j <= 400000000.0)
		tmp = Float64(x * Float64(Float64(-a) * Float64(y1 * 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 = y1 * (i * (x * j));
	tmp = 0.0;
	if (j <= -1.56e+156)
		tmp = t_1;
	elseif (j <= -1e+58)
		tmp = i * (z * -(k * y1));
	elseif (j <= -6.6e-242)
		tmp = a * ((y * y5) * -y3);
	elseif (j <= 400000000.0)
		tmp = x * (-a * (y1 * 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[(y1 * N[(i * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.56e+156], t$95$1, If[LessEqual[j, -1e+58], N[(i * N[(z * (-N[(k * y1), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6.6e-242], N[(a * N[(N[(y * y5), $MachinePrecision] * (-y3)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 400000000.0], N[(x * N[((-a) * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.55999999999999992e156 or 4e8 < j

   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 y1 around -inf 40.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 40.2%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 40.2%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 40.2%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 40.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 40.2%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 40.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 40.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 40.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 40.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 40.2%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around 0 49.0%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   7. Taylor expanded in j around inf 45.5%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 45.5%

         \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(\left(-1 \cdot i\right) \cdot \left(j \cdot x\right)\right)} \]

      2. neg-mul-1 45.5%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(-i\right)} \cdot \left(j \cdot x\right)\right) \]

      3. *-commutative 45.5%

         \[\leadsto \left(-y1\right) \cdot \left(\left(-i\right) \cdot \color{blue}{\left(x \cdot j\right)}\right) \]

   9. Simplified 45.5%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(\left(-i\right) \cdot \left(x \cdot j\right)\right)} \]

   if -1.55999999999999992e156 < j < -9.99999999999999944e57

   1. Initial program 36.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 55.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 55.7%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 55.7%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 55.7%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 55.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 55.7%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 55.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 55.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 55.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 55.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 55.7%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around 0 53.5%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 48.3%

      \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - \color{blue}{x \cdot \left(-1 \cdot \frac{i \cdot \left(k \cdot z\right)}{x} + i \cdot j\right)}\right) \]
   8. Step-by-step derivation

      1. +-commutative 48.3%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \color{blue}{\left(i \cdot j + -1 \cdot \frac{i \cdot \left(k \cdot z\right)}{x}\right)}\right) \]

      2. mul-1-neg 48.3%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \left(i \cdot j + \color{blue}{\left(-\frac{i \cdot \left(k \cdot z\right)}{x}\right)}\right)\right) \]

      3. unsub-neg 48.3%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \color{blue}{\left(i \cdot j - \frac{i \cdot \left(k \cdot z\right)}{x}\right)}\right) \]

      4. associate-/l* 48.3%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \left(i \cdot j - \color{blue}{i \cdot \frac{k \cdot z}{x}}\right)\right) \]

      5. *-commutative 48.3%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \left(i \cdot j - i \cdot \frac{\color{blue}{z \cdot k}}{x}\right)\right) \]

   9. Simplified 48.3%

      \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - \color{blue}{x \cdot \left(i \cdot j - i \cdot \frac{z \cdot k}{x}\right)}\right) \]

   10. Taylor expanded in k around inf 33.1%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 33.1%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. associate-*r* 43.3%

          \[\leadsto -i \cdot \color{blue}{\left(\left(k \cdot y1\right) \cdot z\right)} \]

   12. Simplified 43.3%

       \[\leadsto \color{blue}{-i \cdot \left(\left(k \cdot y1\right) \cdot z\right)} \]

   if -9.99999999999999944e57 < j < -6.59999999999999963e-242

   1. Initial program 32.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 38.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 38.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      2. mul-1-neg 38.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(x \cdot y - t \cdot z\right) + \color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)}\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. unsub-neg 38.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      4. *-commutative 38.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(\color{blue}{y \cdot x} - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      5. *-commutative 38.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      6. *-commutative 38.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. mul-1-neg 38.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \color{blue}{\left(-y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      8. *-commutative 38.3%

         \[\leadsto a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - \color{blue}{y3 \cdot y}\right)\right)\right) \]

   5. Simplified 38.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(y \cdot x - t \cdot z\right) - y1 \cdot \left(y2 \cdot x - z \cdot y3\right)\right) - \left(-y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around -inf 38.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 38.9%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

      2. neg-mul-1 38.9%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]

   8. Simplified 38.9%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

   9. Taylor expanded in y around inf 29.6%

      \[\leadsto \left(-a\right) \cdot \left(y3 \cdot \color{blue}{\left(y \cdot y5\right)}\right) \]

   if -6.59999999999999963e-242 < j < 4e8

   1. Initial program 49.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 51.4%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y2 around inf 40.1%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around 0 31.7%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(y1 \cdot y2\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 31.7%

         \[\leadsto x \cdot \color{blue}{\left(\left(-1 \cdot a\right) \cdot \left(y1 \cdot y2\right)\right)} \]

      2. neg-mul-1 31.7%

         \[\leadsto x \cdot \left(\color{blue}{\left(-a\right)} \cdot \left(y1 \cdot y2\right)\right) \]

   7. Simplified 31.7%

      \[\leadsto x \cdot \color{blue}{\left(\left(-a\right) \cdot \left(y1 \cdot y2\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.56 \cdot 10^{+156}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -1 \cdot 10^{+58}:\\ \;\;\;\;i \cdot \left(z \cdot \left(-k \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -6.6 \cdot 10^{-242}:\\ \;\;\;\;a \cdot \left(\left(y \cdot y5\right) \cdot \left(-y3\right)\right)\\ \mathbf{elif}\;j \leq 400000000:\\ \;\;\;\;x \cdot \left(\left(-a\right) \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 20.2% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 600:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+183}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y1 (* z y3)))))
   (if (<= z -5.5e+166)
     t_1
     (if (<= z 600.0)
       (* i (* j (* x y1)))
       (if (<= z 4.3e+183) (* x (* c (* y0 y2))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y1 * (z * y3));
	double tmp;
	if (z <= -5.5e+166) {
		tmp = t_1;
	} else if (z <= 600.0) {
		tmp = i * (j * (x * y1));
	} else if (z <= 4.3e+183) {
		tmp = x * (c * (y0 * y2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y1 * (z * y3))
    if (z <= (-5.5d+166)) then
        tmp = t_1
    else if (z <= 600.0d0) then
        tmp = i * (j * (x * y1))
    else if (z <= 4.3d+183) then
        tmp = x * (c * (y0 * y2))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y1 * (z * y3));
	double tmp;
	if (z <= -5.5e+166) {
		tmp = t_1;
	} else if (z <= 600.0) {
		tmp = i * (j * (x * y1));
	} else if (z <= 4.3e+183) {
		tmp = x * (c * (y0 * y2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y1 * (z * y3))
	tmp = 0
	if z <= -5.5e+166:
		tmp = t_1
	elif z <= 600.0:
		tmp = i * (j * (x * y1))
	elif z <= 4.3e+183:
		tmp = x * (c * (y0 * y2))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y1 * Float64(z * y3)))
	tmp = 0.0
	if (z <= -5.5e+166)
		tmp = t_1;
	elseif (z <= 600.0)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (z <= 4.3e+183)
		tmp = Float64(x * Float64(c * Float64(y0 * y2)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y1 * (z * y3));
	tmp = 0.0;
	if (z <= -5.5e+166)
		tmp = t_1;
	elseif (z <= 600.0)
		tmp = i * (j * (x * y1));
	elseif (z <= 4.3e+183)
		tmp = x * (c * (y0 * y2));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e+166], t$95$1, If[LessEqual[z, 600.0], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.3e+183], N[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.50000000000000008e166 or 4.3000000000000004e183 < z

   1. Initial program 21.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 41.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 41.0%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 41.0%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 41.0%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 41.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 41.0%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 41.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 41.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 41.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 41.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 41.0%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around 0 52.5%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   7. Taylor expanded in y3 around inf 43.1%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

   if -5.50000000000000008e166 < z < 600

   1. Initial program 39.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 41.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 41.1%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 41.1%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 41.1%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 41.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 41.1%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 41.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 41.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 41.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 41.1%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 41.1%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around 0 39.7%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   7. Taylor expanded in j around inf 21.3%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]

   if 600 < z < 4.3000000000000004e183

   1. Initial program 40.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 43.2%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y2 around inf 32.1%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around inf 30.1%

      \[\leadsto x \cdot \color{blue}{\left(c \cdot \left(y0 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 30.1%

         \[\leadsto x \cdot \left(c \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

   7. Simplified 30.1%

      \[\leadsto x \cdot \color{blue}{\left(c \cdot \left(y2 \cdot y0\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 28.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+166}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 600:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+183}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 22.0% accurate, 5.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -1.25 \cdot 10^{-93} \lor \neg \left(k \leq 11500\right):\\ \;\;\;\;i \cdot \left(z \cdot \left(-k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= k -1.25e-93) (not (<= k 11500.0)))
   (* i (* z (- (* k y1))))
   (* c (* x (* y0 y2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((k <= -1.25e-93) || !(k <= 11500.0)) {
		tmp = i * (z * -(k * y1));
	} else {
		tmp = c * (x * (y0 * 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 ((k <= (-1.25d-93)) .or. (.not. (k <= 11500.0d0))) then
        tmp = i * (z * -(k * y1))
    else
        tmp = c * (x * (y0 * 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 ((k <= -1.25e-93) || !(k <= 11500.0)) {
		tmp = i * (z * -(k * y1));
	} else {
		tmp = c * (x * (y0 * 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 (k <= -1.25e-93) or not (k <= 11500.0):
		tmp = i * (z * -(k * y1))
	else:
		tmp = c * (x * (y0 * 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 ((k <= -1.25e-93) || !(k <= 11500.0))
		tmp = Float64(i * Float64(z * Float64(-Float64(k * y1))));
	else
		tmp = Float64(c * Float64(x * Float64(y0 * 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 ((k <= -1.25e-93) || ~((k <= 11500.0)))
		tmp = i * (z * -(k * y1));
	else
		tmp = c * (x * (y0 * 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[Or[LessEqual[k, -1.25e-93], N[Not[LessEqual[k, 11500.0]], $MachinePrecision]], N[(i * N[(z * (-N[(k * y1), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if k < -1.24999999999999999e-93 or 11500 < k

   1. Initial program 33.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 40.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 40.7%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 40.7%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 40.7%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 40.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 40.7%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 40.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 40.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 40.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 40.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 40.7%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around 0 43.2%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 41.0%

      \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - \color{blue}{x \cdot \left(-1 \cdot \frac{i \cdot \left(k \cdot z\right)}{x} + i \cdot j\right)}\right) \]
   8. Step-by-step derivation

      1. +-commutative 41.0%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \color{blue}{\left(i \cdot j + -1 \cdot \frac{i \cdot \left(k \cdot z\right)}{x}\right)}\right) \]

      2. mul-1-neg 41.0%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \left(i \cdot j + \color{blue}{\left(-\frac{i \cdot \left(k \cdot z\right)}{x}\right)}\right)\right) \]

      3. unsub-neg 41.0%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \color{blue}{\left(i \cdot j - \frac{i \cdot \left(k \cdot z\right)}{x}\right)}\right) \]

      4. associate-/l* 43.0%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \left(i \cdot j - \color{blue}{i \cdot \frac{k \cdot z}{x}}\right)\right) \]

      5. *-commutative 43.0%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \left(i \cdot j - i \cdot \frac{\color{blue}{z \cdot k}}{x}\right)\right) \]

   9. Simplified 43.0%

      \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - \color{blue}{x \cdot \left(i \cdot j - i \cdot \frac{z \cdot k}{x}\right)}\right) \]

   10. Taylor expanded in k around inf 28.7%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 28.7%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. associate-*r* 32.7%

          \[\leadsto -i \cdot \color{blue}{\left(\left(k \cdot y1\right) \cdot z\right)} \]

   12. Simplified 32.7%

       \[\leadsto \color{blue}{-i \cdot \left(\left(k \cdot y1\right) \cdot z\right)} \]

   if -1.24999999999999999e-93 < k < 11500

   1. Initial program 37.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 48.0%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y2 around inf 37.2%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around inf 27.1%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 27.1%

         \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

   7. Simplified 27.1%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.25 \cdot 10^{-93} \lor \neg \left(k \leq 11500\right):\\ \;\;\;\;i \cdot \left(z \cdot \left(-k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 21.7% accurate, 5.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(j \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-55}:\\ \;\;\;\;i \cdot \left(z \cdot \left(-k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(x \cdot y1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -6.5e+36)
   (* b (* j (* x (- y0))))
   (if (<= x 1.15e-55) (* i (* z (- (* k y1)))) (* (* 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 (x <= -6.5e+36) {
		tmp = b * (j * (x * -y0));
	} else if (x <= 1.15e-55) {
		tmp = i * (z * -(k * y1));
	} 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 (x <= (-6.5d+36)) then
        tmp = b * (j * (x * -y0))
    else if (x <= 1.15d-55) then
        tmp = i * (z * -(k * y1))
    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 (x <= -6.5e+36) {
		tmp = b * (j * (x * -y0));
	} else if (x <= 1.15e-55) {
		tmp = i * (z * -(k * y1));
	} 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 x <= -6.5e+36:
		tmp = b * (j * (x * -y0))
	elif x <= 1.15e-55:
		tmp = i * (z * -(k * y1))
	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 (x <= -6.5e+36)
		tmp = Float64(b * Float64(j * Float64(x * Float64(-y0))));
	elseif (x <= 1.15e-55)
		tmp = Float64(i * Float64(z * Float64(-Float64(k * y1))));
	else
		tmp = Float64(Float64(i * 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 (x <= -6.5e+36)
		tmp = b * (j * (x * -y0));
	elseif (x <= 1.15e-55)
		tmp = i * (z * -(k * y1));
	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[LessEqual[x, -6.5e+36], N[(b * N[(j * N[(x * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e-55], N[(i * N[(z * (-N[(k * y1), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], N[(N[(i * j), $MachinePrecision] * N[(x * y1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.4999999999999998e36

   1. Initial program 30.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 57.5%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around 0 56.2%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf 41.1%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot \left(x \cdot y0\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 41.1%

         \[\leadsto \color{blue}{-b \cdot \left(j \cdot \left(x \cdot y0\right)\right)} \]

      2. distribute-rgt-neg-in 41.1%

         \[\leadsto \color{blue}{b \cdot \left(-j \cdot \left(x \cdot y0\right)\right)} \]

      3. *-commutative 41.1%

         \[\leadsto b \cdot \left(-\color{blue}{\left(x \cdot y0\right) \cdot j}\right) \]

      4. distribute-rgt-neg-in 41.1%

         \[\leadsto b \cdot \color{blue}{\left(\left(x \cdot y0\right) \cdot \left(-j\right)\right)} \]

   7. Simplified 41.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(x \cdot y0\right) \cdot \left(-j\right)\right)} \]

   if -6.4999999999999998e36 < x < 1.15000000000000006e-55

   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 38.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 38.6%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 38.6%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 38.6%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 38.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 38.6%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 38.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 38.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 38.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 38.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 38.6%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around 0 34.3%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 35.8%

      \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - \color{blue}{x \cdot \left(-1 \cdot \frac{i \cdot \left(k \cdot z\right)}{x} + i \cdot j\right)}\right) \]
   8. Step-by-step derivation

      1. +-commutative 35.8%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \color{blue}{\left(i \cdot j + -1 \cdot \frac{i \cdot \left(k \cdot z\right)}{x}\right)}\right) \]

      2. mul-1-neg 35.8%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \left(i \cdot j + \color{blue}{\left(-\frac{i \cdot \left(k \cdot z\right)}{x}\right)}\right)\right) \]

      3. unsub-neg 35.8%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \color{blue}{\left(i \cdot j - \frac{i \cdot \left(k \cdot z\right)}{x}\right)}\right) \]

      4. associate-/l* 36.6%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \left(i \cdot j - \color{blue}{i \cdot \frac{k \cdot z}{x}}\right)\right) \]

      5. *-commutative 36.6%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \left(i \cdot j - i \cdot \frac{\color{blue}{z \cdot k}}{x}\right)\right) \]

   9. Simplified 36.6%

      \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - \color{blue}{x \cdot \left(i \cdot j - i \cdot \frac{z \cdot k}{x}\right)}\right) \]

   10. Taylor expanded in k around inf 22.3%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 22.3%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. associate-*r* 24.8%

          \[\leadsto -i \cdot \color{blue}{\left(\left(k \cdot y1\right) \cdot z\right)} \]

   12. Simplified 24.8%

       \[\leadsto \color{blue}{-i \cdot \left(\left(k \cdot y1\right) \cdot z\right)} \]

   if 1.15000000000000006e-55 < x

   1. Initial program 30.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 48.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 48.0%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 48.0%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 48.0%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 48.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 48.0%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 48.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 48.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 48.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 48.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 48.0%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around 0 54.5%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   7. Taylor expanded in j around inf 31.4%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 31.5%

         \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(x \cdot y1\right)} \]

      2. *-commutative 31.5%

         \[\leadsto \left(i \cdot j\right) \cdot \color{blue}{\left(y1 \cdot x\right)} \]

   9. Simplified 31.5%

      \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(y1 \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 30.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(j \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-55}:\\ \;\;\;\;i \cdot \left(z \cdot \left(-k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(x \cdot y1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 21.1% accurate, 5.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+45}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \left(b \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-54}:\\ \;\;\;\;i \cdot \left(z \cdot \left(-k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(x \cdot y1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -3.2e+45)
   (* (* x y0) (* b (- j)))
   (if (<= x 3e-54) (* i (* z (- (* k y1)))) (* (* 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 (x <= -3.2e+45) {
		tmp = (x * y0) * (b * -j);
	} else if (x <= 3e-54) {
		tmp = i * (z * -(k * y1));
	} 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 (x <= (-3.2d+45)) then
        tmp = (x * y0) * (b * -j)
    else if (x <= 3d-54) then
        tmp = i * (z * -(k * y1))
    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 (x <= -3.2e+45) {
		tmp = (x * y0) * (b * -j);
	} else if (x <= 3e-54) {
		tmp = i * (z * -(k * y1));
	} 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 x <= -3.2e+45:
		tmp = (x * y0) * (b * -j)
	elif x <= 3e-54:
		tmp = i * (z * -(k * y1))
	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 (x <= -3.2e+45)
		tmp = Float64(Float64(x * y0) * Float64(b * Float64(-j)));
	elseif (x <= 3e-54)
		tmp = Float64(i * Float64(z * Float64(-Float64(k * y1))));
	else
		tmp = Float64(Float64(i * 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 (x <= -3.2e+45)
		tmp = (x * y0) * (b * -j);
	elseif (x <= 3e-54)
		tmp = i * (z * -(k * y1));
	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[LessEqual[x, -3.2e+45], N[(N[(x * y0), $MachinePrecision] * N[(b * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e-54], N[(i * N[(z * (-N[(k * y1), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], N[(N[(i * j), $MachinePrecision] * N[(x * y1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.2000000000000003e45

   1. Initial program 30.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 57.5%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around 0 56.2%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf 41.1%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(j \cdot \left(x \cdot y0\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 41.1%

         \[\leadsto \color{blue}{-b \cdot \left(j \cdot \left(x \cdot y0\right)\right)} \]

      2. associate-*r* 38.0%

         \[\leadsto -\color{blue}{\left(b \cdot j\right) \cdot \left(x \cdot y0\right)} \]

      3. *-commutative 38.0%

         \[\leadsto -\color{blue}{\left(j \cdot b\right)} \cdot \left(x \cdot y0\right) \]

   7. Simplified 38.0%

      \[\leadsto \color{blue}{-\left(j \cdot b\right) \cdot \left(x \cdot y0\right)} \]

   if -3.2000000000000003e45 < x < 3.00000000000000009e-54

   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 38.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 38.6%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 38.6%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 38.6%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 38.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 38.6%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 38.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 38.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 38.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 38.6%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 38.6%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around 0 34.3%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   7. Taylor expanded in x around inf 35.8%

      \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - \color{blue}{x \cdot \left(-1 \cdot \frac{i \cdot \left(k \cdot z\right)}{x} + i \cdot j\right)}\right) \]
   8. Step-by-step derivation

      1. +-commutative 35.8%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \color{blue}{\left(i \cdot j + -1 \cdot \frac{i \cdot \left(k \cdot z\right)}{x}\right)}\right) \]

      2. mul-1-neg 35.8%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \left(i \cdot j + \color{blue}{\left(-\frac{i \cdot \left(k \cdot z\right)}{x}\right)}\right)\right) \]

      3. unsub-neg 35.8%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \color{blue}{\left(i \cdot j - \frac{i \cdot \left(k \cdot z\right)}{x}\right)}\right) \]

      4. associate-/l* 36.6%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \left(i \cdot j - \color{blue}{i \cdot \frac{k \cdot z}{x}}\right)\right) \]

      5. *-commutative 36.6%

         \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - x \cdot \left(i \cdot j - i \cdot \frac{\color{blue}{z \cdot k}}{x}\right)\right) \]

   9. Simplified 36.6%

      \[\leadsto \left(-y1\right) \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - \color{blue}{x \cdot \left(i \cdot j - i \cdot \frac{z \cdot k}{x}\right)}\right) \]

   10. Taylor expanded in k around inf 22.3%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 22.3%

          \[\leadsto \color{blue}{-i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)} \]

       2. associate-*r* 24.8%

          \[\leadsto -i \cdot \color{blue}{\left(\left(k \cdot y1\right) \cdot z\right)} \]

   12. Simplified 24.8%

       \[\leadsto \color{blue}{-i \cdot \left(\left(k \cdot y1\right) \cdot z\right)} \]

   if 3.00000000000000009e-54 < x

   1. Initial program 30.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 48.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 48.0%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 48.0%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 48.0%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 48.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 48.0%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 48.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 48.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 48.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 48.0%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 48.0%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around 0 54.5%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   7. Taylor expanded in j around inf 31.4%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 31.5%

         \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(x \cdot y1\right)} \]

      2. *-commutative 31.5%

         \[\leadsto \left(i \cdot j\right) \cdot \color{blue}{\left(y1 \cdot x\right)} \]

   9. Simplified 31.5%

      \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(y1 \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 29.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+45}:\\ \;\;\;\;\left(x \cdot y0\right) \cdot \left(b \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-54}:\\ \;\;\;\;i \cdot \left(z \cdot \left(-k \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(x \cdot y1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 34: 21.5% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -6 \cdot 10^{+119} \lor \neg \left(y0 \leq 3.2 \cdot 10^{-76}\right):\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y0 -6e+119) (not (<= y0 3.2e-76)))
   (* c (* x (* y0 y2)))
   (* x (* i (* j 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 <= -6e+119) || !(y0 <= 3.2e-76)) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = x * (i * (j * 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 <= (-6d+119)) .or. (.not. (y0 <= 3.2d-76))) then
        tmp = c * (x * (y0 * y2))
    else
        tmp = x * (i * (j * 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 <= -6e+119) || !(y0 <= 3.2e-76)) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = x * (i * (j * 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 <= -6e+119) or not (y0 <= 3.2e-76):
		tmp = c * (x * (y0 * y2))
	else:
		tmp = x * (i * (j * 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 <= -6e+119) || !(y0 <= 3.2e-76))
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	else
		tmp = Float64(x * Float64(i * Float64(j * 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 <= -6e+119) || ~((y0 <= 3.2e-76)))
		tmp = c * (x * (y0 * y2));
	else
		tmp = x * (i * (j * 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, -6e+119], N[Not[LessEqual[y0, 3.2e-76]], $MachinePrecision]], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(i * N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y0 < -6.00000000000000002e119 or 3.1999999999999998e-76 < y0

   1. Initial program 30.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 45.4%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y2 around inf 35.9%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around inf 28.9%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 28.9%

         \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

   7. Simplified 28.9%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0\right)\right)} \]

   if -6.00000000000000002e119 < y0 < 3.1999999999999998e-76

   1. Initial program 39.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 39.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around 0 35.6%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in i around inf 26.0%

      \[\leadsto x \cdot \color{blue}{\left(i \cdot \left(j \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 26.0%

         \[\leadsto x \cdot \left(i \cdot \color{blue}{\left(y1 \cdot j\right)}\right) \]

   7. Simplified 26.0%

      \[\leadsto x \cdot \color{blue}{\left(i \cdot \left(y1 \cdot j\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 27.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -6 \cdot 10^{+119} \lor \neg \left(y0 \leq 3.2 \cdot 10^{-76}\right):\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 35: 20.7% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.45 \cdot 10^{+110} \lor \neg \left(j \leq 2.3 \cdot 10^{+33}\right):\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= j -1.45e+110) (not (<= j 2.3e+33)))
   (* i (* j (* x y1)))
   (* c (* x (* y0 y2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((j <= -1.45e+110) || !(j <= 2.3e+33)) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = c * (x * (y0 * 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 ((j <= (-1.45d+110)) .or. (.not. (j <= 2.3d+33))) then
        tmp = i * (j * (x * y1))
    else
        tmp = c * (x * (y0 * 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 ((j <= -1.45e+110) || !(j <= 2.3e+33)) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = c * (x * (y0 * 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 (j <= -1.45e+110) or not (j <= 2.3e+33):
		tmp = i * (j * (x * y1))
	else:
		tmp = c * (x * (y0 * 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 ((j <= -1.45e+110) || !(j <= 2.3e+33))
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	else
		tmp = Float64(c * Float64(x * Float64(y0 * 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 ((j <= -1.45e+110) || ~((j <= 2.3e+33)))
		tmp = i * (j * (x * y1));
	else
		tmp = c * (x * (y0 * 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[Or[LessEqual[j, -1.45e+110], N[Not[LessEqual[j, 2.3e+33]], $MachinePrecision]], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.45e110 or 2.30000000000000011e33 < j

   1. Initial program 27.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 42.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 42.2%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 42.2%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 42.2%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 42.2%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around 0 51.8%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   7. Taylor expanded in j around inf 37.6%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]

   if -1.45e110 < j < 2.30000000000000011e33

   1. Initial program 41.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 42.4%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y2 around inf 29.4%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around inf 18.2%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 18.2%

         \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

   7. Simplified 18.2%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 26.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.45 \cdot 10^{+110} \lor \neg \left(j \leq 2.3 \cdot 10^{+33}\right):\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 36: 20.5% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -4.4 \cdot 10^{+253} \lor \neg \left(y1 \leq 9.8 \cdot 10^{+92}\right):\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y1 -4.4e+253) (not (<= y1 9.8e+92)))
   (* a (* z (* y1 y3)))
   (* c (* x (* y0 y2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y1 <= -4.4e+253) || !(y1 <= 9.8e+92)) {
		tmp = a * (z * (y1 * y3));
	} else {
		tmp = c * (x * (y0 * 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 ((y1 <= (-4.4d+253)) .or. (.not. (y1 <= 9.8d+92))) then
        tmp = a * (z * (y1 * y3))
    else
        tmp = c * (x * (y0 * 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 ((y1 <= -4.4e+253) || !(y1 <= 9.8e+92)) {
		tmp = a * (z * (y1 * y3));
	} else {
		tmp = c * (x * (y0 * 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 (y1 <= -4.4e+253) or not (y1 <= 9.8e+92):
		tmp = a * (z * (y1 * y3))
	else:
		tmp = c * (x * (y0 * 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 ((y1 <= -4.4e+253) || !(y1 <= 9.8e+92))
		tmp = Float64(a * Float64(z * Float64(y1 * y3)));
	else
		tmp = Float64(c * Float64(x * Float64(y0 * 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 ((y1 <= -4.4e+253) || ~((y1 <= 9.8e+92)))
		tmp = a * (z * (y1 * y3));
	else
		tmp = c * (x * (y0 * 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[Or[LessEqual[y1, -4.4e+253], N[Not[LessEqual[y1, 9.8e+92]], $MachinePrecision]], N[(a * N[(z * N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y1 < -4.40000000000000011e253 or 9.8000000000000003e92 < y1

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y1 around -inf 59.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 59.7%

         \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. neg-mul-1 59.7%

         \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      3. +-commutative 59.7%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. mul-1-neg 59.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. unsub-neg 59.7%

         \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      6. *-commutative 59.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      7. *-commutative 59.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      8. *-commutative 59.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      9. *-commutative 59.7%

         \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

   5. Simplified 59.7%

      \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

   6. Taylor expanded in y4 around 0 65.9%

      \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   7. Taylor expanded in y3 around inf 36.0%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 38.8%

         \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

   9. Simplified 38.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(y1 \cdot y3\right) \cdot z\right)} \]

   if -4.40000000000000011e253 < y1 < 9.8000000000000003e92

   1. Initial program 35.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 44.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y2 around inf 28.2%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around inf 20.4%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 20.4%

         \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

   7. Simplified 20.4%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 25.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -4.4 \cdot 10^{+253} \lor \neg \left(y1 \leq 9.8 \cdot 10^{+92}\right):\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 37: 22.5% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -9.5 \cdot 10^{+118}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 5.4:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -9.5e+118)
   (* c (* x (* y0 y2)))
   (if (<= y0 5.4) (* x (* i (* j y1))) (* x (* y2 (* c 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 (y0 <= -9.5e+118) {
		tmp = c * (x * (y0 * y2));
	} else if (y0 <= 5.4) {
		tmp = x * (i * (j * y1));
	} else {
		tmp = x * (y2 * (c * 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 (y0 <= (-9.5d+118)) then
        tmp = c * (x * (y0 * y2))
    else if (y0 <= 5.4d0) then
        tmp = x * (i * (j * y1))
    else
        tmp = x * (y2 * (c * 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 (y0 <= -9.5e+118) {
		tmp = c * (x * (y0 * y2));
	} else if (y0 <= 5.4) {
		tmp = x * (i * (j * y1));
	} else {
		tmp = x * (y2 * (c * 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 y0 <= -9.5e+118:
		tmp = c * (x * (y0 * y2))
	elif y0 <= 5.4:
		tmp = x * (i * (j * y1))
	else:
		tmp = x * (y2 * (c * 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 (y0 <= -9.5e+118)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (y0 <= 5.4)
		tmp = Float64(x * Float64(i * Float64(j * y1)));
	else
		tmp = Float64(x * Float64(y2 * Float64(c * 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 (y0 <= -9.5e+118)
		tmp = c * (x * (y0 * y2));
	elseif (y0 <= 5.4)
		tmp = x * (i * (j * y1));
	else
		tmp = x * (y2 * (c * 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[LessEqual[y0, -9.5e+118], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 5.4], N[(x * N[(i * N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y2 * N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y0 < -9.49999999999999974e118

   1. Initial program 33.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 43.4%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y2 around inf 36.5%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around inf 36.8%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 36.8%

         \[\leadsto c \cdot \left(x \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \]

   7. Simplified 36.8%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y2 \cdot y0\right)\right)} \]

   if -9.49999999999999974e118 < y0 < 5.4000000000000004

   1. Initial program 39.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 41.2%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y around 0 37.3%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in i around inf 25.9%

      \[\leadsto x \cdot \color{blue}{\left(i \cdot \left(j \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 25.9%

         \[\leadsto x \cdot \left(i \cdot \color{blue}{\left(y1 \cdot j\right)}\right) \]

   7. Simplified 25.9%

      \[\leadsto x \cdot \color{blue}{\left(i \cdot \left(y1 \cdot j\right)\right)} \]

   if 5.4000000000000004 < y0

   1. Initial program 26.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 44.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   4. Taylor expanded in y2 around inf 34.7%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]

   5. Taylor expanded in c around inf 26.1%

      \[\leadsto x \cdot \left(y2 \cdot \color{blue}{\left(c \cdot y0\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 27.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -9.5 \cdot 10^{+118}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 5.4:\\ \;\;\;\;x \cdot \left(i \cdot \left(j \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 38: 16.8% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* y1 (* z y3))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y1 * (z * y3));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * (y1 * (z * y3))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y1 * (z * y3));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (y1 * (z * y3))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(y1 * Float64(z * y3)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (y1 * (z * y3));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 35.3%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Add Preprocessing

3. Taylor expanded in y1 around -inf 42.7%

   \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
4. Step-by-step derivation

   1. associate-*r* 42.7%

      \[\leadsto \color{blue}{\left(-1 \cdot y1\right) \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   2. neg-mul-1 42.7%

      \[\leadsto \color{blue}{\left(-y1\right)} \cdot \left(\left(-1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   3. +-commutative 42.7%

      \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + -1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   4. mul-1-neg 42.7%

      \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) + \color{blue}{\left(-y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   5. unsub-neg 42.7%

      \[\leadsto \left(-y1\right) \cdot \left(\color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   6. *-commutative 42.7%

      \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   7. *-commutative 42.7%

      \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   8. *-commutative 42.7%

      \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - \color{blue}{y3 \cdot j}\right)\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right) \]

   9. *-commutative 42.7%

      \[\leadsto \left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - \color{blue}{z \cdot k}\right)\right) \]

5. Simplified 42.7%

   \[\leadsto \color{blue}{\left(-y1\right) \cdot \left(\left(a \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - i \cdot \left(j \cdot x - z \cdot k\right)\right)} \]

6. Taylor expanded in y4 around 0 44.2%

   \[\leadsto \left(-y1\right) \cdot \color{blue}{\left(a \cdot \left(x \cdot y2 - y3 \cdot z\right) - i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

7. Taylor expanded in y3 around inf 16.8%

   \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

8. Final simplification 16.8%

   \[\leadsto a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right) \]
9. Add Preprocessing

Developer target: 26.6% 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 2024103 
(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)))))