Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 29.5% → 39.5%

Time: 1.7min

Alternatives: 41

Speedup: 4.1×

• 89.2% 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: 29.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 39.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_2 := c \cdot y4 - a \cdot y5\\ t_3 := y \cdot t_2\\ t_4 := b \cdot y0 - i \cdot y1\\ t_5 := y \cdot \left(a \cdot b - c \cdot i\right)\\ t_6 := x \cdot \left(\left(t_5 + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_7 := j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\\ t_8 := y1 \cdot y4 - y0 \cdot y5\\ t_9 := c \cdot i - a \cdot b\\ t_10 := a \cdot y1 - c \cdot y0\\ t_11 := z \cdot \left(k \cdot t_4 + \left(t \cdot t_9 + y3 \cdot t_10\right)\right)\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{-60}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-212}:\\ \;\;\;\;y3 \cdot \left(t_3 + t_7\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-301}:\\ \;\;\;\;\left(t \cdot \left(z \cdot t_9\right) + k \cdot \left(y2 \cdot t_8\right)\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-302}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-292}:\\ \;\;\;\;x \cdot t_5\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-237}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot t_8\right) - x \cdot t_4\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-141}:\\ \;\;\;\;y \cdot \left(y3 \cdot t_2\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-84}:\\ \;\;\;\;t_11\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-32}:\\ \;\;\;\;y3 \cdot \left(t_3 + \left(t_7 + z \cdot t_10\right)\right)\\ \mathbf{elif}\;x \leq 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+139}:\\ \;\;\;\;t_11\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+218}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j))))))
        (t_2 (- (* c y4) (* a y5)))
        (t_3 (* y t_2))
        (t_4 (- (* b y0) (* i y1)))
        (t_5 (* y (- (* a b) (* c i))))
        (t_6
         (*
          x
          (+
           (+ t_5 (* y2 (- (* c y0) (* a y1))))
           (* j (- (* i y1) (* b y0))))))
        (t_7 (* j (- (* y0 y5) (* y1 y4))))
        (t_8 (- (* y1 y4) (* y0 y5)))
        (t_9 (- (* c i) (* a b)))
        (t_10 (- (* a y1) (* c y0)))
        (t_11 (* z (+ (* k t_4) (+ (* t t_9) (* y3 t_10))))))
   (if (<= x -2.1e-60)
     t_6
     (if (<= x -5.5e-212)
       (* y3 (+ t_3 t_7))
       (if (<= x -3.1e-301)
         (+
          (+ (* t (* z t_9)) (* k (* y2 t_8)))
          (* (- (* t y2) (* y y3)) (- (* a y5) (* c y4))))
         (if (<= x -6e-302)
           (* k (* y0 (* y2 (- y5))))
           (if (<= x 6.5e-292)
             (* x t_5)
             (if (<= x 1.65e-237)
               (* j (- (- (* t (- (* b y4) (* i y5))) (* y3 t_8)) (* x t_4)))
               (if (<= x 2e-141)
                 (* y (* y3 t_2))
                 (if (<= x 9e-84)
                   t_11
                   (if (<= x 4.6e-32)
                     (* y3 (+ t_3 (+ t_7 (* z t_10))))
                     (if (<= x 1e+53)
                       t_1
                       (if (<= x 1.02e+139)
                         t_11
                         (if (<= x 4.5e+218) t_1 t_6))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_2 = (c * y4) - (a * y5);
	double t_3 = y * t_2;
	double t_4 = (b * y0) - (i * y1);
	double t_5 = y * ((a * b) - (c * i));
	double t_6 = x * ((t_5 + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double t_7 = j * ((y0 * y5) - (y1 * y4));
	double t_8 = (y1 * y4) - (y0 * y5);
	double t_9 = (c * i) - (a * b);
	double t_10 = (a * y1) - (c * y0);
	double t_11 = z * ((k * t_4) + ((t * t_9) + (y3 * t_10)));
	double tmp;
	if (x <= -2.1e-60) {
		tmp = t_6;
	} else if (x <= -5.5e-212) {
		tmp = y3 * (t_3 + t_7);
	} else if (x <= -3.1e-301) {
		tmp = ((t * (z * t_9)) + (k * (y2 * t_8))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)));
	} else if (x <= -6e-302) {
		tmp = k * (y0 * (y2 * -y5));
	} else if (x <= 6.5e-292) {
		tmp = x * t_5;
	} else if (x <= 1.65e-237) {
		tmp = j * (((t * ((b * y4) - (i * y5))) - (y3 * t_8)) - (x * t_4));
	} else if (x <= 2e-141) {
		tmp = y * (y3 * t_2);
	} else if (x <= 9e-84) {
		tmp = t_11;
	} else if (x <= 4.6e-32) {
		tmp = y3 * (t_3 + (t_7 + (z * t_10)));
	} else if (x <= 1e+53) {
		tmp = t_1;
	} else if (x <= 1.02e+139) {
		tmp = t_11;
	} else if (x <= 4.5e+218) {
		tmp = t_1;
	} else {
		tmp = t_6;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    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 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    t_2 = (c * y4) - (a * y5)
    t_3 = y * t_2
    t_4 = (b * y0) - (i * y1)
    t_5 = y * ((a * b) - (c * i))
    t_6 = x * ((t_5 + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    t_7 = j * ((y0 * y5) - (y1 * y4))
    t_8 = (y1 * y4) - (y0 * y5)
    t_9 = (c * i) - (a * b)
    t_10 = (a * y1) - (c * y0)
    t_11 = z * ((k * t_4) + ((t * t_9) + (y3 * t_10)))
    if (x <= (-2.1d-60)) then
        tmp = t_6
    else if (x <= (-5.5d-212)) then
        tmp = y3 * (t_3 + t_7)
    else if (x <= (-3.1d-301)) then
        tmp = ((t * (z * t_9)) + (k * (y2 * t_8))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))
    else if (x <= (-6d-302)) then
        tmp = k * (y0 * (y2 * -y5))
    else if (x <= 6.5d-292) then
        tmp = x * t_5
    else if (x <= 1.65d-237) then
        tmp = j * (((t * ((b * y4) - (i * y5))) - (y3 * t_8)) - (x * t_4))
    else if (x <= 2d-141) then
        tmp = y * (y3 * t_2)
    else if (x <= 9d-84) then
        tmp = t_11
    else if (x <= 4.6d-32) then
        tmp = y3 * (t_3 + (t_7 + (z * t_10)))
    else if (x <= 1d+53) then
        tmp = t_1
    else if (x <= 1.02d+139) then
        tmp = t_11
    else if (x <= 4.5d+218) then
        tmp = t_1
    else
        tmp = t_6
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_2 = (c * y4) - (a * y5);
	double t_3 = y * t_2;
	double t_4 = (b * y0) - (i * y1);
	double t_5 = y * ((a * b) - (c * i));
	double t_6 = x * ((t_5 + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double t_7 = j * ((y0 * y5) - (y1 * y4));
	double t_8 = (y1 * y4) - (y0 * y5);
	double t_9 = (c * i) - (a * b);
	double t_10 = (a * y1) - (c * y0);
	double t_11 = z * ((k * t_4) + ((t * t_9) + (y3 * t_10)));
	double tmp;
	if (x <= -2.1e-60) {
		tmp = t_6;
	} else if (x <= -5.5e-212) {
		tmp = y3 * (t_3 + t_7);
	} else if (x <= -3.1e-301) {
		tmp = ((t * (z * t_9)) + (k * (y2 * t_8))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)));
	} else if (x <= -6e-302) {
		tmp = k * (y0 * (y2 * -y5));
	} else if (x <= 6.5e-292) {
		tmp = x * t_5;
	} else if (x <= 1.65e-237) {
		tmp = j * (((t * ((b * y4) - (i * y5))) - (y3 * t_8)) - (x * t_4));
	} else if (x <= 2e-141) {
		tmp = y * (y3 * t_2);
	} else if (x <= 9e-84) {
		tmp = t_11;
	} else if (x <= 4.6e-32) {
		tmp = y3 * (t_3 + (t_7 + (z * t_10)));
	} else if (x <= 1e+53) {
		tmp = t_1;
	} else if (x <= 1.02e+139) {
		tmp = t_11;
	} else if (x <= 4.5e+218) {
		tmp = t_1;
	} else {
		tmp = t_6;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	t_2 = (c * y4) - (a * y5)
	t_3 = y * t_2
	t_4 = (b * y0) - (i * y1)
	t_5 = y * ((a * b) - (c * i))
	t_6 = x * ((t_5 + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	t_7 = j * ((y0 * y5) - (y1 * y4))
	t_8 = (y1 * y4) - (y0 * y5)
	t_9 = (c * i) - (a * b)
	t_10 = (a * y1) - (c * y0)
	t_11 = z * ((k * t_4) + ((t * t_9) + (y3 * t_10)))
	tmp = 0
	if x <= -2.1e-60:
		tmp = t_6
	elif x <= -5.5e-212:
		tmp = y3 * (t_3 + t_7)
	elif x <= -3.1e-301:
		tmp = ((t * (z * t_9)) + (k * (y2 * t_8))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))
	elif x <= -6e-302:
		tmp = k * (y0 * (y2 * -y5))
	elif x <= 6.5e-292:
		tmp = x * t_5
	elif x <= 1.65e-237:
		tmp = j * (((t * ((b * y4) - (i * y5))) - (y3 * t_8)) - (x * t_4))
	elif x <= 2e-141:
		tmp = y * (y3 * t_2)
	elif x <= 9e-84:
		tmp = t_11
	elif x <= 4.6e-32:
		tmp = y3 * (t_3 + (t_7 + (z * t_10)))
	elif x <= 1e+53:
		tmp = t_1
	elif x <= 1.02e+139:
		tmp = t_11
	elif x <= 4.5e+218:
		tmp = t_1
	else:
		tmp = t_6
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	t_2 = Float64(Float64(c * y4) - Float64(a * y5))
	t_3 = Float64(y * t_2)
	t_4 = Float64(Float64(b * y0) - Float64(i * y1))
	t_5 = Float64(y * Float64(Float64(a * b) - Float64(c * i)))
	t_6 = Float64(x * Float64(Float64(t_5 + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_7 = Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4)))
	t_8 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_9 = Float64(Float64(c * i) - Float64(a * b))
	t_10 = Float64(Float64(a * y1) - Float64(c * y0))
	t_11 = Float64(z * Float64(Float64(k * t_4) + Float64(Float64(t * t_9) + Float64(y3 * t_10))))
	tmp = 0.0
	if (x <= -2.1e-60)
		tmp = t_6;
	elseif (x <= -5.5e-212)
		tmp = Float64(y3 * Float64(t_3 + t_7));
	elseif (x <= -3.1e-301)
		tmp = Float64(Float64(Float64(t * Float64(z * t_9)) + Float64(k * Float64(y2 * t_8))) + Float64(Float64(Float64(t * y2) - Float64(y * y3)) * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (x <= -6e-302)
		tmp = Float64(k * Float64(y0 * Float64(y2 * Float64(-y5))));
	elseif (x <= 6.5e-292)
		tmp = Float64(x * t_5);
	elseif (x <= 1.65e-237)
		tmp = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) - Float64(y3 * t_8)) - Float64(x * t_4)));
	elseif (x <= 2e-141)
		tmp = Float64(y * Float64(y3 * t_2));
	elseif (x <= 9e-84)
		tmp = t_11;
	elseif (x <= 4.6e-32)
		tmp = Float64(y3 * Float64(t_3 + Float64(t_7 + Float64(z * t_10))));
	elseif (x <= 1e+53)
		tmp = t_1;
	elseif (x <= 1.02e+139)
		tmp = t_11;
	elseif (x <= 4.5e+218)
		tmp = t_1;
	else
		tmp = t_6;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	t_2 = (c * y4) - (a * y5);
	t_3 = y * t_2;
	t_4 = (b * y0) - (i * y1);
	t_5 = y * ((a * b) - (c * i));
	t_6 = x * ((t_5 + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	t_7 = j * ((y0 * y5) - (y1 * y4));
	t_8 = (y1 * y4) - (y0 * y5);
	t_9 = (c * i) - (a * b);
	t_10 = (a * y1) - (c * y0);
	t_11 = z * ((k * t_4) + ((t * t_9) + (y3 * t_10)));
	tmp = 0.0;
	if (x <= -2.1e-60)
		tmp = t_6;
	elseif (x <= -5.5e-212)
		tmp = y3 * (t_3 + t_7);
	elseif (x <= -3.1e-301)
		tmp = ((t * (z * t_9)) + (k * (y2 * t_8))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)));
	elseif (x <= -6e-302)
		tmp = k * (y0 * (y2 * -y5));
	elseif (x <= 6.5e-292)
		tmp = x * t_5;
	elseif (x <= 1.65e-237)
		tmp = j * (((t * ((b * y4) - (i * y5))) - (y3 * t_8)) - (x * t_4));
	elseif (x <= 2e-141)
		tmp = y * (y3 * t_2);
	elseif (x <= 9e-84)
		tmp = t_11;
	elseif (x <= 4.6e-32)
		tmp = y3 * (t_3 + (t_7 + (z * t_10)));
	elseif (x <= 1e+53)
		tmp = t_1;
	elseif (x <= 1.02e+139)
		tmp = t_11;
	elseif (x <= 4.5e+218)
		tmp = t_1;
	else
		tmp = t_6;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x * N[(N[(t$95$5 + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$11 = N[(z * N[(N[(k * t$95$4), $MachinePrecision] + N[(N[(t * t$95$9), $MachinePrecision] + N[(y3 * t$95$10), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.1e-60], t$95$6, If[LessEqual[x, -5.5e-212], N[(y3 * N[(t$95$3 + t$95$7), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.1e-301], N[(N[(N[(t * N[(z * t$95$9), $MachinePrecision]), $MachinePrecision] + N[(k * N[(y2 * t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6e-302], N[(k * N[(y0 * N[(y2 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e-292], N[(x * t$95$5), $MachinePrecision], If[LessEqual[x, 1.65e-237], N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y3 * t$95$8), $MachinePrecision]), $MachinePrecision] - N[(x * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e-141], N[(y * N[(y3 * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e-84], t$95$11, If[LessEqual[x, 4.6e-32], N[(y3 * N[(t$95$3 + N[(t$95$7 + N[(z * t$95$10), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1e+53], t$95$1, If[LessEqual[x, 1.02e+139], t$95$11, If[LessEqual[x, 4.5e+218], t$95$1, t$95$6]]]]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if x < -2.09999999999999991e-60 or 4.50000000000000008e218 < x

   1. Initial program 29.5%

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

   3. Simplified 29.5%

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

   5. Taylor expanded in x around inf 68.9%

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

   if -2.09999999999999991e-60 < x < -5.49999999999999995e-212

   1. Initial program 23.1%

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

   3. Taylor expanded in t around inf 38.7%

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

   4. Taylor expanded in y3 around inf 62.4%

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

      1. distribute-lft-out-- 62.4%

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

   6. Simplified 62.4%

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

   if -5.49999999999999995e-212 < x < -3.10000000000000014e-301

   1. Initial program 50.7%

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

   3. Taylor expanded in t around inf 50.3%

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

   4. Taylor expanded in j around 0 60.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right) + k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot \left(t \cdot y2 - y \cdot y3\right)} \]

   if -3.10000000000000014e-301 < x < -5.99999999999999978e-302

   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 y2 around inf 0.0%

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

   4. Taylor expanded in y0 around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

      5. *-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

      3. *-commutative 100.0%

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

   9. Simplified 100.0%

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

   if -5.99999999999999978e-302 < x < 6.4999999999999997e-292

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in x around inf 45.0%

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

   6. Taylor expanded in y around inf 78.3%

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

   if 6.4999999999999997e-292 < x < 1.6500000000000001e-237

   1. Initial program 20.3%

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

   3. Taylor expanded in j around inf 73.5%

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

   if 1.6500000000000001e-237 < x < 2.0000000000000001e-141

   1. Initial program 17.6%

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

   3. Taylor expanded in t around inf 23.4%

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

   4. Taylor expanded in y around inf 65.2%

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

   if 2.0000000000000001e-141 < x < 9.00000000000000031e-84 or 9.9999999999999999e52 < x < 1.02e139

   1. Initial program 18.2%

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

   3. Simplified 18.2%

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

   5. Taylor expanded in z around -inf 57.9%

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

   if 9.00000000000000031e-84 < x < 4.6000000000000001e-32

   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 y3 around -inf 73.3%

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

   if 4.6000000000000001e-32 < x < 9.9999999999999999e52 or 1.02e139 < x < 4.50000000000000008e218

   1. Initial program 35.4%

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

   3. Simplified 35.4%

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

   5. Taylor expanded in b around inf 61.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-212}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-301}:\\ \;\;\;\;\left(t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right) + k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-302}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-292}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-237}:\\ \;\;\;\;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) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-141}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-84}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-32}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;x \leq 10^{+53}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+139}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.5 \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{else}:\\ \;\;\;\;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)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 52.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 88.1%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.6%

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

   5. Taylor expanded in x around inf 44.6%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.2%

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

Alternative 3: 39.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y4 - a \cdot y5\\ t_2 := y \cdot t_1\\ t_3 := y \cdot \left(a \cdot b - c \cdot i\right)\\ t_4 := x \cdot \left(\left(t_3 + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_5 := j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\\ t_6 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{-60}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-303}:\\ \;\;\;\;y3 \cdot \left(t_2 + t_5\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-292}:\\ \;\;\;\;x \cdot t_3\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-238}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-113}:\\ \;\;\;\;y \cdot \left(y3 \cdot t_1\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-78}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(z \cdot c - j \cdot y5\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-32}:\\ \;\;\;\;y3 \cdot \left(t_2 + \left(t_5 + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+53}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+160}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right) + \left(c \cdot \left(z \cdot t - x \cdot y\right) - j \cdot \left(t \cdot y5\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+215}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y4) (* a y5)))
        (t_2 (* y t_1))
        (t_3 (* y (- (* a b) (* c i))))
        (t_4
         (*
          x
          (+
           (+ t_3 (* y2 (- (* c y0) (* a y1))))
           (* j (- (* i y1) (* b y0))))))
        (t_5 (* j (- (* y0 y5) (* y1 y4))))
        (t_6
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j)))))))
   (if (<= x -2.3e-60)
     t_4
     (if (<= x -1.9e-303)
       (* y3 (+ t_2 t_5))
       (if (<= x 6.5e-292)
         (* x t_3)
         (if (<= x 2e-238)
           (*
            j
            (-
             (- (* t (- (* b y4) (* i y5))) (* y3 (- (* y1 y4) (* y0 y5))))
             (* x (- (* b y0) (* i y1)))))
           (if (<= x 2.2e-113)
             (* y (* y3 t_1))
             (if (<= x 1.9e-78)
               (* (* t i) (- (* z c) (* j y5)))
               (if (<= x 4.2e-32)
                 (* y3 (+ t_2 (+ t_5 (* z (- (* a y1) (* c y0))))))
                 (if (<= x 1.1e+53)
                   t_6
                   (if (<= x 2e+160)
                     (*
                      i
                      (+
                       (* j (* x y1))
                       (- (* c (- (* z t) (* x y))) (* j (* t y5)))))
                     (if (<= x 2.2e+215) t_6 t_4))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y4) - (a * y5);
	double t_2 = y * t_1;
	double t_3 = y * ((a * b) - (c * i));
	double t_4 = x * ((t_3 + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double t_5 = j * ((y0 * y5) - (y1 * y4));
	double t_6 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (x <= -2.3e-60) {
		tmp = t_4;
	} else if (x <= -1.9e-303) {
		tmp = y3 * (t_2 + t_5);
	} else if (x <= 6.5e-292) {
		tmp = x * t_3;
	} else if (x <= 2e-238) {
		tmp = j * (((t * ((b * y4) - (i * y5))) - (y3 * ((y1 * y4) - (y0 * y5)))) - (x * ((b * y0) - (i * y1))));
	} else if (x <= 2.2e-113) {
		tmp = y * (y3 * t_1);
	} else if (x <= 1.9e-78) {
		tmp = (t * i) * ((z * c) - (j * y5));
	} else if (x <= 4.2e-32) {
		tmp = y3 * (t_2 + (t_5 + (z * ((a * y1) - (c * y0)))));
	} else if (x <= 1.1e+53) {
		tmp = t_6;
	} else if (x <= 2e+160) {
		tmp = i * ((j * (x * y1)) + ((c * ((z * t) - (x * y))) - (j * (t * y5))));
	} else if (x <= 2.2e+215) {
		tmp = t_6;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = (c * y4) - (a * y5)
    t_2 = y * t_1
    t_3 = y * ((a * b) - (c * i))
    t_4 = x * ((t_3 + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    t_5 = j * ((y0 * y5) - (y1 * y4))
    t_6 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    if (x <= (-2.3d-60)) then
        tmp = t_4
    else if (x <= (-1.9d-303)) then
        tmp = y3 * (t_2 + t_5)
    else if (x <= 6.5d-292) then
        tmp = x * t_3
    else if (x <= 2d-238) then
        tmp = j * (((t * ((b * y4) - (i * y5))) - (y3 * ((y1 * y4) - (y0 * y5)))) - (x * ((b * y0) - (i * y1))))
    else if (x <= 2.2d-113) then
        tmp = y * (y3 * t_1)
    else if (x <= 1.9d-78) then
        tmp = (t * i) * ((z * c) - (j * y5))
    else if (x <= 4.2d-32) then
        tmp = y3 * (t_2 + (t_5 + (z * ((a * y1) - (c * y0)))))
    else if (x <= 1.1d+53) then
        tmp = t_6
    else if (x <= 2d+160) then
        tmp = i * ((j * (x * y1)) + ((c * ((z * t) - (x * y))) - (j * (t * y5))))
    else if (x <= 2.2d+215) then
        tmp = t_6
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y4) - (a * y5);
	double t_2 = y * t_1;
	double t_3 = y * ((a * b) - (c * i));
	double t_4 = x * ((t_3 + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double t_5 = j * ((y0 * y5) - (y1 * y4));
	double t_6 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double tmp;
	if (x <= -2.3e-60) {
		tmp = t_4;
	} else if (x <= -1.9e-303) {
		tmp = y3 * (t_2 + t_5);
	} else if (x <= 6.5e-292) {
		tmp = x * t_3;
	} else if (x <= 2e-238) {
		tmp = j * (((t * ((b * y4) - (i * y5))) - (y3 * ((y1 * y4) - (y0 * y5)))) - (x * ((b * y0) - (i * y1))));
	} else if (x <= 2.2e-113) {
		tmp = y * (y3 * t_1);
	} else if (x <= 1.9e-78) {
		tmp = (t * i) * ((z * c) - (j * y5));
	} else if (x <= 4.2e-32) {
		tmp = y3 * (t_2 + (t_5 + (z * ((a * y1) - (c * y0)))));
	} else if (x <= 1.1e+53) {
		tmp = t_6;
	} else if (x <= 2e+160) {
		tmp = i * ((j * (x * y1)) + ((c * ((z * t) - (x * y))) - (j * (t * y5))));
	} else if (x <= 2.2e+215) {
		tmp = t_6;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * y4) - (a * y5)
	t_2 = y * t_1
	t_3 = y * ((a * b) - (c * i))
	t_4 = x * ((t_3 + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	t_5 = j * ((y0 * y5) - (y1 * y4))
	t_6 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	tmp = 0
	if x <= -2.3e-60:
		tmp = t_4
	elif x <= -1.9e-303:
		tmp = y3 * (t_2 + t_5)
	elif x <= 6.5e-292:
		tmp = x * t_3
	elif x <= 2e-238:
		tmp = j * (((t * ((b * y4) - (i * y5))) - (y3 * ((y1 * y4) - (y0 * y5)))) - (x * ((b * y0) - (i * y1))))
	elif x <= 2.2e-113:
		tmp = y * (y3 * t_1)
	elif x <= 1.9e-78:
		tmp = (t * i) * ((z * c) - (j * y5))
	elif x <= 4.2e-32:
		tmp = y3 * (t_2 + (t_5 + (z * ((a * y1) - (c * y0)))))
	elif x <= 1.1e+53:
		tmp = t_6
	elif x <= 2e+160:
		tmp = i * ((j * (x * y1)) + ((c * ((z * t) - (x * y))) - (j * (t * y5))))
	elif x <= 2.2e+215:
		tmp = t_6
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y4) - Float64(a * y5))
	t_2 = Float64(y * t_1)
	t_3 = Float64(y * Float64(Float64(a * b) - Float64(c * i)))
	t_4 = Float64(x * Float64(Float64(t_3 + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_5 = Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4)))
	t_6 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	tmp = 0.0
	if (x <= -2.3e-60)
		tmp = t_4;
	elseif (x <= -1.9e-303)
		tmp = Float64(y3 * Float64(t_2 + t_5));
	elseif (x <= 6.5e-292)
		tmp = Float64(x * t_3);
	elseif (x <= 2e-238)
		tmp = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) - Float64(y3 * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) - Float64(x * Float64(Float64(b * y0) - Float64(i * y1)))));
	elseif (x <= 2.2e-113)
		tmp = Float64(y * Float64(y3 * t_1));
	elseif (x <= 1.9e-78)
		tmp = Float64(Float64(t * i) * Float64(Float64(z * c) - Float64(j * y5)));
	elseif (x <= 4.2e-32)
		tmp = Float64(y3 * Float64(t_2 + Float64(t_5 + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (x <= 1.1e+53)
		tmp = t_6;
	elseif (x <= 2e+160)
		tmp = Float64(i * Float64(Float64(j * Float64(x * y1)) + Float64(Float64(c * Float64(Float64(z * t) - Float64(x * y))) - Float64(j * Float64(t * y5)))));
	elseif (x <= 2.2e+215)
		tmp = t_6;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (c * y4) - (a * y5);
	t_2 = y * t_1;
	t_3 = y * ((a * b) - (c * i));
	t_4 = x * ((t_3 + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	t_5 = j * ((y0 * y5) - (y1 * y4));
	t_6 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	tmp = 0.0;
	if (x <= -2.3e-60)
		tmp = t_4;
	elseif (x <= -1.9e-303)
		tmp = y3 * (t_2 + t_5);
	elseif (x <= 6.5e-292)
		tmp = x * t_3;
	elseif (x <= 2e-238)
		tmp = j * (((t * ((b * y4) - (i * y5))) - (y3 * ((y1 * y4) - (y0 * y5)))) - (x * ((b * y0) - (i * y1))));
	elseif (x <= 2.2e-113)
		tmp = y * (y3 * t_1);
	elseif (x <= 1.9e-78)
		tmp = (t * i) * ((z * c) - (j * y5));
	elseif (x <= 4.2e-32)
		tmp = y3 * (t_2 + (t_5 + (z * ((a * y1) - (c * y0)))));
	elseif (x <= 1.1e+53)
		tmp = t_6;
	elseif (x <= 2e+160)
		tmp = i * ((j * (x * y1)) + ((c * ((z * t) - (x * y))) - (j * (t * y5))));
	elseif (x <= 2.2e+215)
		tmp = t_6;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(t$95$3 + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = 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[x, -2.3e-60], t$95$4, If[LessEqual[x, -1.9e-303], N[(y3 * N[(t$95$2 + t$95$5), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e-292], N[(x * t$95$3), $MachinePrecision], If[LessEqual[x, 2e-238], N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y3 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e-113], N[(y * N[(y3 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e-78], N[(N[(t * i), $MachinePrecision] * N[(N[(z * c), $MachinePrecision] - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e-32], N[(y3 * N[(t$95$2 + N[(t$95$5 + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e+53], t$95$6, If[LessEqual[x, 2e+160], N[(i * N[(N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision] + N[(N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e+215], t$95$6, t$95$4]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if x < -2.3000000000000001e-60 or 2.2000000000000001e215 < x

   1. Initial program 29.5%

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

   3. Simplified 29.5%

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

   5. Taylor expanded in x around inf 68.9%

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

   if -2.3000000000000001e-60 < x < -1.90000000000000005e-303

   1. Initial program 29.9%

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

   3. Taylor expanded in t around inf 40.8%

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

   4. Taylor expanded in y3 around inf 51.4%

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

      1. distribute-lft-out-- 51.4%

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

   6. Simplified 51.4%

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

   if -1.90000000000000005e-303 < x < 6.4999999999999997e-292

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in x around inf 45.0%

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

   6. Taylor expanded in y around inf 78.3%

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

   if 6.4999999999999997e-292 < x < 2e-238

   1. Initial program 20.3%

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

   3. Taylor expanded in j around inf 73.5%

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

   if 2e-238 < x < 2.20000000000000004e-113

   1. Initial program 20.8%

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

   3. Taylor expanded in t around inf 25.2%

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

   4. Taylor expanded in y around inf 55.1%

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

   if 2.20000000000000004e-113 < x < 1.8999999999999999e-78

   1. Initial program 16.7%

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

   3. Taylor expanded in t around inf 34.2%

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

   4. Taylor expanded in i around inf 67.2%

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

      1. associate-*r* 67.2%

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

      2. +-commutative 67.2%

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

      3. mul-1-neg 67.2%

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

      4. unsub-neg 67.2%

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

   6. Simplified 67.2%

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

   if 1.8999999999999999e-78 < x < 4.1999999999999998e-32

   1. Initial program 40.3%

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

   3. Taylor expanded in y3 around -inf 80.2%

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

   if 4.1999999999999998e-32 < x < 1.09999999999999999e53 or 2.00000000000000001e160 < x < 2.2000000000000001e215

   1. Initial program 37.0%

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

   3. Simplified 37.0%

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

   5. Taylor expanded in b around inf 63.4%

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

   if 1.09999999999999999e53 < x < 2.00000000000000001e160

   1. Initial program 16.0%

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

   3. Simplified 16.0%

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

   5. Taylor expanded in i around -inf 36.6%

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

   6. Taylor expanded in k around 0 52.6%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + j \cdot \left(t \cdot y5\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-303}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-292}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-238}:\\ \;\;\;\;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) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-113}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-78}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(z \cdot c - j \cdot y5\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-32}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+53}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+160}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right) + \left(c \cdot \left(z \cdot t - x \cdot y\right) - j \cdot \left(t \cdot y5\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+215}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;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)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 39.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot y1 - c \cdot y0\\ t_2 := c \cdot y4 - a \cdot y5\\ t_3 := y \cdot t_2\\ t_4 := j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\\ t_5 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_6 := b \cdot y0 - i \cdot y1\\ t_7 := y \cdot \left(a \cdot b - c \cdot i\right)\\ t_8 := x \cdot \left(\left(t_7 + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_9 := z \cdot \left(k \cdot t_6 + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot t_1\right)\right)\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{-60}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-303}:\\ \;\;\;\;y3 \cdot \left(t_3 + t_4\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-292}:\\ \;\;\;\;x \cdot t_7\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-238}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - x \cdot t_6\right)\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-137}:\\ \;\;\;\;y \cdot \left(y3 \cdot t_2\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-84}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-32}:\\ \;\;\;\;y3 \cdot \left(t_3 + \left(t_4 + z \cdot t_1\right)\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+53}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+138}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+216}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_8\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a y1) (* c y0)))
        (t_2 (- (* c y4) (* a y5)))
        (t_3 (* y t_2))
        (t_4 (* j (- (* y0 y5) (* y1 y4))))
        (t_5
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
           (* y0 (- (* z k) (* x j))))))
        (t_6 (- (* b y0) (* i y1)))
        (t_7 (* y (- (* a b) (* c i))))
        (t_8
         (*
          x
          (+
           (+ t_7 (* y2 (- (* c y0) (* a y1))))
           (* j (- (* i y1) (* b y0))))))
        (t_9 (* z (+ (* k t_6) (+ (* t (- (* c i) (* a b))) (* y3 t_1))))))
   (if (<= x -2.3e-60)
     t_8
     (if (<= x -1.95e-303)
       (* y3 (+ t_3 t_4))
       (if (<= x 6.5e-292)
         (* x t_7)
         (if (<= x 5.2e-238)
           (*
            j
            (-
             (- (* t (- (* b y4) (* i y5))) (* y3 (- (* y1 y4) (* y0 y5))))
             (* x t_6)))
           (if (<= x 1.22e-137)
             (* y (* y3 t_2))
             (if (<= x 2.05e-84)
               t_9
               (if (<= x 4.3e-32)
                 (* y3 (+ t_3 (+ t_4 (* z t_1))))
                 (if (<= x 1.35e+53)
                   t_5
                   (if (<= x 1.65e+138)
                     t_9
                     (if (<= x 4.5e+216) t_5 t_8))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y1) - (c * y0);
	double t_2 = (c * y4) - (a * y5);
	double t_3 = y * t_2;
	double t_4 = j * ((y0 * y5) - (y1 * y4));
	double t_5 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_6 = (b * y0) - (i * y1);
	double t_7 = y * ((a * b) - (c * i));
	double t_8 = x * ((t_7 + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double t_9 = z * ((k * t_6) + ((t * ((c * i) - (a * b))) + (y3 * t_1)));
	double tmp;
	if (x <= -2.3e-60) {
		tmp = t_8;
	} else if (x <= -1.95e-303) {
		tmp = y3 * (t_3 + t_4);
	} else if (x <= 6.5e-292) {
		tmp = x * t_7;
	} else if (x <= 5.2e-238) {
		tmp = j * (((t * ((b * y4) - (i * y5))) - (y3 * ((y1 * y4) - (y0 * y5)))) - (x * t_6));
	} else if (x <= 1.22e-137) {
		tmp = y * (y3 * t_2);
	} else if (x <= 2.05e-84) {
		tmp = t_9;
	} else if (x <= 4.3e-32) {
		tmp = y3 * (t_3 + (t_4 + (z * t_1)));
	} else if (x <= 1.35e+53) {
		tmp = t_5;
	} else if (x <= 1.65e+138) {
		tmp = t_9;
	} else if (x <= 4.5e+216) {
		tmp = t_5;
	} else {
		tmp = t_8;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (a * y1) - (c * y0)
    t_2 = (c * y4) - (a * y5)
    t_3 = y * t_2
    t_4 = j * ((y0 * y5) - (y1 * y4))
    t_5 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    t_6 = (b * y0) - (i * y1)
    t_7 = y * ((a * b) - (c * i))
    t_8 = x * ((t_7 + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    t_9 = z * ((k * t_6) + ((t * ((c * i) - (a * b))) + (y3 * t_1)))
    if (x <= (-2.3d-60)) then
        tmp = t_8
    else if (x <= (-1.95d-303)) then
        tmp = y3 * (t_3 + t_4)
    else if (x <= 6.5d-292) then
        tmp = x * t_7
    else if (x <= 5.2d-238) then
        tmp = j * (((t * ((b * y4) - (i * y5))) - (y3 * ((y1 * y4) - (y0 * y5)))) - (x * t_6))
    else if (x <= 1.22d-137) then
        tmp = y * (y3 * t_2)
    else if (x <= 2.05d-84) then
        tmp = t_9
    else if (x <= 4.3d-32) then
        tmp = y3 * (t_3 + (t_4 + (z * t_1)))
    else if (x <= 1.35d+53) then
        tmp = t_5
    else if (x <= 1.65d+138) then
        tmp = t_9
    else if (x <= 4.5d+216) then
        tmp = t_5
    else
        tmp = t_8
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y1) - (c * y0);
	double t_2 = (c * y4) - (a * y5);
	double t_3 = y * t_2;
	double t_4 = j * ((y0 * y5) - (y1 * y4));
	double t_5 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	double t_6 = (b * y0) - (i * y1);
	double t_7 = y * ((a * b) - (c * i));
	double t_8 = x * ((t_7 + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double t_9 = z * ((k * t_6) + ((t * ((c * i) - (a * b))) + (y3 * t_1)));
	double tmp;
	if (x <= -2.3e-60) {
		tmp = t_8;
	} else if (x <= -1.95e-303) {
		tmp = y3 * (t_3 + t_4);
	} else if (x <= 6.5e-292) {
		tmp = x * t_7;
	} else if (x <= 5.2e-238) {
		tmp = j * (((t * ((b * y4) - (i * y5))) - (y3 * ((y1 * y4) - (y0 * y5)))) - (x * t_6));
	} else if (x <= 1.22e-137) {
		tmp = y * (y3 * t_2);
	} else if (x <= 2.05e-84) {
		tmp = t_9;
	} else if (x <= 4.3e-32) {
		tmp = y3 * (t_3 + (t_4 + (z * t_1)));
	} else if (x <= 1.35e+53) {
		tmp = t_5;
	} else if (x <= 1.65e+138) {
		tmp = t_9;
	} else if (x <= 4.5e+216) {
		tmp = t_5;
	} else {
		tmp = t_8;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (a * y1) - (c * y0)
	t_2 = (c * y4) - (a * y5)
	t_3 = y * t_2
	t_4 = j * ((y0 * y5) - (y1 * y4))
	t_5 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	t_6 = (b * y0) - (i * y1)
	t_7 = y * ((a * b) - (c * i))
	t_8 = x * ((t_7 + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	t_9 = z * ((k * t_6) + ((t * ((c * i) - (a * b))) + (y3 * t_1)))
	tmp = 0
	if x <= -2.3e-60:
		tmp = t_8
	elif x <= -1.95e-303:
		tmp = y3 * (t_3 + t_4)
	elif x <= 6.5e-292:
		tmp = x * t_7
	elif x <= 5.2e-238:
		tmp = j * (((t * ((b * y4) - (i * y5))) - (y3 * ((y1 * y4) - (y0 * y5)))) - (x * t_6))
	elif x <= 1.22e-137:
		tmp = y * (y3 * t_2)
	elif x <= 2.05e-84:
		tmp = t_9
	elif x <= 4.3e-32:
		tmp = y3 * (t_3 + (t_4 + (z * t_1)))
	elif x <= 1.35e+53:
		tmp = t_5
	elif x <= 1.65e+138:
		tmp = t_9
	elif x <= 4.5e+216:
		tmp = t_5
	else:
		tmp = t_8
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(a * y1) - Float64(c * y0))
	t_2 = Float64(Float64(c * y4) - Float64(a * y5))
	t_3 = Float64(y * t_2)
	t_4 = Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4)))
	t_5 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))))
	t_6 = Float64(Float64(b * y0) - Float64(i * y1))
	t_7 = Float64(y * Float64(Float64(a * b) - Float64(c * i)))
	t_8 = Float64(x * Float64(Float64(t_7 + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_9 = Float64(z * Float64(Float64(k * t_6) + Float64(Float64(t * Float64(Float64(c * i) - Float64(a * b))) + Float64(y3 * t_1))))
	tmp = 0.0
	if (x <= -2.3e-60)
		tmp = t_8;
	elseif (x <= -1.95e-303)
		tmp = Float64(y3 * Float64(t_3 + t_4));
	elseif (x <= 6.5e-292)
		tmp = Float64(x * t_7);
	elseif (x <= 5.2e-238)
		tmp = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) - Float64(y3 * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) - Float64(x * t_6)));
	elseif (x <= 1.22e-137)
		tmp = Float64(y * Float64(y3 * t_2));
	elseif (x <= 2.05e-84)
		tmp = t_9;
	elseif (x <= 4.3e-32)
		tmp = Float64(y3 * Float64(t_3 + Float64(t_4 + Float64(z * t_1))));
	elseif (x <= 1.35e+53)
		tmp = t_5;
	elseif (x <= 1.65e+138)
		tmp = t_9;
	elseif (x <= 4.5e+216)
		tmp = t_5;
	else
		tmp = t_8;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (a * y1) - (c * y0);
	t_2 = (c * y4) - (a * y5);
	t_3 = y * t_2;
	t_4 = j * ((y0 * y5) - (y1 * y4));
	t_5 = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	t_6 = (b * y0) - (i * y1);
	t_7 = y * ((a * b) - (c * i));
	t_8 = x * ((t_7 + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	t_9 = z * ((k * t_6) + ((t * ((c * i) - (a * b))) + (y3 * t_1)));
	tmp = 0.0;
	if (x <= -2.3e-60)
		tmp = t_8;
	elseif (x <= -1.95e-303)
		tmp = y3 * (t_3 + t_4);
	elseif (x <= 6.5e-292)
		tmp = x * t_7;
	elseif (x <= 5.2e-238)
		tmp = j * (((t * ((b * y4) - (i * y5))) - (y3 * ((y1 * y4) - (y0 * y5)))) - (x * t_6));
	elseif (x <= 1.22e-137)
		tmp = y * (y3 * t_2);
	elseif (x <= 2.05e-84)
		tmp = t_9;
	elseif (x <= 4.3e-32)
		tmp = y3 * (t_3 + (t_4 + (z * t_1)));
	elseif (x <= 1.35e+53)
		tmp = t_5;
	elseif (x <= 1.65e+138)
		tmp = t_9;
	elseif (x <= 4.5e+216)
		tmp = t_5;
	else
		tmp = t_8;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(x * N[(N[(t$95$7 + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(z * N[(N[(k * t$95$6), $MachinePrecision] + N[(N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.3e-60], t$95$8, If[LessEqual[x, -1.95e-303], N[(y3 * N[(t$95$3 + t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e-292], N[(x * t$95$7), $MachinePrecision], If[LessEqual[x, 5.2e-238], N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y3 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.22e-137], N[(y * N[(y3 * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.05e-84], t$95$9, If[LessEqual[x, 4.3e-32], N[(y3 * N[(t$95$3 + N[(t$95$4 + N[(z * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.35e+53], t$95$5, If[LessEqual[x, 1.65e+138], t$95$9, If[LessEqual[x, 4.5e+216], t$95$5, t$95$8]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if x < -2.3000000000000001e-60 or 4.50000000000000025e216 < x

   1. Initial program 29.5%

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

   3. Simplified 29.5%

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

   5. Taylor expanded in x around inf 68.9%

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

   if -2.3000000000000001e-60 < x < -1.95e-303

   1. Initial program 29.9%

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

   3. Taylor expanded in t around inf 40.8%

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

   4. Taylor expanded in y3 around inf 51.4%

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

      1. distribute-lft-out-- 51.4%

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

   6. Simplified 51.4%

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

   if -1.95e-303 < x < 6.4999999999999997e-292

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in x around inf 45.0%

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

   6. Taylor expanded in y around inf 78.3%

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

   if 6.4999999999999997e-292 < x < 5.2000000000000002e-238

   1. Initial program 20.3%

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

   3. Taylor expanded in j around inf 73.5%

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

   if 5.2000000000000002e-238 < x < 1.21999999999999997e-137

   1. Initial program 17.6%

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

   3. Taylor expanded in t around inf 23.4%

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

   4. Taylor expanded in y around inf 65.2%

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

   if 1.21999999999999997e-137 < x < 2.05000000000000003e-84 or 1.3500000000000001e53 < x < 1.64999999999999989e138

   1. Initial program 18.2%

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

   3. Simplified 18.2%

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

   5. Taylor expanded in z around -inf 57.9%

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

   if 2.05000000000000003e-84 < x < 4.2999999999999999e-32

   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 y3 around -inf 73.3%

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

   if 4.2999999999999999e-32 < x < 1.3500000000000001e53 or 1.64999999999999989e138 < x < 4.50000000000000025e216

   1. Initial program 35.4%

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

   3. Simplified 35.4%

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

   5. Taylor expanded in b around inf 61.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-303}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-292}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-238}:\\ \;\;\;\;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) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-137}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-84}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-32}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+53}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+138}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(t \cdot \left(c \cdot i - a \cdot b\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+216}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;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)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 35.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\\ t_2 := y5 \cdot \left(y \cdot k - t \cdot j\right)\\ t_3 := j \cdot \left(x \cdot y1\right)\\ t_4 := y \cdot \left(c \cdot y4 - a \cdot y5\right)\\ t_5 := y3 \cdot \left(t_4 + t_1\right)\\ \mathbf{if}\;j \leq -8 \cdot 10^{+37}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + t_2\right)\\ \mathbf{elif}\;j \leq -1.2 \cdot 10^{-132}:\\ \;\;\;\;i \cdot \left(t_3 + \left(c \cdot \left(z \cdot t - x \cdot y\right) - j \cdot \left(t \cdot y5\right)\right)\right)\\ \mathbf{elif}\;j \leq -9 \cdot 10^{-181}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{-194}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \left(y1 \cdot y3 - t \cdot b\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{-281}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 2.15 \cdot 10^{-157}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{-105}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 9 \cdot 10^{+57}:\\ \;\;\;\;y3 \cdot \left(t_4 + \left(t_1 + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{+202}:\\ \;\;\;\;i \cdot \left(t_3 + t_2\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+284}:\\ \;\;\;\;\left(b \cdot y0\right) \cdot \left(z \cdot k - x \cdot j\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{+305}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(b \cdot \left(z \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (- (* y0 y5) (* y1 y4))))
        (t_2 (* y5 (- (* y k) (* t j))))
        (t_3 (* j (* x y1)))
        (t_4 (* y (- (* c y4) (* a y5))))
        (t_5 (* y3 (+ t_4 t_1))))
   (if (<= j -8e+37)
     (* i (+ (* y1 (- (* x j) (* z k))) t_2))
     (if (<= j -1.2e-132)
       (* i (+ t_3 (- (* c (- (* z t) (* x y))) (* j (* t y5)))))
       (if (<= j -9e-181)
         t_5
         (if (<= j -4.2e-194)
           (* (* z a) (- (* y1 y3) (* t b)))
           (if (<= j 1.45e-281)
             (*
              y2
              (+
               (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
               (* t (- (* a y5) (* c y4)))))
             (if (<= j 2.15e-157)
               t_5
               (if (<= j 4.5e-105)
                 (* y0 (* y2 (- (* x c) (* k y5))))
                 (if (<= j 9e+57)
                   (* y3 (+ t_4 (+ t_1 (* z (- (* a y1) (* c y0))))))
                   (if (<= j 5.8e+202)
                     (* i (+ t_3 t_2))
                     (if (<= j 8e+284)
                       (* (* b y0) (- (* z k) (* x j)))
                       (if (<= j 3e+305) t_5 (* k (* b (* z y0))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * ((y0 * y5) - (y1 * y4));
	double t_2 = y5 * ((y * k) - (t * j));
	double t_3 = j * (x * y1);
	double t_4 = y * ((c * y4) - (a * y5));
	double t_5 = y3 * (t_4 + t_1);
	double tmp;
	if (j <= -8e+37) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + t_2);
	} else if (j <= -1.2e-132) {
		tmp = i * (t_3 + ((c * ((z * t) - (x * y))) - (j * (t * y5))));
	} else if (j <= -9e-181) {
		tmp = t_5;
	} else if (j <= -4.2e-194) {
		tmp = (z * a) * ((y1 * y3) - (t * b));
	} else if (j <= 1.45e-281) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (j <= 2.15e-157) {
		tmp = t_5;
	} else if (j <= 4.5e-105) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (j <= 9e+57) {
		tmp = y3 * (t_4 + (t_1 + (z * ((a * y1) - (c * y0)))));
	} else if (j <= 5.8e+202) {
		tmp = i * (t_3 + t_2);
	} else if (j <= 8e+284) {
		tmp = (b * y0) * ((z * k) - (x * j));
	} else if (j <= 3e+305) {
		tmp = t_5;
	} else {
		tmp = k * (b * (z * y0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = j * ((y0 * y5) - (y1 * y4))
    t_2 = y5 * ((y * k) - (t * j))
    t_3 = j * (x * y1)
    t_4 = y * ((c * y4) - (a * y5))
    t_5 = y3 * (t_4 + t_1)
    if (j <= (-8d+37)) then
        tmp = i * ((y1 * ((x * j) - (z * k))) + t_2)
    else if (j <= (-1.2d-132)) then
        tmp = i * (t_3 + ((c * ((z * t) - (x * y))) - (j * (t * y5))))
    else if (j <= (-9d-181)) then
        tmp = t_5
    else if (j <= (-4.2d-194)) then
        tmp = (z * a) * ((y1 * y3) - (t * b))
    else if (j <= 1.45d-281) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    else if (j <= 2.15d-157) then
        tmp = t_5
    else if (j <= 4.5d-105) then
        tmp = y0 * (y2 * ((x * c) - (k * y5)))
    else if (j <= 9d+57) then
        tmp = y3 * (t_4 + (t_1 + (z * ((a * y1) - (c * y0)))))
    else if (j <= 5.8d+202) then
        tmp = i * (t_3 + t_2)
    else if (j <= 8d+284) then
        tmp = (b * y0) * ((z * k) - (x * j))
    else if (j <= 3d+305) then
        tmp = t_5
    else
        tmp = k * (b * (z * y0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * ((y0 * y5) - (y1 * y4));
	double t_2 = y5 * ((y * k) - (t * j));
	double t_3 = j * (x * y1);
	double t_4 = y * ((c * y4) - (a * y5));
	double t_5 = y3 * (t_4 + t_1);
	double tmp;
	if (j <= -8e+37) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + t_2);
	} else if (j <= -1.2e-132) {
		tmp = i * (t_3 + ((c * ((z * t) - (x * y))) - (j * (t * y5))));
	} else if (j <= -9e-181) {
		tmp = t_5;
	} else if (j <= -4.2e-194) {
		tmp = (z * a) * ((y1 * y3) - (t * b));
	} else if (j <= 1.45e-281) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (j <= 2.15e-157) {
		tmp = t_5;
	} else if (j <= 4.5e-105) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (j <= 9e+57) {
		tmp = y3 * (t_4 + (t_1 + (z * ((a * y1) - (c * y0)))));
	} else if (j <= 5.8e+202) {
		tmp = i * (t_3 + t_2);
	} else if (j <= 8e+284) {
		tmp = (b * y0) * ((z * k) - (x * j));
	} else if (j <= 3e+305) {
		tmp = t_5;
	} else {
		tmp = k * (b * (z * y0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * ((y0 * y5) - (y1 * y4))
	t_2 = y5 * ((y * k) - (t * j))
	t_3 = j * (x * y1)
	t_4 = y * ((c * y4) - (a * y5))
	t_5 = y3 * (t_4 + t_1)
	tmp = 0
	if j <= -8e+37:
		tmp = i * ((y1 * ((x * j) - (z * k))) + t_2)
	elif j <= -1.2e-132:
		tmp = i * (t_3 + ((c * ((z * t) - (x * y))) - (j * (t * y5))))
	elif j <= -9e-181:
		tmp = t_5
	elif j <= -4.2e-194:
		tmp = (z * a) * ((y1 * y3) - (t * b))
	elif j <= 1.45e-281:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	elif j <= 2.15e-157:
		tmp = t_5
	elif j <= 4.5e-105:
		tmp = y0 * (y2 * ((x * c) - (k * y5)))
	elif j <= 9e+57:
		tmp = y3 * (t_4 + (t_1 + (z * ((a * y1) - (c * y0)))))
	elif j <= 5.8e+202:
		tmp = i * (t_3 + t_2)
	elif j <= 8e+284:
		tmp = (b * y0) * ((z * k) - (x * j))
	elif j <= 3e+305:
		tmp = t_5
	else:
		tmp = k * (b * (z * y0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4)))
	t_2 = Float64(y5 * Float64(Float64(y * k) - Float64(t * j)))
	t_3 = Float64(j * Float64(x * y1))
	t_4 = Float64(y * Float64(Float64(c * y4) - Float64(a * y5)))
	t_5 = Float64(y3 * Float64(t_4 + t_1))
	tmp = 0.0
	if (j <= -8e+37)
		tmp = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + t_2));
	elseif (j <= -1.2e-132)
		tmp = Float64(i * Float64(t_3 + Float64(Float64(c * Float64(Float64(z * t) - Float64(x * y))) - Float64(j * Float64(t * y5)))));
	elseif (j <= -9e-181)
		tmp = t_5;
	elseif (j <= -4.2e-194)
		tmp = Float64(Float64(z * a) * Float64(Float64(y1 * y3) - Float64(t * b)));
	elseif (j <= 1.45e-281)
		tmp = 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)))));
	elseif (j <= 2.15e-157)
		tmp = t_5;
	elseif (j <= 4.5e-105)
		tmp = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))));
	elseif (j <= 9e+57)
		tmp = Float64(y3 * Float64(t_4 + Float64(t_1 + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (j <= 5.8e+202)
		tmp = Float64(i * Float64(t_3 + t_2));
	elseif (j <= 8e+284)
		tmp = Float64(Float64(b * y0) * Float64(Float64(z * k) - Float64(x * j)));
	elseif (j <= 3e+305)
		tmp = t_5;
	else
		tmp = Float64(k * Float64(b * Float64(z * y0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * ((y0 * y5) - (y1 * y4));
	t_2 = y5 * ((y * k) - (t * j));
	t_3 = j * (x * y1);
	t_4 = y * ((c * y4) - (a * y5));
	t_5 = y3 * (t_4 + t_1);
	tmp = 0.0;
	if (j <= -8e+37)
		tmp = i * ((y1 * ((x * j) - (z * k))) + t_2);
	elseif (j <= -1.2e-132)
		tmp = i * (t_3 + ((c * ((z * t) - (x * y))) - (j * (t * y5))));
	elseif (j <= -9e-181)
		tmp = t_5;
	elseif (j <= -4.2e-194)
		tmp = (z * a) * ((y1 * y3) - (t * b));
	elseif (j <= 1.45e-281)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	elseif (j <= 2.15e-157)
		tmp = t_5;
	elseif (j <= 4.5e-105)
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	elseif (j <= 9e+57)
		tmp = y3 * (t_4 + (t_1 + (z * ((a * y1) - (c * y0)))));
	elseif (j <= 5.8e+202)
		tmp = i * (t_3 + t_2);
	elseif (j <= 8e+284)
		tmp = (b * y0) * ((z * k) - (x * j));
	elseif (j <= 3e+305)
		tmp = t_5;
	else
		tmp = k * (b * (z * y0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y3 * N[(t$95$4 + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -8e+37], N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.2e-132], N[(i * N[(t$95$3 + N[(N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -9e-181], t$95$5, If[LessEqual[j, -4.2e-194], N[(N[(z * a), $MachinePrecision] * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.45e-281], 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[j, 2.15e-157], t$95$5, If[LessEqual[j, 4.5e-105], N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9e+57], N[(y3 * N[(t$95$4 + N[(t$95$1 + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.8e+202], N[(i * N[(t$95$3 + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8e+284], N[(N[(b * y0), $MachinePrecision] * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3e+305], t$95$5, N[(k * N[(b * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if j < -7.99999999999999963e37

   1. Initial program 19.6%

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

   3. Simplified 19.6%

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

   5. Taylor expanded in i around -inf 44.2%

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

   6. Taylor expanded in c around 0 56.4%

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

   if -7.99999999999999963e37 < j < -1.20000000000000008e-132

   1. Initial program 22.6%

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

   3. Simplified 22.6%

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

   5. Taylor expanded in i around -inf 40.5%

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

   6. Taylor expanded in k around 0 48.0%

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

   if -1.20000000000000008e-132 < j < -8.9999999999999998e-181 or 1.44999999999999995e-281 < j < 2.1499999999999999e-157 or 8.00000000000000063e284 < j < 2.99999999999999982e305

   1. Initial program 27.6%

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

   3. Taylor expanded in t around inf 32.2%

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

   4. Taylor expanded in y3 around inf 63.7%

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

      1. distribute-lft-out-- 63.7%

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

   6. Simplified 63.7%

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

   if -8.9999999999999998e-181 < j < -4.2e-194

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around -inf 75.0%

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

   6. Taylor expanded in a around inf 77.0%

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

      1. associate-*r* 77.0%

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

      2. +-commutative 77.0%

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

      3. mul-1-neg 77.0%

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

      4. unsub-neg 77.0%

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

   8. Simplified 77.0%

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

   if -4.2e-194 < j < 1.44999999999999995e-281

   1. Initial program 56.2%

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

   3. Taylor expanded in y2 around inf 64.8%

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

   if 2.1499999999999999e-157 < j < 4.4999999999999997e-105

   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 y2 around inf 60.0%

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

   4. Taylor expanded in y0 around inf 80.2%

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

      1. +-commutative 80.2%

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

      2. mul-1-neg 80.2%

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

      3. unsub-neg 80.2%

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

      4. *-commutative 80.2%

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

      5. *-commutative 80.2%

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

   6. Simplified 80.2%

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

   if 4.4999999999999997e-105 < j < 8.99999999999999991e57

   1. Initial program 37.3%

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

   3. Taylor expanded in y3 around -inf 69.0%

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

   if 8.99999999999999991e57 < j < 5.7999999999999999e202

   1. Initial program 29.5%

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

   3. Simplified 31.9%

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

   5. Taylor expanded in i around -inf 44.6%

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

   6. Taylor expanded in c around 0 54.4%

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

   7. Taylor expanded in j around inf 59.3%

      \[\leadsto -1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right) - \color{blue}{j \cdot \left(x \cdot y1\right)}\right)\right) \]
   8. Step-by-step derivation

      1. *-commutative 59.3%

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

   9. Simplified 59.3%

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

   if 5.7999999999999999e202 < j < 8.00000000000000063e284

   1. Initial program 23.5%

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

   3. Simplified 23.5%

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

   5. Taylor expanded in b around inf 53.1%

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

   6. Taylor expanded in y0 around inf 71.0%

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

      1. associate-*r* 71.0%

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

      2. *-commutative 71.0%

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

      3. *-commutative 71.0%

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

   8. Simplified 71.0%

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

   if 2.99999999999999982e305 < j

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around -inf 50.0%

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

   6. Taylor expanded in k around inf 50.0%

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

   7. Taylor expanded in i around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

      3. *-commutative 100.0%

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

   9. Simplified 100.0%

      \[\leadsto -1 \cdot \left(k \cdot \color{blue}{\left(\left(-b\right) \cdot \left(z \cdot y0\right)\right)}\right) \]
3. Recombined 10 regimes into one program.

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8 \cdot 10^{+37}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -1.2 \cdot 10^{-132}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right) + \left(c \cdot \left(z \cdot t - x \cdot y\right) - j \cdot \left(t \cdot y5\right)\right)\right)\\ \mathbf{elif}\;j \leq -9 \cdot 10^{-181}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{-194}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \left(y1 \cdot y3 - t \cdot b\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{-281}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 2.15 \cdot 10^{-157}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{-105}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 9 \cdot 10^{+57}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{+202}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+284}:\\ \;\;\;\;\left(b \cdot y0\right) \cdot \left(z \cdot k - x \cdot j\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{+305}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(b \cdot \left(z \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 41.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot y4 - y0 \cdot y5\\ t_2 := j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot t_1\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ t_3 := y \cdot \left(c \cdot y4 - a \cdot y5\right)\\ t_4 := j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\\ t_5 := y3 \cdot \left(t_3 + t_4\right)\\ \mathbf{if}\;j \leq -2.6 \cdot 10^{+79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -4.45 \cdot 10^{-128}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-282}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot t_1 + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-157}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-105}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 9 \cdot 10^{+42}:\\ \;\;\;\;y3 \cdot \left(t_3 + \left(t_4 + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{+155}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{+266}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y1 y4) (* y0 y5)))
        (t_2
         (*
          j
          (-
           (- (* t (- (* b y4) (* i y5))) (* y3 t_1))
           (* x (- (* b y0) (* i y1))))))
        (t_3 (* y (- (* c y4) (* a y5))))
        (t_4 (* j (- (* y0 y5) (* y1 y4))))
        (t_5 (* y3 (+ t_3 t_4))))
   (if (<= j -2.6e+79)
     t_2
     (if (<= j -4.45e-128)
       (*
        b
        (+
         (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
         (* y0 (- (* z k) (* x j)))))
       (if (<= j 6.2e-282)
         (*
          y2
          (+
           (+ (* k t_1) (* x (- (* c y0) (* a y1))))
           (* t (- (* a y5) (* c y4)))))
         (if (<= j 2.3e-157)
           t_5
           (if (<= j 2.6e-105)
             (* y0 (* y2 (- (* x c) (* k y5))))
             (if (<= j 9e+42)
               (* y3 (+ t_3 (+ t_4 (* z (- (* a y1) (* c y0))))))
               (if (<= j 4e+155)
                 (*
                  i
                  (+ (* y1 (- (* x j) (* z k))) (* y5 (- (* y k) (* t j)))))
                 (if (<= j 2.6e+266) t_2 t_5))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double t_2 = j * (((t * ((b * y4) - (i * y5))) - (y3 * t_1)) - (x * ((b * y0) - (i * y1))));
	double t_3 = y * ((c * y4) - (a * y5));
	double t_4 = j * ((y0 * y5) - (y1 * y4));
	double t_5 = y3 * (t_3 + t_4);
	double tmp;
	if (j <= -2.6e+79) {
		tmp = t_2;
	} else if (j <= -4.45e-128) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (j <= 6.2e-282) {
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (j <= 2.3e-157) {
		tmp = t_5;
	} else if (j <= 2.6e-105) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (j <= 9e+42) {
		tmp = y3 * (t_3 + (t_4 + (z * ((a * y1) - (c * y0)))));
	} else if (j <= 4e+155) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j))));
	} else if (j <= 2.6e+266) {
		tmp = t_2;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (y1 * y4) - (y0 * y5)
    t_2 = j * (((t * ((b * y4) - (i * y5))) - (y3 * t_1)) - (x * ((b * y0) - (i * y1))))
    t_3 = y * ((c * y4) - (a * y5))
    t_4 = j * ((y0 * y5) - (y1 * y4))
    t_5 = y3 * (t_3 + t_4)
    if (j <= (-2.6d+79)) then
        tmp = t_2
    else if (j <= (-4.45d-128)) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    else if (j <= 6.2d-282) then
        tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    else if (j <= 2.3d-157) then
        tmp = t_5
    else if (j <= 2.6d-105) then
        tmp = y0 * (y2 * ((x * c) - (k * y5)))
    else if (j <= 9d+42) then
        tmp = y3 * (t_3 + (t_4 + (z * ((a * y1) - (c * y0)))))
    else if (j <= 4d+155) then
        tmp = i * ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j))))
    else if (j <= 2.6d+266) then
        tmp = t_2
    else
        tmp = t_5
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y1 * y4) - (y0 * y5);
	double t_2 = j * (((t * ((b * y4) - (i * y5))) - (y3 * t_1)) - (x * ((b * y0) - (i * y1))));
	double t_3 = y * ((c * y4) - (a * y5));
	double t_4 = j * ((y0 * y5) - (y1 * y4));
	double t_5 = y3 * (t_3 + t_4);
	double tmp;
	if (j <= -2.6e+79) {
		tmp = t_2;
	} else if (j <= -4.45e-128) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (j <= 6.2e-282) {
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (j <= 2.3e-157) {
		tmp = t_5;
	} else if (j <= 2.6e-105) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (j <= 9e+42) {
		tmp = y3 * (t_3 + (t_4 + (z * ((a * y1) - (c * y0)))));
	} else if (j <= 4e+155) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j))));
	} else if (j <= 2.6e+266) {
		tmp = t_2;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y1 * y4) - (y0 * y5)
	t_2 = j * (((t * ((b * y4) - (i * y5))) - (y3 * t_1)) - (x * ((b * y0) - (i * y1))))
	t_3 = y * ((c * y4) - (a * y5))
	t_4 = j * ((y0 * y5) - (y1 * y4))
	t_5 = y3 * (t_3 + t_4)
	tmp = 0
	if j <= -2.6e+79:
		tmp = t_2
	elif j <= -4.45e-128:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	elif j <= 6.2e-282:
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	elif j <= 2.3e-157:
		tmp = t_5
	elif j <= 2.6e-105:
		tmp = y0 * (y2 * ((x * c) - (k * y5)))
	elif j <= 9e+42:
		tmp = y3 * (t_3 + (t_4 + (z * ((a * y1) - (c * y0)))))
	elif j <= 4e+155:
		tmp = i * ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j))))
	elif j <= 2.6e+266:
		tmp = t_2
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_2 = Float64(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) - Float64(y3 * t_1)) - Float64(x * Float64(Float64(b * y0) - Float64(i * y1)))))
	t_3 = Float64(y * Float64(Float64(c * y4) - Float64(a * y5)))
	t_4 = Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4)))
	t_5 = Float64(y3 * Float64(t_3 + t_4))
	tmp = 0.0
	if (j <= -2.6e+79)
		tmp = t_2;
	elseif (j <= -4.45e-128)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (j <= 6.2e-282)
		tmp = Float64(y2 * Float64(Float64(Float64(k * t_1) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (j <= 2.3e-157)
		tmp = t_5;
	elseif (j <= 2.6e-105)
		tmp = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))));
	elseif (j <= 9e+42)
		tmp = Float64(y3 * Float64(t_3 + Float64(t_4 + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (j <= 4e+155)
		tmp = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(y5 * Float64(Float64(y * k) - Float64(t * j)))));
	elseif (j <= 2.6e+266)
		tmp = t_2;
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y1 * y4) - (y0 * y5);
	t_2 = j * (((t * ((b * y4) - (i * y5))) - (y3 * t_1)) - (x * ((b * y0) - (i * y1))));
	t_3 = y * ((c * y4) - (a * y5));
	t_4 = j * ((y0 * y5) - (y1 * y4));
	t_5 = y3 * (t_3 + t_4);
	tmp = 0.0;
	if (j <= -2.6e+79)
		tmp = t_2;
	elseif (j <= -4.45e-128)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	elseif (j <= 6.2e-282)
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	elseif (j <= 2.3e-157)
		tmp = t_5;
	elseif (j <= 2.6e-105)
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	elseif (j <= 9e+42)
		tmp = y3 * (t_3 + (t_4 + (z * ((a * y1) - (c * y0)))));
	elseif (j <= 4e+155)
		tmp = i * ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j))));
	elseif (j <= 2.6e+266)
		tmp = t_2;
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y3 * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y3 * N[(t$95$3 + t$95$4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.6e+79], t$95$2, If[LessEqual[j, -4.45e-128], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.2e-282], N[(y2 * N[(N[(N[(k * t$95$1), $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[j, 2.3e-157], t$95$5, If[LessEqual[j, 2.6e-105], N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9e+42], N[(y3 * N[(t$95$3 + N[(t$95$4 + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4e+155], N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.6e+266], t$95$2, t$95$5]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -2.60000000000000015e79 or 4.00000000000000003e155 < j < 2.60000000000000014e266

   1. Initial program 20.2%

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

   3. Taylor expanded in j around inf 64.0%

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

   if -2.60000000000000015e79 < j < -4.4499999999999998e-128

   1. Initial program 25.6%

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

   3. Simplified 25.6%

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

   5. Taylor expanded in b around inf 47.7%

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

   if -4.4499999999999998e-128 < j < 6.20000000000000027e-282

   1. Initial program 43.7%

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

   3. Taylor expanded in y2 around inf 54.5%

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

   if 6.20000000000000027e-282 < j < 2.29999999999999989e-157 or 2.60000000000000014e266 < j

   1. Initial program 22.9%

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

   3. Taylor expanded in t around inf 27.7%

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

   4. Taylor expanded in y3 around inf 64.9%

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

      1. distribute-lft-out-- 64.9%

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

   6. Simplified 64.9%

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

   if 2.29999999999999989e-157 < j < 2.5999999999999999e-105

   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 y2 around inf 60.0%

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

   4. Taylor expanded in y0 around inf 80.2%

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

      1. +-commutative 80.2%

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

      2. mul-1-neg 80.2%

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

      3. unsub-neg 80.2%

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

      4. *-commutative 80.2%

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

      5. *-commutative 80.2%

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

   6. Simplified 80.2%

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

   if 2.5999999999999999e-105 < j < 9.00000000000000025e42

   1. Initial program 38.2%

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

   3. Taylor expanded in y3 around -inf 69.6%

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

   if 9.00000000000000025e42 < j < 4.00000000000000003e155

   1. Initial program 31.5%

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

   3. Simplified 34.6%

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

   5. Taylor expanded in i around -inf 56.9%

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

   6. Taylor expanded in c around 0 66.3%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.6 \cdot 10^{+79}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -4.45 \cdot 10^{-128}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-282}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-157}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-105}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 9 \cdot 10^{+42}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{+155}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{+266}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) - y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 36.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(c \cdot y4 - a \cdot y5\right)\\ t_2 := j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\\ t_3 := z \cdot k - x \cdot j\\ t_4 := y5 \cdot \left(y \cdot k - t \cdot j\right)\\ t_5 := y3 \cdot \left(t_1 + t_2\right)\\ \mathbf{if}\;j \leq -2.3 \cdot 10^{+72}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + t_4\right)\\ \mathbf{elif}\;j \leq -1 \cdot 10^{-128}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot t_3\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{-283}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{-155}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{-104}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{+57}:\\ \;\;\;\;y3 \cdot \left(t_1 + \left(t_2 + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{+202}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right) + t_4\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{+282}:\\ \;\;\;\;\left(b \cdot y0\right) \cdot t_3\\ \mathbf{elif}\;j \leq 3 \cdot 10^{+305}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(b \cdot \left(z \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y (- (* c y4) (* a y5))))
        (t_2 (* j (- (* y0 y5) (* y1 y4))))
        (t_3 (- (* z k) (* x j)))
        (t_4 (* y5 (- (* y k) (* t j))))
        (t_5 (* y3 (+ t_1 t_2))))
   (if (<= j -2.3e+72)
     (* i (+ (* y1 (- (* x j) (* z k))) t_4))
     (if (<= j -1e-128)
       (*
        b
        (+
         (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
         (* y0 t_3)))
       (if (<= j 8.5e-283)
         (*
          y2
          (+
           (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
           (* t (- (* a y5) (* c y4)))))
         (if (<= j 2.4e-155)
           t_5
           (if (<= j 1.05e-104)
             (* y0 (* y2 (- (* x c) (* k y5))))
             (if (<= j 7.2e+57)
               (* y3 (+ t_1 (+ t_2 (* z (- (* a y1) (* c y0))))))
               (if (<= j 6.4e+202)
                 (* i (+ (* j (* x y1)) t_4))
                 (if (<= j 1.05e+282)
                   (* (* b y0) t_3)
                   (if (<= j 3e+305) t_5 (* k (* b (* z y0))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * ((c * y4) - (a * y5));
	double t_2 = j * ((y0 * y5) - (y1 * y4));
	double t_3 = (z * k) - (x * j);
	double t_4 = y5 * ((y * k) - (t * j));
	double t_5 = y3 * (t_1 + t_2);
	double tmp;
	if (j <= -2.3e+72) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + t_4);
	} else if (j <= -1e-128) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * t_3));
	} else if (j <= 8.5e-283) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (j <= 2.4e-155) {
		tmp = t_5;
	} else if (j <= 1.05e-104) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (j <= 7.2e+57) {
		tmp = y3 * (t_1 + (t_2 + (z * ((a * y1) - (c * y0)))));
	} else if (j <= 6.4e+202) {
		tmp = i * ((j * (x * y1)) + t_4);
	} else if (j <= 1.05e+282) {
		tmp = (b * y0) * t_3;
	} else if (j <= 3e+305) {
		tmp = t_5;
	} else {
		tmp = k * (b * (z * y0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = y * ((c * y4) - (a * y5))
    t_2 = j * ((y0 * y5) - (y1 * y4))
    t_3 = (z * k) - (x * j)
    t_4 = y5 * ((y * k) - (t * j))
    t_5 = y3 * (t_1 + t_2)
    if (j <= (-2.3d+72)) then
        tmp = i * ((y1 * ((x * j) - (z * k))) + t_4)
    else if (j <= (-1d-128)) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * t_3))
    else if (j <= 8.5d-283) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    else if (j <= 2.4d-155) then
        tmp = t_5
    else if (j <= 1.05d-104) then
        tmp = y0 * (y2 * ((x * c) - (k * y5)))
    else if (j <= 7.2d+57) then
        tmp = y3 * (t_1 + (t_2 + (z * ((a * y1) - (c * y0)))))
    else if (j <= 6.4d+202) then
        tmp = i * ((j * (x * y1)) + t_4)
    else if (j <= 1.05d+282) then
        tmp = (b * y0) * t_3
    else if (j <= 3d+305) then
        tmp = t_5
    else
        tmp = k * (b * (z * y0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * ((c * y4) - (a * y5));
	double t_2 = j * ((y0 * y5) - (y1 * y4));
	double t_3 = (z * k) - (x * j);
	double t_4 = y5 * ((y * k) - (t * j));
	double t_5 = y3 * (t_1 + t_2);
	double tmp;
	if (j <= -2.3e+72) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + t_4);
	} else if (j <= -1e-128) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * t_3));
	} else if (j <= 8.5e-283) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (j <= 2.4e-155) {
		tmp = t_5;
	} else if (j <= 1.05e-104) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (j <= 7.2e+57) {
		tmp = y3 * (t_1 + (t_2 + (z * ((a * y1) - (c * y0)))));
	} else if (j <= 6.4e+202) {
		tmp = i * ((j * (x * y1)) + t_4);
	} else if (j <= 1.05e+282) {
		tmp = (b * y0) * t_3;
	} else if (j <= 3e+305) {
		tmp = t_5;
	} else {
		tmp = k * (b * (z * y0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y * ((c * y4) - (a * y5))
	t_2 = j * ((y0 * y5) - (y1 * y4))
	t_3 = (z * k) - (x * j)
	t_4 = y5 * ((y * k) - (t * j))
	t_5 = y3 * (t_1 + t_2)
	tmp = 0
	if j <= -2.3e+72:
		tmp = i * ((y1 * ((x * j) - (z * k))) + t_4)
	elif j <= -1e-128:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * t_3))
	elif j <= 8.5e-283:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	elif j <= 2.4e-155:
		tmp = t_5
	elif j <= 1.05e-104:
		tmp = y0 * (y2 * ((x * c) - (k * y5)))
	elif j <= 7.2e+57:
		tmp = y3 * (t_1 + (t_2 + (z * ((a * y1) - (c * y0)))))
	elif j <= 6.4e+202:
		tmp = i * ((j * (x * y1)) + t_4)
	elif j <= 1.05e+282:
		tmp = (b * y0) * t_3
	elif j <= 3e+305:
		tmp = t_5
	else:
		tmp = k * (b * (z * y0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y * Float64(Float64(c * y4) - Float64(a * y5)))
	t_2 = Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4)))
	t_3 = Float64(Float64(z * k) - Float64(x * j))
	t_4 = Float64(y5 * Float64(Float64(y * k) - Float64(t * j)))
	t_5 = Float64(y3 * Float64(t_1 + t_2))
	tmp = 0.0
	if (j <= -2.3e+72)
		tmp = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + t_4));
	elseif (j <= -1e-128)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * t_3)));
	elseif (j <= 8.5e-283)
		tmp = 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)))));
	elseif (j <= 2.4e-155)
		tmp = t_5;
	elseif (j <= 1.05e-104)
		tmp = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))));
	elseif (j <= 7.2e+57)
		tmp = Float64(y3 * Float64(t_1 + Float64(t_2 + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (j <= 6.4e+202)
		tmp = Float64(i * Float64(Float64(j * Float64(x * y1)) + t_4));
	elseif (j <= 1.05e+282)
		tmp = Float64(Float64(b * y0) * t_3);
	elseif (j <= 3e+305)
		tmp = t_5;
	else
		tmp = Float64(k * Float64(b * Float64(z * y0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y * ((c * y4) - (a * y5));
	t_2 = j * ((y0 * y5) - (y1 * y4));
	t_3 = (z * k) - (x * j);
	t_4 = y5 * ((y * k) - (t * j));
	t_5 = y3 * (t_1 + t_2);
	tmp = 0.0;
	if (j <= -2.3e+72)
		tmp = i * ((y1 * ((x * j) - (z * k))) + t_4);
	elseif (j <= -1e-128)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * t_3));
	elseif (j <= 8.5e-283)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	elseif (j <= 2.4e-155)
		tmp = t_5;
	elseif (j <= 1.05e-104)
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	elseif (j <= 7.2e+57)
		tmp = y3 * (t_1 + (t_2 + (z * ((a * y1) - (c * y0)))));
	elseif (j <= 6.4e+202)
		tmp = i * ((j * (x * y1)) + t_4);
	elseif (j <= 1.05e+282)
		tmp = (b * y0) * t_3;
	elseif (j <= 3e+305)
		tmp = t_5;
	else
		tmp = k * (b * (z * y0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y3 * N[(t$95$1 + t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.3e+72], N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1e-128], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.5e-283], 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[j, 2.4e-155], t$95$5, If[LessEqual[j, 1.05e-104], N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.2e+57], N[(y3 * N[(t$95$1 + N[(t$95$2 + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.4e+202], N[(i * N[(N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.05e+282], N[(N[(b * y0), $MachinePrecision] * t$95$3), $MachinePrecision], If[LessEqual[j, 3e+305], t$95$5, N[(k * N[(b * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if j < -2.3e72

   1. Initial program 17.6%

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

   3. Simplified 17.6%

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

   5. Taylor expanded in i around -inf 44.5%

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

   6. Taylor expanded in c around 0 58.0%

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

   if -2.3e72 < j < -1.00000000000000005e-128

   1. Initial program 25.1%

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

   3. Simplified 25.1%

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

   5. Taylor expanded in b around inf 48.6%

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

   if -1.00000000000000005e-128 < j < 8.49999999999999997e-283

   1. Initial program 43.7%

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

   3. Taylor expanded in y2 around inf 54.5%

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

   if 8.49999999999999997e-283 < j < 2.4e-155 or 1.04999999999999994e282 < j < 2.99999999999999982e305

   1. Initial program 26.2%

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

   3. Taylor expanded in t around inf 28.8%

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

   4. Taylor expanded in y3 around inf 65.7%

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

      1. distribute-lft-out-- 65.7%

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

   6. Simplified 65.7%

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

   if 2.4e-155 < j < 1.04999999999999999e-104

   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 y2 around inf 60.0%

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

   4. Taylor expanded in y0 around inf 80.2%

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

      1. +-commutative 80.2%

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

      2. mul-1-neg 80.2%

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

      3. unsub-neg 80.2%

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

      4. *-commutative 80.2%

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

      5. *-commutative 80.2%

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

   6. Simplified 80.2%

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

   if 1.04999999999999999e-104 < j < 7.2000000000000005e57

   1. Initial program 37.3%

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

   3. Taylor expanded in y3 around -inf 69.0%

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

   if 7.2000000000000005e57 < j < 6.40000000000000024e202

   1. Initial program 29.5%

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

   3. Simplified 31.9%

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

   5. Taylor expanded in i around -inf 44.6%

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

   6. Taylor expanded in c around 0 54.4%

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

   7. Taylor expanded in j around inf 59.3%

      \[\leadsto -1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right) - \color{blue}{j \cdot \left(x \cdot y1\right)}\right)\right) \]
   8. Step-by-step derivation

      1. *-commutative 59.3%

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

   9. Simplified 59.3%

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

   if 6.40000000000000024e202 < j < 1.04999999999999994e282

   1. Initial program 23.5%

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

   3. Simplified 23.5%

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

   5. Taylor expanded in b around inf 53.1%

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

   6. Taylor expanded in y0 around inf 71.0%

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

      1. associate-*r* 71.0%

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

      2. *-commutative 71.0%

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

      3. *-commutative 71.0%

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

   8. Simplified 71.0%

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

   if 2.99999999999999982e305 < j

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around -inf 50.0%

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

   6. Taylor expanded in k around inf 50.0%

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

   7. Taylor expanded in i around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

      3. *-commutative 100.0%

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

   9. Simplified 100.0%

      \[\leadsto -1 \cdot \left(k \cdot \color{blue}{\left(\left(-b\right) \cdot \left(z \cdot y0\right)\right)}\right) \]
3. Recombined 9 regimes into one program.

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.3 \cdot 10^{+72}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -1 \cdot 10^{-128}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{-283}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{-155}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{-104}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{+57}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{+202}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{+282}:\\ \;\;\;\;\left(b \cdot y0\right) \cdot \left(z \cdot k - x \cdot j\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{+305}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(b \cdot \left(z \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 34.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y4 - a \cdot y5\\ t_2 := y3 \cdot \left(y \cdot t_1 + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ t_3 := y5 \cdot \left(y \cdot k - t \cdot j\right)\\ \mathbf{if}\;j \leq -9.6 \cdot 10^{+20}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right) + t_3\right)\\ \mathbf{elif}\;j \leq -1.52 \cdot 10^{-61}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -1.2 \cdot 10^{-132}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;j \leq -5.9 \cdot 10^{-241}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.22 \cdot 10^{-284}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;j \leq 1.26 \cdot 10^{-151}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-67}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \left(y1 \cdot y3 - t \cdot b\right)\\ \mathbf{elif}\;j \leq 1.55 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \left(y3 \cdot t_1\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+181}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + t_3\right)\\ \mathbf{elif}\;j \leq 3.1 \cdot 10^{+251}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y4) (* a y5)))
        (t_2 (* y3 (+ (* y t_1) (* j (- (* y0 y5) (* y1 y4))))))
        (t_3 (* y5 (- (* y k) (* t j)))))
   (if (<= j -9.6e+20)
     (* i (+ (* j (* x y1)) t_3))
     (if (<= j -1.52e-61)
       (* y2 (+ (* x (- (* c y0) (* a y1))) (* t (- (* a y5) (* c y4)))))
       (if (<= j -1.2e-132)
         (* i (* c (- (* z t) (* x y))))
         (if (<= j -5.9e-241)
           t_2
           (if (<= j 1.22e-284)
             (* y1 (* y2 (- (* k y4) (* x a))))
             (if (<= j 1.26e-151)
               t_2
               (if (<= j 3.5e-67)
                 (* (* z a) (- (* y1 y3) (* t b)))
                 (if (<= j 1.55e+41)
                   (* y (* y3 t_1))
                   (if (<= j 9.5e+181)
                     (* i (+ (* y1 (- (* x j) (* z k))) t_3))
                     (if (<= j 3.1e+251)
                       (* b (* j (- (* t y4) (* x y0))))
                       t_2))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y4) - (a * y5);
	double t_2 = y3 * ((y * t_1) + (j * ((y0 * y5) - (y1 * y4))));
	double t_3 = y5 * ((y * k) - (t * j));
	double tmp;
	if (j <= -9.6e+20) {
		tmp = i * ((j * (x * y1)) + t_3);
	} else if (j <= -1.52e-61) {
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))));
	} else if (j <= -1.2e-132) {
		tmp = i * (c * ((z * t) - (x * y)));
	} else if (j <= -5.9e-241) {
		tmp = t_2;
	} else if (j <= 1.22e-284) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (j <= 1.26e-151) {
		tmp = t_2;
	} else if (j <= 3.5e-67) {
		tmp = (z * a) * ((y1 * y3) - (t * b));
	} else if (j <= 1.55e+41) {
		tmp = y * (y3 * t_1);
	} else if (j <= 9.5e+181) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + t_3);
	} else if (j <= 3.1e+251) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (c * y4) - (a * y5)
    t_2 = y3 * ((y * t_1) + (j * ((y0 * y5) - (y1 * y4))))
    t_3 = y5 * ((y * k) - (t * j))
    if (j <= (-9.6d+20)) then
        tmp = i * ((j * (x * y1)) + t_3)
    else if (j <= (-1.52d-61)) then
        tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))))
    else if (j <= (-1.2d-132)) then
        tmp = i * (c * ((z * t) - (x * y)))
    else if (j <= (-5.9d-241)) then
        tmp = t_2
    else if (j <= 1.22d-284) then
        tmp = y1 * (y2 * ((k * y4) - (x * a)))
    else if (j <= 1.26d-151) then
        tmp = t_2
    else if (j <= 3.5d-67) then
        tmp = (z * a) * ((y1 * y3) - (t * b))
    else if (j <= 1.55d+41) then
        tmp = y * (y3 * t_1)
    else if (j <= 9.5d+181) then
        tmp = i * ((y1 * ((x * j) - (z * k))) + t_3)
    else if (j <= 3.1d+251) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y4) - (a * y5);
	double t_2 = y3 * ((y * t_1) + (j * ((y0 * y5) - (y1 * y4))));
	double t_3 = y5 * ((y * k) - (t * j));
	double tmp;
	if (j <= -9.6e+20) {
		tmp = i * ((j * (x * y1)) + t_3);
	} else if (j <= -1.52e-61) {
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))));
	} else if (j <= -1.2e-132) {
		tmp = i * (c * ((z * t) - (x * y)));
	} else if (j <= -5.9e-241) {
		tmp = t_2;
	} else if (j <= 1.22e-284) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (j <= 1.26e-151) {
		tmp = t_2;
	} else if (j <= 3.5e-67) {
		tmp = (z * a) * ((y1 * y3) - (t * b));
	} else if (j <= 1.55e+41) {
		tmp = y * (y3 * t_1);
	} else if (j <= 9.5e+181) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + t_3);
	} else if (j <= 3.1e+251) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * y4) - (a * y5)
	t_2 = y3 * ((y * t_1) + (j * ((y0 * y5) - (y1 * y4))))
	t_3 = y5 * ((y * k) - (t * j))
	tmp = 0
	if j <= -9.6e+20:
		tmp = i * ((j * (x * y1)) + t_3)
	elif j <= -1.52e-61:
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))))
	elif j <= -1.2e-132:
		tmp = i * (c * ((z * t) - (x * y)))
	elif j <= -5.9e-241:
		tmp = t_2
	elif j <= 1.22e-284:
		tmp = y1 * (y2 * ((k * y4) - (x * a)))
	elif j <= 1.26e-151:
		tmp = t_2
	elif j <= 3.5e-67:
		tmp = (z * a) * ((y1 * y3) - (t * b))
	elif j <= 1.55e+41:
		tmp = y * (y3 * t_1)
	elif j <= 9.5e+181:
		tmp = i * ((y1 * ((x * j) - (z * k))) + t_3)
	elif j <= 3.1e+251:
		tmp = b * (j * ((t * y4) - (x * y0)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y4) - Float64(a * y5))
	t_2 = Float64(y3 * Float64(Float64(y * t_1) + Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4)))))
	t_3 = Float64(y5 * Float64(Float64(y * k) - Float64(t * j)))
	tmp = 0.0
	if (j <= -9.6e+20)
		tmp = Float64(i * Float64(Float64(j * Float64(x * y1)) + t_3));
	elseif (j <= -1.52e-61)
		tmp = Float64(y2 * Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (j <= -1.2e-132)
		tmp = Float64(i * Float64(c * Float64(Float64(z * t) - Float64(x * y))));
	elseif (j <= -5.9e-241)
		tmp = t_2;
	elseif (j <= 1.22e-284)
		tmp = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (j <= 1.26e-151)
		tmp = t_2;
	elseif (j <= 3.5e-67)
		tmp = Float64(Float64(z * a) * Float64(Float64(y1 * y3) - Float64(t * b)));
	elseif (j <= 1.55e+41)
		tmp = Float64(y * Float64(y3 * t_1));
	elseif (j <= 9.5e+181)
		tmp = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + t_3));
	elseif (j <= 3.1e+251)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (c * y4) - (a * y5);
	t_2 = y3 * ((y * t_1) + (j * ((y0 * y5) - (y1 * y4))));
	t_3 = y5 * ((y * k) - (t * j));
	tmp = 0.0;
	if (j <= -9.6e+20)
		tmp = i * ((j * (x * y1)) + t_3);
	elseif (j <= -1.52e-61)
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))));
	elseif (j <= -1.2e-132)
		tmp = i * (c * ((z * t) - (x * y)));
	elseif (j <= -5.9e-241)
		tmp = t_2;
	elseif (j <= 1.22e-284)
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	elseif (j <= 1.26e-151)
		tmp = t_2;
	elseif (j <= 3.5e-67)
		tmp = (z * a) * ((y1 * y3) - (t * b));
	elseif (j <= 1.55e+41)
		tmp = y * (y3 * t_1);
	elseif (j <= 9.5e+181)
		tmp = i * ((y1 * ((x * j) - (z * k))) + t_3);
	elseif (j <= 3.1e+251)
		tmp = b * (j * ((t * y4) - (x * y0)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y3 * N[(N[(y * t$95$1), $MachinePrecision] + N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -9.6e+20], N[(i * N[(N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.52e-61], N[(y2 * N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.2e-132], N[(i * N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -5.9e-241], t$95$2, If[LessEqual[j, 1.22e-284], N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.26e-151], t$95$2, If[LessEqual[j, 3.5e-67], N[(N[(z * a), $MachinePrecision] * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.55e+41], N[(y * N[(y3 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9.5e+181], N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.1e+251], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if j < -9.6e20

   1. Initial program 18.3%

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

   3. Simplified 18.3%

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

   5. Taylor expanded in i around -inf 42.9%

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

   6. Taylor expanded in c around 0 54.4%

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

   7. Taylor expanded in j around inf 56.0%

      \[\leadsto -1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right) - \color{blue}{j \cdot \left(x \cdot y1\right)}\right)\right) \]
   8. Step-by-step derivation

      1. *-commutative 56.0%

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

   9. Simplified 56.0%

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

   if -9.6e20 < j < -1.52000000000000003e-61

   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 y2 around inf 53.6%

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

   4. Taylor expanded in k around 0 53.6%

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

   if -1.52000000000000003e-61 < j < -1.20000000000000008e-132

   1. Initial program 24.1%

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

   3. Simplified 24.1%

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

   5. Taylor expanded in i around -inf 43.5%

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

   6. Taylor expanded in c around inf 34.6%

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

      1. *-commutative 34.6%

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

      2. neg-mul-1 34.6%

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

      3. +-commutative 34.6%

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

      4. fma-udef 34.6%

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

      5. associate-*r* 48.2%

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

      6. *-commutative 48.2%

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

      7. fma-udef 48.2%

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

      8. unsub-neg 48.2%

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

      9. *-commutative 48.2%

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

   8. Simplified 48.2%

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

   if -1.20000000000000008e-132 < j < -5.8999999999999998e-241 or 1.22e-284 < j < 1.2600000000000001e-151 or 3.0999999999999998e251 < j

   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 t around inf 33.0%

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

   4. Taylor expanded in y3 around inf 58.2%

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

      1. distribute-lft-out-- 58.2%

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

   6. Simplified 58.2%

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

   if -5.8999999999999998e-241 < j < 1.22e-284

   1. Initial program 53.3%

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

   3. Taylor expanded in y2 around inf 59.2%

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

   4. Taylor expanded in y1 around inf 42.0%

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

      1. +-commutative 42.0%

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

      2. mul-1-neg 42.0%

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

      3. unsub-neg 42.0%

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

      4. *-commutative 42.0%

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

      5. *-commutative 42.0%

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

   6. Simplified 42.0%

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

   if 1.2600000000000001e-151 < j < 3.5e-67

   1. Initial program 21.4%

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

   3. Simplified 21.4%

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

   5. Taylor expanded in z around -inf 78.7%

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

   6. Taylor expanded in a around inf 65.1%

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

      1. associate-*r* 65.1%

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

      2. +-commutative 65.1%

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

      3. mul-1-neg 65.1%

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

      4. unsub-neg 65.1%

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

   8. Simplified 65.1%

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

   if 3.5e-67 < j < 1.55e41

   1. Initial program 44.1%

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

   3. Taylor expanded in t around inf 33.9%

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

   4. Taylor expanded in y around inf 77.9%

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

   if 1.55e41 < j < 9.50000000000000032e181

   1. Initial program 33.6%

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

   3. Simplified 36.3%

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

   5. Taylor expanded in i around -inf 50.7%

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

   6. Taylor expanded in c around 0 61.9%

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

   if 9.50000000000000032e181 < j < 3.0999999999999998e251

   1. Initial program 21.1%

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

   3. Simplified 21.1%

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

   5. Taylor expanded in b around inf 42.5%

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

   6. Taylor expanded in j around inf 63.9%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.6 \cdot 10^{+20}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -1.52 \cdot 10^{-61}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -1.2 \cdot 10^{-132}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;j \leq -5.9 \cdot 10^{-241}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 1.22 \cdot 10^{-284}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;j \leq 1.26 \cdot 10^{-151}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-67}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \left(y1 \cdot y3 - t \cdot b\right)\\ \mathbf{elif}\;j \leq 1.55 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+181}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 3.1 \cdot 10^{+251}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 34.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ t_2 := \left(z \cdot a\right) \cdot \left(y1 \cdot y3 - t \cdot b\right)\\ t_3 := j \cdot \left(x \cdot y1\right)\\ t_4 := y5 \cdot \left(y \cdot k - t \cdot j\right)\\ \mathbf{if}\;j \leq -1.2 \cdot 10^{+38}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + t_4\right)\\ \mathbf{elif}\;j \leq -1.15 \cdot 10^{-132}:\\ \;\;\;\;i \cdot \left(t_3 + \left(c \cdot \left(z \cdot t - x \cdot y\right) - j \cdot \left(t \cdot y5\right)\right)\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -8 \cdot 10^{-195}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-281}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 5.7 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{+202}:\\ \;\;\;\;i \cdot \left(t_3 + t_4\right)\\ \mathbf{elif}\;j \leq 1.18 \cdot 10^{+283}:\\ \;\;\;\;\left(b \cdot y0\right) \cdot \left(z \cdot k - x \cdot j\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{+305}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(b \cdot \left(z \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (* y3 (+ (* y (- (* c y4) (* a y5))) (* j (- (* y0 y5) (* y1 y4))))))
        (t_2 (* (* z a) (- (* y1 y3) (* t b))))
        (t_3 (* j (* x y1)))
        (t_4 (* y5 (- (* y k) (* t j)))))
   (if (<= j -1.2e+38)
     (* i (+ (* y1 (- (* x j) (* z k))) t_4))
     (if (<= j -1.15e-132)
       (* i (+ t_3 (- (* c (- (* z t) (* x y))) (* j (* t y5)))))
       (if (<= j -8.5e-181)
         t_1
         (if (<= j -8e-195)
           t_2
           (if (<= j 1.7e-281)
             (*
              y2
              (+
               (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
               (* t (- (* a y5) (* c y4)))))
             (if (<= j 5.7e-152)
               t_1
               (if (<= j 1.45e+57)
                 t_2
                 (if (<= j 4.8e+202)
                   (* i (+ t_3 t_4))
                   (if (<= j 1.18e+283)
                     (* (* b y0) (- (* z k) (* x j)))
                     (if (<= j 3e+305) t_1 (* k (* b (* z y0)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	double t_2 = (z * a) * ((y1 * y3) - (t * b));
	double t_3 = j * (x * y1);
	double t_4 = y5 * ((y * k) - (t * j));
	double tmp;
	if (j <= -1.2e+38) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + t_4);
	} else if (j <= -1.15e-132) {
		tmp = i * (t_3 + ((c * ((z * t) - (x * y))) - (j * (t * y5))));
	} else if (j <= -8.5e-181) {
		tmp = t_1;
	} else if (j <= -8e-195) {
		tmp = t_2;
	} else if (j <= 1.7e-281) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (j <= 5.7e-152) {
		tmp = t_1;
	} else if (j <= 1.45e+57) {
		tmp = t_2;
	} else if (j <= 4.8e+202) {
		tmp = i * (t_3 + t_4);
	} else if (j <= 1.18e+283) {
		tmp = (b * y0) * ((z * k) - (x * j));
	} else if (j <= 3e+305) {
		tmp = t_1;
	} else {
		tmp = k * (b * (z * y0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))))
    t_2 = (z * a) * ((y1 * y3) - (t * b))
    t_3 = j * (x * y1)
    t_4 = y5 * ((y * k) - (t * j))
    if (j <= (-1.2d+38)) then
        tmp = i * ((y1 * ((x * j) - (z * k))) + t_4)
    else if (j <= (-1.15d-132)) then
        tmp = i * (t_3 + ((c * ((z * t) - (x * y))) - (j * (t * y5))))
    else if (j <= (-8.5d-181)) then
        tmp = t_1
    else if (j <= (-8d-195)) then
        tmp = t_2
    else if (j <= 1.7d-281) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    else if (j <= 5.7d-152) then
        tmp = t_1
    else if (j <= 1.45d+57) then
        tmp = t_2
    else if (j <= 4.8d+202) then
        tmp = i * (t_3 + t_4)
    else if (j <= 1.18d+283) then
        tmp = (b * y0) * ((z * k) - (x * j))
    else if (j <= 3d+305) then
        tmp = t_1
    else
        tmp = k * (b * (z * y0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	double t_2 = (z * a) * ((y1 * y3) - (t * b));
	double t_3 = j * (x * y1);
	double t_4 = y5 * ((y * k) - (t * j));
	double tmp;
	if (j <= -1.2e+38) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + t_4);
	} else if (j <= -1.15e-132) {
		tmp = i * (t_3 + ((c * ((z * t) - (x * y))) - (j * (t * y5))));
	} else if (j <= -8.5e-181) {
		tmp = t_1;
	} else if (j <= -8e-195) {
		tmp = t_2;
	} else if (j <= 1.7e-281) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (j <= 5.7e-152) {
		tmp = t_1;
	} else if (j <= 1.45e+57) {
		tmp = t_2;
	} else if (j <= 4.8e+202) {
		tmp = i * (t_3 + t_4);
	} else if (j <= 1.18e+283) {
		tmp = (b * y0) * ((z * k) - (x * j));
	} else if (j <= 3e+305) {
		tmp = t_1;
	} else {
		tmp = k * (b * (z * y0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))))
	t_2 = (z * a) * ((y1 * y3) - (t * b))
	t_3 = j * (x * y1)
	t_4 = y5 * ((y * k) - (t * j))
	tmp = 0
	if j <= -1.2e+38:
		tmp = i * ((y1 * ((x * j) - (z * k))) + t_4)
	elif j <= -1.15e-132:
		tmp = i * (t_3 + ((c * ((z * t) - (x * y))) - (j * (t * y5))))
	elif j <= -8.5e-181:
		tmp = t_1
	elif j <= -8e-195:
		tmp = t_2
	elif j <= 1.7e-281:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	elif j <= 5.7e-152:
		tmp = t_1
	elif j <= 1.45e+57:
		tmp = t_2
	elif j <= 4.8e+202:
		tmp = i * (t_3 + t_4)
	elif j <= 1.18e+283:
		tmp = (b * y0) * ((z * k) - (x * j))
	elif j <= 3e+305:
		tmp = t_1
	else:
		tmp = k * (b * (z * y0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4)))))
	t_2 = Float64(Float64(z * a) * Float64(Float64(y1 * y3) - Float64(t * b)))
	t_3 = Float64(j * Float64(x * y1))
	t_4 = Float64(y5 * Float64(Float64(y * k) - Float64(t * j)))
	tmp = 0.0
	if (j <= -1.2e+38)
		tmp = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + t_4));
	elseif (j <= -1.15e-132)
		tmp = Float64(i * Float64(t_3 + Float64(Float64(c * Float64(Float64(z * t) - Float64(x * y))) - Float64(j * Float64(t * y5)))));
	elseif (j <= -8.5e-181)
		tmp = t_1;
	elseif (j <= -8e-195)
		tmp = t_2;
	elseif (j <= 1.7e-281)
		tmp = 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)))));
	elseif (j <= 5.7e-152)
		tmp = t_1;
	elseif (j <= 1.45e+57)
		tmp = t_2;
	elseif (j <= 4.8e+202)
		tmp = Float64(i * Float64(t_3 + t_4));
	elseif (j <= 1.18e+283)
		tmp = Float64(Float64(b * y0) * Float64(Float64(z * k) - Float64(x * j)));
	elseif (j <= 3e+305)
		tmp = t_1;
	else
		tmp = Float64(k * Float64(b * Float64(z * y0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y3 * ((y * ((c * y4) - (a * y5))) + (j * ((y0 * y5) - (y1 * y4))));
	t_2 = (z * a) * ((y1 * y3) - (t * b));
	t_3 = j * (x * y1);
	t_4 = y5 * ((y * k) - (t * j));
	tmp = 0.0;
	if (j <= -1.2e+38)
		tmp = i * ((y1 * ((x * j) - (z * k))) + t_4);
	elseif (j <= -1.15e-132)
		tmp = i * (t_3 + ((c * ((z * t) - (x * y))) - (j * (t * y5))));
	elseif (j <= -8.5e-181)
		tmp = t_1;
	elseif (j <= -8e-195)
		tmp = t_2;
	elseif (j <= 1.7e-281)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	elseif (j <= 5.7e-152)
		tmp = t_1;
	elseif (j <= 1.45e+57)
		tmp = t_2;
	elseif (j <= 4.8e+202)
		tmp = i * (t_3 + t_4);
	elseif (j <= 1.18e+283)
		tmp = (b * y0) * ((z * k) - (x * j));
	elseif (j <= 3e+305)
		tmp = t_1;
	else
		tmp = k * (b * (z * y0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * a), $MachinePrecision] * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.2e+38], N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.15e-132], N[(i * N[(t$95$3 + N[(N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -8.5e-181], t$95$1, If[LessEqual[j, -8e-195], t$95$2, If[LessEqual[j, 1.7e-281], 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[j, 5.7e-152], t$95$1, If[LessEqual[j, 1.45e+57], t$95$2, If[LessEqual[j, 4.8e+202], N[(i * N[(t$95$3 + t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.18e+283], N[(N[(b * y0), $MachinePrecision] * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3e+305], t$95$1, N[(k * N[(b * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if j < -1.20000000000000009e38

   1. Initial program 19.6%

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

   3. Simplified 19.6%

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

   5. Taylor expanded in i around -inf 44.2%

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

   6. Taylor expanded in c around 0 56.4%

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

   if -1.20000000000000009e38 < j < -1.15000000000000002e-132

   1. Initial program 22.6%

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

   3. Simplified 22.6%

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

   5. Taylor expanded in i around -inf 40.5%

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

   6. Taylor expanded in k around 0 48.0%

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

   if -1.15000000000000002e-132 < j < -8.49999999999999953e-181 or 1.7e-281 < j < 5.7000000000000004e-152 or 1.18000000000000003e283 < j < 2.99999999999999982e305

   1. Initial program 27.6%

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

   3. Taylor expanded in t around inf 32.2%

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

   4. Taylor expanded in y3 around inf 63.7%

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

      1. distribute-lft-out-- 63.7%

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

   6. Simplified 63.7%

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

   if -8.49999999999999953e-181 < j < -8.0000000000000007e-195 or 5.7000000000000004e-152 < j < 1.4500000000000001e57

   1. Initial program 26.6%

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

   3. Simplified 26.6%

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

   5. Taylor expanded in z around -inf 57.2%

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

   6. Taylor expanded in a around inf 61.3%

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

      1. associate-*r* 58.2%

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

      2. +-commutative 58.2%

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

      3. mul-1-neg 58.2%

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

      4. unsub-neg 58.2%

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

   8. Simplified 58.2%

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

   if -8.0000000000000007e-195 < j < 1.7e-281

   1. Initial program 56.2%

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

   3. Taylor expanded in y2 around inf 64.8%

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

   if 1.4500000000000001e57 < j < 4.8000000000000004e202

   1. Initial program 29.5%

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

   3. Simplified 31.9%

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

   5. Taylor expanded in i around -inf 44.6%

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

   6. Taylor expanded in c around 0 54.4%

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

   7. Taylor expanded in j around inf 59.3%

      \[\leadsto -1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right) - \color{blue}{j \cdot \left(x \cdot y1\right)}\right)\right) \]
   8. Step-by-step derivation

      1. *-commutative 59.3%

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

   9. Simplified 59.3%

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

   if 4.8000000000000004e202 < j < 1.18000000000000003e283

   1. Initial program 23.5%

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

   3. Simplified 23.5%

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

   5. Taylor expanded in b around inf 53.1%

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

   6. Taylor expanded in y0 around inf 71.0%

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

      1. associate-*r* 71.0%

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

      2. *-commutative 71.0%

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

      3. *-commutative 71.0%

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

   8. Simplified 71.0%

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

   if 2.99999999999999982e305 < j

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around -inf 50.0%

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

   6. Taylor expanded in k around inf 50.0%

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

   7. Taylor expanded in i around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

      3. *-commutative 100.0%

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

   9. Simplified 100.0%

      \[\leadsto -1 \cdot \left(k \cdot \color{blue}{\left(\left(-b\right) \cdot \left(z \cdot y0\right)\right)}\right) \]
3. Recombined 8 regimes into one program.

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.2 \cdot 10^{+38}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -1.15 \cdot 10^{-132}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right) + \left(c \cdot \left(z \cdot t - x \cdot y\right) - j \cdot \left(t \cdot y5\right)\right)\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-181}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -8 \cdot 10^{-195}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \left(y1 \cdot y3 - t \cdot b\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-281}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 5.7 \cdot 10^{-152}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{+57}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \left(y1 \cdot y3 - t \cdot b\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{+202}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 1.18 \cdot 10^{+283}:\\ \;\;\;\;\left(b \cdot y0\right) \cdot \left(z \cdot k - x \cdot j\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{+305}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(b \cdot \left(z \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 30.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(j \cdot \left(x \cdot y1\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ t_2 := y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{if}\;j \leq -1.25 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.3 \cdot 10^{-28}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -1.5 \cdot 10^{-62}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -9.2 \cdot 10^{-133}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-187}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;j \leq -6.1 \cdot 10^{-207}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;j \leq -2.9 \cdot 10^{-304}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;j \leq 2.25 \cdot 10^{-155}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-68}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \left(y1 \cdot y3 - t \cdot b\right)\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{+86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+202}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot y0\right) \cdot \left(z \cdot k - x \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (+ (* j (* x y1)) (* y5 (- (* y k) (* t j))))))
        (t_2 (* y (* y3 (- (* c y4) (* a y5))))))
   (if (<= j -1.25e+79)
     t_1
     (if (<= j -2.3e-28)
       (* b (* y (- (* x a) (* k y4))))
       (if (<= j -1.5e-62)
         (* c (* y2 (- (* x y0) (* t y4))))
         (if (<= j -9.2e-133)
           (* i (* c (- (* z t) (* x y))))
           (if (<= j -6e-187)
             (* c (* y4 (* t (- y2))))
             (if (<= j -6.1e-207)
               (* x (* y (- (* a b) (* c i))))
               (if (<= j -2.9e-304)
                 (* y1 (* y2 (- (* k y4) (* x a))))
                 (if (<= j 2.25e-155)
                   t_2
                   (if (<= j 3.6e-68)
                     (* (* z a) (- (* y1 y3) (* t b)))
                     (if (<= j 3.3e+86)
                       t_2
                       (if (<= j 4.5e+202)
                         t_1
                         (* (* b y0) (- (* z k) (* x j))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * ((j * (x * y1)) + (y5 * ((y * k) - (t * j))));
	double t_2 = y * (y3 * ((c * y4) - (a * y5)));
	double tmp;
	if (j <= -1.25e+79) {
		tmp = t_1;
	} else if (j <= -2.3e-28) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (j <= -1.5e-62) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (j <= -9.2e-133) {
		tmp = i * (c * ((z * t) - (x * y)));
	} else if (j <= -6e-187) {
		tmp = c * (y4 * (t * -y2));
	} else if (j <= -6.1e-207) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (j <= -2.9e-304) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (j <= 2.25e-155) {
		tmp = t_2;
	} else if (j <= 3.6e-68) {
		tmp = (z * a) * ((y1 * y3) - (t * b));
	} else if (j <= 3.3e+86) {
		tmp = t_2;
	} else if (j <= 4.5e+202) {
		tmp = t_1;
	} else {
		tmp = (b * y0) * ((z * k) - (x * 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) :: t_2
    real(8) :: tmp
    t_1 = i * ((j * (x * y1)) + (y5 * ((y * k) - (t * j))))
    t_2 = y * (y3 * ((c * y4) - (a * y5)))
    if (j <= (-1.25d+79)) then
        tmp = t_1
    else if (j <= (-2.3d-28)) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (j <= (-1.5d-62)) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (j <= (-9.2d-133)) then
        tmp = i * (c * ((z * t) - (x * y)))
    else if (j <= (-6d-187)) then
        tmp = c * (y4 * (t * -y2))
    else if (j <= (-6.1d-207)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (j <= (-2.9d-304)) then
        tmp = y1 * (y2 * ((k * y4) - (x * a)))
    else if (j <= 2.25d-155) then
        tmp = t_2
    else if (j <= 3.6d-68) then
        tmp = (z * a) * ((y1 * y3) - (t * b))
    else if (j <= 3.3d+86) then
        tmp = t_2
    else if (j <= 4.5d+202) then
        tmp = t_1
    else
        tmp = (b * y0) * ((z * k) - (x * 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 = i * ((j * (x * y1)) + (y5 * ((y * k) - (t * j))));
	double t_2 = y * (y3 * ((c * y4) - (a * y5)));
	double tmp;
	if (j <= -1.25e+79) {
		tmp = t_1;
	} else if (j <= -2.3e-28) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (j <= -1.5e-62) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (j <= -9.2e-133) {
		tmp = i * (c * ((z * t) - (x * y)));
	} else if (j <= -6e-187) {
		tmp = c * (y4 * (t * -y2));
	} else if (j <= -6.1e-207) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (j <= -2.9e-304) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (j <= 2.25e-155) {
		tmp = t_2;
	} else if (j <= 3.6e-68) {
		tmp = (z * a) * ((y1 * y3) - (t * b));
	} else if (j <= 3.3e+86) {
		tmp = t_2;
	} else if (j <= 4.5e+202) {
		tmp = t_1;
	} else {
		tmp = (b * y0) * ((z * k) - (x * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * ((j * (x * y1)) + (y5 * ((y * k) - (t * j))))
	t_2 = y * (y3 * ((c * y4) - (a * y5)))
	tmp = 0
	if j <= -1.25e+79:
		tmp = t_1
	elif j <= -2.3e-28:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif j <= -1.5e-62:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif j <= -9.2e-133:
		tmp = i * (c * ((z * t) - (x * y)))
	elif j <= -6e-187:
		tmp = c * (y4 * (t * -y2))
	elif j <= -6.1e-207:
		tmp = x * (y * ((a * b) - (c * i)))
	elif j <= -2.9e-304:
		tmp = y1 * (y2 * ((k * y4) - (x * a)))
	elif j <= 2.25e-155:
		tmp = t_2
	elif j <= 3.6e-68:
		tmp = (z * a) * ((y1 * y3) - (t * b))
	elif j <= 3.3e+86:
		tmp = t_2
	elif j <= 4.5e+202:
		tmp = t_1
	else:
		tmp = (b * y0) * ((z * k) - (x * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(Float64(j * Float64(x * y1)) + Float64(y5 * Float64(Float64(y * k) - Float64(t * j)))))
	t_2 = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))
	tmp = 0.0
	if (j <= -1.25e+79)
		tmp = t_1;
	elseif (j <= -2.3e-28)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (j <= -1.5e-62)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (j <= -9.2e-133)
		tmp = Float64(i * Float64(c * Float64(Float64(z * t) - Float64(x * y))));
	elseif (j <= -6e-187)
		tmp = Float64(c * Float64(y4 * Float64(t * Float64(-y2))));
	elseif (j <= -6.1e-207)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (j <= -2.9e-304)
		tmp = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (j <= 2.25e-155)
		tmp = t_2;
	elseif (j <= 3.6e-68)
		tmp = Float64(Float64(z * a) * Float64(Float64(y1 * y3) - Float64(t * b)));
	elseif (j <= 3.3e+86)
		tmp = t_2;
	elseif (j <= 4.5e+202)
		tmp = t_1;
	else
		tmp = Float64(Float64(b * y0) * Float64(Float64(z * k) - Float64(x * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * ((j * (x * y1)) + (y5 * ((y * k) - (t * j))));
	t_2 = y * (y3 * ((c * y4) - (a * y5)));
	tmp = 0.0;
	if (j <= -1.25e+79)
		tmp = t_1;
	elseif (j <= -2.3e-28)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (j <= -1.5e-62)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (j <= -9.2e-133)
		tmp = i * (c * ((z * t) - (x * y)));
	elseif (j <= -6e-187)
		tmp = c * (y4 * (t * -y2));
	elseif (j <= -6.1e-207)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (j <= -2.9e-304)
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	elseif (j <= 2.25e-155)
		tmp = t_2;
	elseif (j <= 3.6e-68)
		tmp = (z * a) * ((y1 * y3) - (t * b));
	elseif (j <= 3.3e+86)
		tmp = t_2;
	elseif (j <= 4.5e+202)
		tmp = t_1;
	else
		tmp = (b * y0) * ((z * k) - (x * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.25e+79], t$95$1, If[LessEqual[j, -2.3e-28], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.5e-62], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -9.2e-133], N[(i * N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6e-187], N[(c * N[(y4 * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6.1e-207], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.9e-304], N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.25e-155], t$95$2, If[LessEqual[j, 3.6e-68], N[(N[(z * a), $MachinePrecision] * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.3e+86], t$95$2, If[LessEqual[j, 4.5e+202], t$95$1, N[(N[(b * y0), $MachinePrecision] * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if j < -1.25e79 or 3.2999999999999999e86 < j < 4.49999999999999978e202

   1. Initial program 23.5%

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

   3. Simplified 24.7%

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

   5. Taylor expanded in i around -inf 45.6%

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

   6. Taylor expanded in c around 0 56.6%

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

   7. Taylor expanded in j around inf 60.3%

      \[\leadsto -1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right) - \color{blue}{j \cdot \left(x \cdot y1\right)}\right)\right) \]
   8. Step-by-step derivation

      1. *-commutative 60.3%

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

   9. Simplified 60.3%

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

   if -1.25e79 < j < -2.29999999999999986e-28

   1. Initial program 22.7%

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

   3. Simplified 22.7%

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

   5. Taylor expanded in b around inf 50.5%

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

   6. Taylor expanded in y around inf 50.8%

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

      1. +-commutative 50.8%

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

      2. mul-1-neg 50.8%

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

      3. unsub-neg 50.8%

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

      4. *-commutative 50.8%

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

      5. *-commutative 50.8%

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

   8. Simplified 50.8%

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

   if -2.29999999999999986e-28 < j < -1.5000000000000001e-62

   1. Initial program 40.0%

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

   3. Taylor expanded in y2 around inf 80.2%

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

   4. Taylor expanded in c around inf 80.3%

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

   if -1.5000000000000001e-62 < j < -9.2000000000000001e-133

   1. Initial program 24.1%

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

   3. Simplified 24.1%

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

   5. Taylor expanded in i around -inf 43.5%

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

   6. Taylor expanded in c around inf 34.6%

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

      1. *-commutative 34.6%

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

      2. neg-mul-1 34.6%

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

      3. +-commutative 34.6%

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

      4. fma-udef 34.6%

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

      5. associate-*r* 48.2%

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

      6. *-commutative 48.2%

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

      7. fma-udef 48.2%

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

      8. unsub-neg 48.2%

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

      9. *-commutative 48.2%

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

   8. Simplified 48.2%

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

   if -9.2000000000000001e-133 < j < -6.00000000000000008e-187

   1. Initial program 27.3%

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

   3. Taylor expanded in y2 around inf 36.8%

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

   4. Taylor expanded in t around inf 37.8%

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

   5. Taylor expanded in a around 0 47.2%

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

      1. associate-*r* 47.2%

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

      2. neg-mul-1 47.2%

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

      3. associate-*r* 47.0%

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

   7. Simplified 47.0%

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

   if -6.00000000000000008e-187 < j < -6.10000000000000008e-207

   1. Initial program 25.0%

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

   3. Simplified 25.0%

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

   5. Taylor expanded in x around inf 75.0%

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

   6. Taylor expanded in y around inf 100.0%

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

   if -6.10000000000000008e-207 < j < -2.9e-304

   1. Initial program 56.2%

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

   3. Taylor expanded in y2 around inf 63.7%

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

   4. Taylor expanded in y1 around inf 50.7%

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

      1. +-commutative 50.7%

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

      2. mul-1-neg 50.7%

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

      3. unsub-neg 50.7%

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

      4. *-commutative 50.7%

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

      5. *-commutative 50.7%

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

   6. Simplified 50.7%

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

   if -2.9e-304 < j < 2.2500000000000002e-155 or 3.60000000000000007e-68 < j < 3.2999999999999999e86

   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 t around inf 30.1%

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

   4. Taylor expanded in y around inf 54.0%

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

   if 2.2500000000000002e-155 < j < 3.60000000000000007e-68

   1. Initial program 21.4%

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

   3. Simplified 21.4%

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

   5. Taylor expanded in z around -inf 78.7%

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

   6. Taylor expanded in a around inf 65.1%

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

      1. associate-*r* 65.1%

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

      2. +-commutative 65.1%

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

      3. mul-1-neg 65.1%

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

      4. unsub-neg 65.1%

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

   8. Simplified 65.1%

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

   if 4.49999999999999978e202 < j

   1. Initial program 18.5%

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

   3. Simplified 18.5%

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

   5. Taylor expanded in b around inf 48.3%

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

   6. Taylor expanded in y0 around inf 59.8%

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

      1. associate-*r* 59.8%

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

      2. *-commutative 59.8%

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

      3. *-commutative 59.8%

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

   8. Simplified 59.8%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.25 \cdot 10^{+79}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -2.3 \cdot 10^{-28}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -1.5 \cdot 10^{-62}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -9.2 \cdot 10^{-133}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-187}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;j \leq -6.1 \cdot 10^{-207}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;j \leq -2.9 \cdot 10^{-304}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;j \leq 2.25 \cdot 10^{-155}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-68}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \left(y1 \cdot y3 - t \cdot b\right)\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+202}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot y0\right) \cdot \left(z \cdot k - x \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 33.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ t_2 := c \cdot y4 - a \cdot y5\\ t_3 := y3 \cdot \left(y \cdot t_2 + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{if}\;j \leq -1.65 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-132}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right) + \left(c \cdot \left(z \cdot t - x \cdot y\right) - j \cdot \left(t \cdot y5\right)\right)\right)\\ \mathbf{elif}\;j \leq -3.3 \cdot 10^{-242}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{-303}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{-158}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{-68}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \left(y1 \cdot y3 - t \cdot b\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \left(y3 \cdot t_2\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{+181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 9.6 \cdot 10^{+250}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (+ (* y1 (- (* x j) (* z k))) (* y5 (- (* y k) (* t j))))))
        (t_2 (- (* c y4) (* a y5)))
        (t_3 (* y3 (+ (* y t_2) (* j (- (* y0 y5) (* y1 y4)))))))
   (if (<= j -1.65e+37)
     t_1
     (if (<= j -1.05e-132)
       (* i (+ (* j (* x y1)) (- (* c (- (* z t) (* x y))) (* j (* t y5)))))
       (if (<= j -3.3e-242)
         t_3
         (if (<= j 1.6e-303)
           (* y1 (* y2 (- (* k y4) (* x a))))
           (if (<= j 1.75e-158)
             t_3
             (if (<= j 1.9e-68)
               (* (* z a) (- (* y1 y3) (* t b)))
               (if (<= j 8e+43)
                 (* y (* y3 t_2))
                 (if (<= j 2.7e+181)
                   t_1
                   (if (<= j 9.6e+250)
                     (* b (* j (- (* t y4) (* x y0))))
                     t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j))));
	double t_2 = (c * y4) - (a * y5);
	double t_3 = y3 * ((y * t_2) + (j * ((y0 * y5) - (y1 * y4))));
	double tmp;
	if (j <= -1.65e+37) {
		tmp = t_1;
	} else if (j <= -1.05e-132) {
		tmp = i * ((j * (x * y1)) + ((c * ((z * t) - (x * y))) - (j * (t * y5))));
	} else if (j <= -3.3e-242) {
		tmp = t_3;
	} else if (j <= 1.6e-303) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (j <= 1.75e-158) {
		tmp = t_3;
	} else if (j <= 1.9e-68) {
		tmp = (z * a) * ((y1 * y3) - (t * b));
	} else if (j <= 8e+43) {
		tmp = y * (y3 * t_2);
	} else if (j <= 2.7e+181) {
		tmp = t_1;
	} else if (j <= 9.6e+250) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} 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 = i * ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j))))
    t_2 = (c * y4) - (a * y5)
    t_3 = y3 * ((y * t_2) + (j * ((y0 * y5) - (y1 * y4))))
    if (j <= (-1.65d+37)) then
        tmp = t_1
    else if (j <= (-1.05d-132)) then
        tmp = i * ((j * (x * y1)) + ((c * ((z * t) - (x * y))) - (j * (t * y5))))
    else if (j <= (-3.3d-242)) then
        tmp = t_3
    else if (j <= 1.6d-303) then
        tmp = y1 * (y2 * ((k * y4) - (x * a)))
    else if (j <= 1.75d-158) then
        tmp = t_3
    else if (j <= 1.9d-68) then
        tmp = (z * a) * ((y1 * y3) - (t * b))
    else if (j <= 8d+43) then
        tmp = y * (y3 * t_2)
    else if (j <= 2.7d+181) then
        tmp = t_1
    else if (j <= 9.6d+250) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    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 = i * ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j))));
	double t_2 = (c * y4) - (a * y5);
	double t_3 = y3 * ((y * t_2) + (j * ((y0 * y5) - (y1 * y4))));
	double tmp;
	if (j <= -1.65e+37) {
		tmp = t_1;
	} else if (j <= -1.05e-132) {
		tmp = i * ((j * (x * y1)) + ((c * ((z * t) - (x * y))) - (j * (t * y5))));
	} else if (j <= -3.3e-242) {
		tmp = t_3;
	} else if (j <= 1.6e-303) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (j <= 1.75e-158) {
		tmp = t_3;
	} else if (j <= 1.9e-68) {
		tmp = (z * a) * ((y1 * y3) - (t * b));
	} else if (j <= 8e+43) {
		tmp = y * (y3 * t_2);
	} else if (j <= 2.7e+181) {
		tmp = t_1;
	} else if (j <= 9.6e+250) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} 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 = i * ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j))))
	t_2 = (c * y4) - (a * y5)
	t_3 = y3 * ((y * t_2) + (j * ((y0 * y5) - (y1 * y4))))
	tmp = 0
	if j <= -1.65e+37:
		tmp = t_1
	elif j <= -1.05e-132:
		tmp = i * ((j * (x * y1)) + ((c * ((z * t) - (x * y))) - (j * (t * y5))))
	elif j <= -3.3e-242:
		tmp = t_3
	elif j <= 1.6e-303:
		tmp = y1 * (y2 * ((k * y4) - (x * a)))
	elif j <= 1.75e-158:
		tmp = t_3
	elif j <= 1.9e-68:
		tmp = (z * a) * ((y1 * y3) - (t * b))
	elif j <= 8e+43:
		tmp = y * (y3 * t_2)
	elif j <= 2.7e+181:
		tmp = t_1
	elif j <= 9.6e+250:
		tmp = b * (j * ((t * y4) - (x * y0)))
	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(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(y5 * Float64(Float64(y * k) - Float64(t * j)))))
	t_2 = Float64(Float64(c * y4) - Float64(a * y5))
	t_3 = Float64(y3 * Float64(Float64(y * t_2) + Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4)))))
	tmp = 0.0
	if (j <= -1.65e+37)
		tmp = t_1;
	elseif (j <= -1.05e-132)
		tmp = Float64(i * Float64(Float64(j * Float64(x * y1)) + Float64(Float64(c * Float64(Float64(z * t) - Float64(x * y))) - Float64(j * Float64(t * y5)))));
	elseif (j <= -3.3e-242)
		tmp = t_3;
	elseif (j <= 1.6e-303)
		tmp = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (j <= 1.75e-158)
		tmp = t_3;
	elseif (j <= 1.9e-68)
		tmp = Float64(Float64(z * a) * Float64(Float64(y1 * y3) - Float64(t * b)));
	elseif (j <= 8e+43)
		tmp = Float64(y * Float64(y3 * t_2));
	elseif (j <= 2.7e+181)
		tmp = t_1;
	elseif (j <= 9.6e+250)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	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 = i * ((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j))));
	t_2 = (c * y4) - (a * y5);
	t_3 = y3 * ((y * t_2) + (j * ((y0 * y5) - (y1 * y4))));
	tmp = 0.0;
	if (j <= -1.65e+37)
		tmp = t_1;
	elseif (j <= -1.05e-132)
		tmp = i * ((j * (x * y1)) + ((c * ((z * t) - (x * y))) - (j * (t * y5))));
	elseif (j <= -3.3e-242)
		tmp = t_3;
	elseif (j <= 1.6e-303)
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	elseif (j <= 1.75e-158)
		tmp = t_3;
	elseif (j <= 1.9e-68)
		tmp = (z * a) * ((y1 * y3) - (t * b));
	elseif (j <= 8e+43)
		tmp = y * (y3 * t_2);
	elseif (j <= 2.7e+181)
		tmp = t_1;
	elseif (j <= 9.6e+250)
		tmp = b * (j * ((t * y4) - (x * y0)));
	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[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y3 * N[(N[(y * t$95$2), $MachinePrecision] + N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.65e+37], t$95$1, If[LessEqual[j, -1.05e-132], N[(i * N[(N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision] + N[(N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.3e-242], t$95$3, If[LessEqual[j, 1.6e-303], N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.75e-158], t$95$3, If[LessEqual[j, 1.9e-68], N[(N[(z * a), $MachinePrecision] * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8e+43], N[(y * N[(y3 * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.7e+181], t$95$1, If[LessEqual[j, 9.6e+250], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -1.65e37 or 8.00000000000000011e43 < j < 2.70000000000000007e181

   1. Initial program 25.0%

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

   3. Simplified 26.1%

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

   5. Taylor expanded in i around -inf 46.7%

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

   6. Taylor expanded in c around 0 58.5%

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

   if -1.65e37 < j < -1.05e-132

   1. Initial program 22.6%

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

   3. Simplified 22.6%

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

   5. Taylor expanded in i around -inf 40.5%

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

   6. Taylor expanded in k around 0 48.0%

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

   if -1.05e-132 < j < -3.29999999999999982e-242 or 1.59999999999999995e-303 < j < 1.75000000000000006e-158 or 9.60000000000000051e250 < j

   1. Initial program 31.6%

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

   3. Taylor expanded in t around inf 34.5%

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

   4. Taylor expanded in y3 around inf 57.1%

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

      1. distribute-lft-out-- 57.1%

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

   6. Simplified 57.1%

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

   if -3.29999999999999982e-242 < j < 1.59999999999999995e-303

   1. Initial program 43.3%

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

   3. Taylor expanded in y2 around inf 64.7%

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

   4. Taylor expanded in y1 around inf 50.7%

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

      1. +-commutative 50.7%

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

      2. mul-1-neg 50.7%

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

      3. unsub-neg 50.7%

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

      4. *-commutative 50.7%

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

      5. *-commutative 50.7%

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

   6. Simplified 50.7%

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

   if 1.75000000000000006e-158 < j < 1.90000000000000019e-68

   1. Initial program 21.4%

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

   3. Simplified 21.4%

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

   5. Taylor expanded in z around -inf 78.7%

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

   6. Taylor expanded in a around inf 65.1%

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

      1. associate-*r* 65.1%

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

      2. +-commutative 65.1%

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

      3. mul-1-neg 65.1%

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

      4. unsub-neg 65.1%

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

   8. Simplified 65.1%

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

   if 1.90000000000000019e-68 < j < 8.00000000000000011e43

   1. Initial program 44.1%

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

   3. Taylor expanded in t around inf 33.9%

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

   4. Taylor expanded in y around inf 77.9%

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

   if 2.70000000000000007e181 < j < 9.60000000000000051e250

   1. Initial program 21.1%

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

   3. Simplified 21.1%

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

   5. Taylor expanded in b around inf 42.5%

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

   6. Taylor expanded in j around inf 63.9%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.65 \cdot 10^{+37}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-132}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right) + \left(c \cdot \left(z \cdot t - x \cdot y\right) - j \cdot \left(t \cdot y5\right)\right)\right)\\ \mathbf{elif}\;j \leq -3.3 \cdot 10^{-242}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{-303}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{-158}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{-68}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \left(y1 \cdot y3 - t \cdot b\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{+181}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 9.6 \cdot 10^{+250}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 31.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(j \cdot \left(x \cdot y1\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ t_2 := y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{if}\;j \leq -1.4 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-62}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -1.02 \cdot 10^{-132}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;j \leq -1.16 \cdot 10^{-186}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;j \leq -2.9 \cdot 10^{-205}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;j \leq -3.6 \cdot 10^{-305}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{-154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 9.2 \cdot 10^{-66}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \left(y1 \cdot y3 - t \cdot b\right)\\ \mathbf{elif}\;j \leq 9 \cdot 10^{+85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{+202}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot y0\right) \cdot \left(z \cdot k - x \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (+ (* j (* x y1)) (* y5 (- (* y k) (* t j))))))
        (t_2 (* y (* y3 (- (* c y4) (* a y5))))))
   (if (<= j -1.4e+21)
     t_1
     (if (<= j -1.05e-62)
       (* y2 (+ (* x (- (* c y0) (* a y1))) (* t (- (* a y5) (* c y4)))))
       (if (<= j -1.02e-132)
         (* i (* c (- (* z t) (* x y))))
         (if (<= j -1.16e-186)
           (* c (* y4 (* t (- y2))))
           (if (<= j -2.9e-205)
             (* x (* y (- (* a b) (* c i))))
             (if (<= j -3.6e-305)
               (* y1 (* y2 (- (* k y4) (* x a))))
               (if (<= j 1.75e-154)
                 t_2
                 (if (<= j 9.2e-66)
                   (* (* z a) (- (* y1 y3) (* t b)))
                   (if (<= j 9e+85)
                     t_2
                     (if (<= j 6.5e+202)
                       t_1
                       (* (* b y0) (- (* z k) (* x j)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * ((j * (x * y1)) + (y5 * ((y * k) - (t * j))));
	double t_2 = y * (y3 * ((c * y4) - (a * y5)));
	double tmp;
	if (j <= -1.4e+21) {
		tmp = t_1;
	} else if (j <= -1.05e-62) {
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))));
	} else if (j <= -1.02e-132) {
		tmp = i * (c * ((z * t) - (x * y)));
	} else if (j <= -1.16e-186) {
		tmp = c * (y4 * (t * -y2));
	} else if (j <= -2.9e-205) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (j <= -3.6e-305) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (j <= 1.75e-154) {
		tmp = t_2;
	} else if (j <= 9.2e-66) {
		tmp = (z * a) * ((y1 * y3) - (t * b));
	} else if (j <= 9e+85) {
		tmp = t_2;
	} else if (j <= 6.5e+202) {
		tmp = t_1;
	} else {
		tmp = (b * y0) * ((z * k) - (x * 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) :: t_2
    real(8) :: tmp
    t_1 = i * ((j * (x * y1)) + (y5 * ((y * k) - (t * j))))
    t_2 = y * (y3 * ((c * y4) - (a * y5)))
    if (j <= (-1.4d+21)) then
        tmp = t_1
    else if (j <= (-1.05d-62)) then
        tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))))
    else if (j <= (-1.02d-132)) then
        tmp = i * (c * ((z * t) - (x * y)))
    else if (j <= (-1.16d-186)) then
        tmp = c * (y4 * (t * -y2))
    else if (j <= (-2.9d-205)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (j <= (-3.6d-305)) then
        tmp = y1 * (y2 * ((k * y4) - (x * a)))
    else if (j <= 1.75d-154) then
        tmp = t_2
    else if (j <= 9.2d-66) then
        tmp = (z * a) * ((y1 * y3) - (t * b))
    else if (j <= 9d+85) then
        tmp = t_2
    else if (j <= 6.5d+202) then
        tmp = t_1
    else
        tmp = (b * y0) * ((z * k) - (x * 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 = i * ((j * (x * y1)) + (y5 * ((y * k) - (t * j))));
	double t_2 = y * (y3 * ((c * y4) - (a * y5)));
	double tmp;
	if (j <= -1.4e+21) {
		tmp = t_1;
	} else if (j <= -1.05e-62) {
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))));
	} else if (j <= -1.02e-132) {
		tmp = i * (c * ((z * t) - (x * y)));
	} else if (j <= -1.16e-186) {
		tmp = c * (y4 * (t * -y2));
	} else if (j <= -2.9e-205) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (j <= -3.6e-305) {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	} else if (j <= 1.75e-154) {
		tmp = t_2;
	} else if (j <= 9.2e-66) {
		tmp = (z * a) * ((y1 * y3) - (t * b));
	} else if (j <= 9e+85) {
		tmp = t_2;
	} else if (j <= 6.5e+202) {
		tmp = t_1;
	} else {
		tmp = (b * y0) * ((z * k) - (x * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * ((j * (x * y1)) + (y5 * ((y * k) - (t * j))))
	t_2 = y * (y3 * ((c * y4) - (a * y5)))
	tmp = 0
	if j <= -1.4e+21:
		tmp = t_1
	elif j <= -1.05e-62:
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))))
	elif j <= -1.02e-132:
		tmp = i * (c * ((z * t) - (x * y)))
	elif j <= -1.16e-186:
		tmp = c * (y4 * (t * -y2))
	elif j <= -2.9e-205:
		tmp = x * (y * ((a * b) - (c * i)))
	elif j <= -3.6e-305:
		tmp = y1 * (y2 * ((k * y4) - (x * a)))
	elif j <= 1.75e-154:
		tmp = t_2
	elif j <= 9.2e-66:
		tmp = (z * a) * ((y1 * y3) - (t * b))
	elif j <= 9e+85:
		tmp = t_2
	elif j <= 6.5e+202:
		tmp = t_1
	else:
		tmp = (b * y0) * ((z * k) - (x * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(Float64(j * Float64(x * y1)) + Float64(y5 * Float64(Float64(y * k) - Float64(t * j)))))
	t_2 = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))
	tmp = 0.0
	if (j <= -1.4e+21)
		tmp = t_1;
	elseif (j <= -1.05e-62)
		tmp = Float64(y2 * Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (j <= -1.02e-132)
		tmp = Float64(i * Float64(c * Float64(Float64(z * t) - Float64(x * y))));
	elseif (j <= -1.16e-186)
		tmp = Float64(c * Float64(y4 * Float64(t * Float64(-y2))));
	elseif (j <= -2.9e-205)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (j <= -3.6e-305)
		tmp = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (j <= 1.75e-154)
		tmp = t_2;
	elseif (j <= 9.2e-66)
		tmp = Float64(Float64(z * a) * Float64(Float64(y1 * y3) - Float64(t * b)));
	elseif (j <= 9e+85)
		tmp = t_2;
	elseif (j <= 6.5e+202)
		tmp = t_1;
	else
		tmp = Float64(Float64(b * y0) * Float64(Float64(z * k) - Float64(x * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * ((j * (x * y1)) + (y5 * ((y * k) - (t * j))));
	t_2 = y * (y3 * ((c * y4) - (a * y5)));
	tmp = 0.0;
	if (j <= -1.4e+21)
		tmp = t_1;
	elseif (j <= -1.05e-62)
		tmp = y2 * ((x * ((c * y0) - (a * y1))) + (t * ((a * y5) - (c * y4))));
	elseif (j <= -1.02e-132)
		tmp = i * (c * ((z * t) - (x * y)));
	elseif (j <= -1.16e-186)
		tmp = c * (y4 * (t * -y2));
	elseif (j <= -2.9e-205)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (j <= -3.6e-305)
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	elseif (j <= 1.75e-154)
		tmp = t_2;
	elseif (j <= 9.2e-66)
		tmp = (z * a) * ((y1 * y3) - (t * b));
	elseif (j <= 9e+85)
		tmp = t_2;
	elseif (j <= 6.5e+202)
		tmp = t_1;
	else
		tmp = (b * y0) * ((z * k) - (x * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.4e+21], t$95$1, If[LessEqual[j, -1.05e-62], N[(y2 * N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.02e-132], N[(i * N[(c * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.16e-186], N[(c * N[(y4 * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.9e-205], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.6e-305], N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.75e-154], t$95$2, If[LessEqual[j, 9.2e-66], N[(N[(z * a), $MachinePrecision] * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9e+85], t$95$2, If[LessEqual[j, 6.5e+202], t$95$1, N[(N[(b * y0), $MachinePrecision] * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if j < -1.4e21 or 9.00000000000000013e85 < j < 6.4999999999999996e202

   1. Initial program 23.7%

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

   3. Simplified 24.7%

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

   5. Taylor expanded in i around -inf 44.1%

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

   6. Taylor expanded in c around 0 54.7%

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

   7. Taylor expanded in j around inf 59.0%

      \[\leadsto -1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right) - \color{blue}{j \cdot \left(x \cdot y1\right)}\right)\right) \]
   8. Step-by-step derivation

      1. *-commutative 59.0%

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

   9. Simplified 59.0%

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

   if -1.4e21 < j < -1.05e-62

   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 y2 around inf 53.6%

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

   4. Taylor expanded in k around 0 53.6%

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

   if -1.05e-62 < j < -1.01999999999999998e-132

   1. Initial program 24.1%

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

   3. Simplified 24.1%

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

   5. Taylor expanded in i around -inf 43.5%

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

   6. Taylor expanded in c around inf 34.6%

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

      1. *-commutative 34.6%

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

      2. neg-mul-1 34.6%

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

      3. +-commutative 34.6%

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

      4. fma-udef 34.6%

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

      5. associate-*r* 48.2%

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

      6. *-commutative 48.2%

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

      7. fma-udef 48.2%

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

      8. unsub-neg 48.2%

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

      9. *-commutative 48.2%

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

   8. Simplified 48.2%

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

   if -1.01999999999999998e-132 < j < -1.15999999999999995e-186

   1. Initial program 27.3%

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

   3. Taylor expanded in y2 around inf 36.8%

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

   4. Taylor expanded in t around inf 37.8%

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

   5. Taylor expanded in a around 0 47.2%

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

      1. associate-*r* 47.2%

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

      2. neg-mul-1 47.2%

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

      3. associate-*r* 47.0%

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

   7. Simplified 47.0%

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

   if -1.15999999999999995e-186 < j < -2.90000000000000018e-205

   1. Initial program 25.0%

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

   3. Simplified 25.0%

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

   5. Taylor expanded in x around inf 75.0%

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

   6. Taylor expanded in y around inf 100.0%

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

   if -2.90000000000000018e-205 < j < -3.60000000000000004e-305

   1. Initial program 56.2%

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

   3. Taylor expanded in y2 around inf 63.7%

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

   4. Taylor expanded in y1 around inf 50.7%

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

      1. +-commutative 50.7%

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

      2. mul-1-neg 50.7%

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

      3. unsub-neg 50.7%

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

      4. *-commutative 50.7%

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

      5. *-commutative 50.7%

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

   6. Simplified 50.7%

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

   if -3.60000000000000004e-305 < j < 1.75e-154 or 9.19999999999999967e-66 < j < 9.00000000000000013e85

   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 t around inf 30.1%

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

   4. Taylor expanded in y around inf 54.0%

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

   if 1.75e-154 < j < 9.19999999999999967e-66

   1. Initial program 21.4%

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

   3. Simplified 21.4%

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

   5. Taylor expanded in z around -inf 78.7%

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

   6. Taylor expanded in a around inf 65.1%

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

      1. associate-*r* 65.1%

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

      2. +-commutative 65.1%

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

      3. mul-1-neg 65.1%

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

      4. unsub-neg 65.1%

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

   8. Simplified 65.1%

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

   if 6.4999999999999996e202 < j

   1. Initial program 18.5%

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

   3. Simplified 18.5%

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

   5. Taylor expanded in b around inf 48.3%

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

   6. Taylor expanded in y0 around inf 59.8%

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

      1. associate-*r* 59.8%

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

      2. *-commutative 59.8%

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

      3. *-commutative 59.8%

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

   8. Simplified 59.8%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.4 \cdot 10^{+21}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-62}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -1.02 \cdot 10^{-132}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;j \leq -1.16 \cdot 10^{-186}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;j \leq -2.9 \cdot 10^{-205}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;j \leq -3.6 \cdot 10^{-305}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{-154}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 9.2 \cdot 10^{-66}:\\ \;\;\;\;\left(z \cdot a\right) \cdot \left(y1 \cdot y3 - t \cdot b\right)\\ \mathbf{elif}\;j \leq 9 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{+202}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot y0\right) \cdot \left(z \cdot k - x \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 28.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{if}\;k \leq -1.66 \cdot 10^{+248}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -4.5 \cdot 10^{+151}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -1.1 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq -3.5 \cdot 10^{-225}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq -1.6 \cdot 10^{-294}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(c \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;k \leq 3.2 \cdot 10^{-192}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;k \leq 2.4 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 4.7 \cdot 10^{+45}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)\\ \mathbf{elif}\;k \leq 2.1 \cdot 10^{+144}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 8.2 \cdot 10^{+246}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y (* y3 (- (* c y4) (* a y5))))))
   (if (<= k -1.66e+248)
     (* b (* y (- (* x a) (* k y4))))
     (if (<= k -4.5e+151)
       (* c (* y2 (- (* x y0) (* t y4))))
       (if (<= k -1.1e-119)
         t_1
         (if (<= k -3.5e-225)
           (* b (* j (- (* t y4) (* x y0))))
           (if (<= k -1.6e-294)
             (* t (* y2 (* c (- y4))))
             (if (<= k 3.2e-192)
               (* x (* y (- (* a b) (* c i))))
               (if (<= k 2.4e-80)
                 t_1
                 (if (<= k 4.7e+45)
                   (* (* t b) (- (* j y4) (* z a)))
                   (if (<= k 2.1e+144)
                     (* b (* x (- (* y a) (* j y0))))
                     (if (<= k 8.2e+246)
                       (* y0 (* y2 (- (* x c) (* k y5))))
                       (* y1 (* y2 (- (* k y4) (* x a))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * (y3 * ((c * y4) - (a * y5)));
	double tmp;
	if (k <= -1.66e+248) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (k <= -4.5e+151) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (k <= -1.1e-119) {
		tmp = t_1;
	} else if (k <= -3.5e-225) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (k <= -1.6e-294) {
		tmp = t * (y2 * (c * -y4));
	} else if (k <= 3.2e-192) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (k <= 2.4e-80) {
		tmp = t_1;
	} else if (k <= 4.7e+45) {
		tmp = (t * b) * ((j * y4) - (z * a));
	} else if (k <= 2.1e+144) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (k <= 8.2e+246) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (y3 * ((c * y4) - (a * y5)))
    if (k <= (-1.66d+248)) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (k <= (-4.5d+151)) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (k <= (-1.1d-119)) then
        tmp = t_1
    else if (k <= (-3.5d-225)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (k <= (-1.6d-294)) then
        tmp = t * (y2 * (c * -y4))
    else if (k <= 3.2d-192) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (k <= 2.4d-80) then
        tmp = t_1
    else if (k <= 4.7d+45) then
        tmp = (t * b) * ((j * y4) - (z * a))
    else if (k <= 2.1d+144) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (k <= 8.2d+246) then
        tmp = y0 * (y2 * ((x * c) - (k * y5)))
    else
        tmp = y1 * (y2 * ((k * y4) - (x * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * (y3 * ((c * y4) - (a * y5)));
	double tmp;
	if (k <= -1.66e+248) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (k <= -4.5e+151) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (k <= -1.1e-119) {
		tmp = t_1;
	} else if (k <= -3.5e-225) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (k <= -1.6e-294) {
		tmp = t * (y2 * (c * -y4));
	} else if (k <= 3.2e-192) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (k <= 2.4e-80) {
		tmp = t_1;
	} else if (k <= 4.7e+45) {
		tmp = (t * b) * ((j * y4) - (z * a));
	} else if (k <= 2.1e+144) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (k <= 8.2e+246) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else {
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y * (y3 * ((c * y4) - (a * y5)))
	tmp = 0
	if k <= -1.66e+248:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif k <= -4.5e+151:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif k <= -1.1e-119:
		tmp = t_1
	elif k <= -3.5e-225:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif k <= -1.6e-294:
		tmp = t * (y2 * (c * -y4))
	elif k <= 3.2e-192:
		tmp = x * (y * ((a * b) - (c * i)))
	elif k <= 2.4e-80:
		tmp = t_1
	elif k <= 4.7e+45:
		tmp = (t * b) * ((j * y4) - (z * a))
	elif k <= 2.1e+144:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif k <= 8.2e+246:
		tmp = y0 * (y2 * ((x * c) - (k * y5)))
	else:
		tmp = y1 * (y2 * ((k * y4) - (x * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))
	tmp = 0.0
	if (k <= -1.66e+248)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (k <= -4.5e+151)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (k <= -1.1e-119)
		tmp = t_1;
	elseif (k <= -3.5e-225)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (k <= -1.6e-294)
		tmp = Float64(t * Float64(y2 * Float64(c * Float64(-y4))));
	elseif (k <= 3.2e-192)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (k <= 2.4e-80)
		tmp = t_1;
	elseif (k <= 4.7e+45)
		tmp = Float64(Float64(t * b) * Float64(Float64(j * y4) - Float64(z * a)));
	elseif (k <= 2.1e+144)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (k <= 8.2e+246)
		tmp = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))));
	else
		tmp = Float64(y1 * Float64(y2 * Float64(Float64(k * y4) - Float64(x * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y * (y3 * ((c * y4) - (a * y5)));
	tmp = 0.0;
	if (k <= -1.66e+248)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (k <= -4.5e+151)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (k <= -1.1e-119)
		tmp = t_1;
	elseif (k <= -3.5e-225)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (k <= -1.6e-294)
		tmp = t * (y2 * (c * -y4));
	elseif (k <= 3.2e-192)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (k <= 2.4e-80)
		tmp = t_1;
	elseif (k <= 4.7e+45)
		tmp = (t * b) * ((j * y4) - (z * a));
	elseif (k <= 2.1e+144)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (k <= 8.2e+246)
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	else
		tmp = y1 * (y2 * ((k * y4) - (x * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -1.66e+248], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -4.5e+151], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.1e-119], t$95$1, If[LessEqual[k, -3.5e-225], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.6e-294], N[(t * N[(y2 * N[(c * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.2e-192], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.4e-80], t$95$1, If[LessEqual[k, 4.7e+45], N[(N[(t * b), $MachinePrecision] * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.1e+144], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 8.2e+246], N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(y2 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if k < -1.66e248

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in b around inf 41.7%

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

   6. Taylor expanded in y around inf 67.1%

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

      1. +-commutative 67.1%

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

      2. mul-1-neg 67.1%

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

      3. unsub-neg 67.1%

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

      4. *-commutative 67.1%

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

      5. *-commutative 67.1%

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

   8. Simplified 67.1%

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

   if -1.66e248 < k < -4.4999999999999999e151

   1. Initial program 23.1%

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

   3. Taylor expanded in y2 around inf 62.0%

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

   4. Taylor expanded in c around inf 55.9%

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

   if -4.4999999999999999e151 < k < -1.1e-119 or 3.2000000000000002e-192 < k < 2.3999999999999999e-80

   1. Initial program 31.5%

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

   3. Taylor expanded in t around inf 39.5%

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

   4. Taylor expanded in y around inf 48.0%

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

   if -1.1e-119 < k < -3.4999999999999997e-225

   1. Initial program 50.2%

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

   3. Simplified 50.2%

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

   5. Taylor expanded in b around inf 46.5%

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

   6. Taylor expanded in j around inf 38.0%

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

   if -3.4999999999999997e-225 < k < -1.6000000000000001e-294

   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 y2 around inf 47.5%

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

   4. Taylor expanded in t around inf 58.4%

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

   5. Taylor expanded in a around 0 63.9%

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

      1. mul-1-neg 63.9%

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

      2. distribute-lft-neg-out 63.9%

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

      3. *-commutative 63.9%

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

   7. Simplified 63.9%

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

   if -1.6000000000000001e-294 < k < 3.2000000000000002e-192

   1. Initial program 16.9%

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

   3. Simplified 16.9%

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

   5. Taylor expanded in x around inf 38.2%

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

   6. Taylor expanded in y around inf 51.2%

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

   if 2.3999999999999999e-80 < k < 4.70000000000000002e45

   1. Initial program 11.4%

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

   3. Simplified 11.4%

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

   5. Taylor expanded in b around inf 30.6%

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

   6. Taylor expanded in t around inf 45.9%

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

      1. associate-*r* 56.3%

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

      2. +-commutative 56.3%

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

      3. mul-1-neg 56.3%

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

      4. unsub-neg 56.3%

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

   8. Simplified 56.3%

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

   if 4.70000000000000002e45 < k < 2.09999999999999996e144

   1. Initial program 47.9%

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

   3. Simplified 47.9%

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

   5. Taylor expanded in x around inf 53.1%

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

   6. Taylor expanded in b around inf 53.7%

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

   if 2.09999999999999996e144 < k < 8.19999999999999951e246

   1. Initial program 19.0%

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

   3. Taylor expanded in y2 around inf 33.4%

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

   4. Taylor expanded in y0 around inf 52.9%

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

      1. +-commutative 52.9%

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

      2. mul-1-neg 52.9%

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

      3. unsub-neg 52.9%

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

      4. *-commutative 52.9%

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

      5. *-commutative 52.9%

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

   6. Simplified 52.9%

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

   if 8.19999999999999951e246 < k

   1. Initial program 21.4%

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

   3. Taylor expanded in y2 around inf 42.9%

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

   4. Taylor expanded in y1 around inf 71.5%

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

      1. +-commutative 71.5%

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

      2. mul-1-neg 71.5%

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

      3. unsub-neg 71.5%

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

      4. *-commutative 71.5%

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

      5. *-commutative 71.5%

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

   6. Simplified 71.5%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.66 \cdot 10^{+248}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -4.5 \cdot 10^{+151}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -1.1 \cdot 10^{-119}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq -3.5 \cdot 10^{-225}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq -1.6 \cdot 10^{-294}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(c \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;k \leq 3.2 \cdot 10^{-192}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;k \leq 2.4 \cdot 10^{-80}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 4.7 \cdot 10^{+45}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(j \cdot y4 - z \cdot a\right)\\ \mathbf{elif}\;k \leq 2.1 \cdot 10^{+144}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 8.2 \cdot 10^{+246}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 31.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{if}\;y0 \leq -5.8 \cdot 10^{+103}:\\ \;\;\;\;z \cdot \left(y0 \cdot \left(b \cdot k - c \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -1.15 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq -5.3 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -2.3 \cdot 10^{-147}:\\ \;\;\;\;\left(i \cdot k\right) \cdot \left(z \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;y0 \leq -5.8 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -2 \cdot 10^{-261}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 5.5 \cdot 10^{-209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq 1.5 \cdot 10^{-99}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 4.8 \cdot 10^{-51}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 1.45 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* x (- (* j y1) (* y c))))))
   (if (<= y0 -5.8e+103)
     (* z (* y0 (- (* b k) (* c y3))))
     (if (<= y0 -1.15e+33)
       (* t (* y2 (- (* a y5) (* c y4))))
       (if (<= y0 -5.3e-76)
         t_1
         (if (<= y0 -2.3e-147)
           (* (* i k) (* z (- y1)))
           (if (<= y0 -5.8e-192)
             t_1
             (if (<= y0 -2e-261)
               (* x (* y (- (* a b) (* c i))))
               (if (<= y0 5.5e-209)
                 t_1
                 (if (<= y0 1.5e-99)
                   (* a (* y2 (- (* t y5) (* x y1))))
                   (if (<= y0 4.8e-51)
                     (* i (* y1 (- (* x j) (* z k))))
                     (if (<= y0 1.45e+95)
                       (* y (* y3 (- (* c y4) (* a y5))))
                       (* y0 (* y5 (- (* j y3) (* k y2))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (x * ((j * y1) - (y * c)));
	double tmp;
	if (y0 <= -5.8e+103) {
		tmp = z * (y0 * ((b * k) - (c * y3)));
	} else if (y0 <= -1.15e+33) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (y0 <= -5.3e-76) {
		tmp = t_1;
	} else if (y0 <= -2.3e-147) {
		tmp = (i * k) * (z * -y1);
	} else if (y0 <= -5.8e-192) {
		tmp = t_1;
	} else if (y0 <= -2e-261) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y0 <= 5.5e-209) {
		tmp = t_1;
	} else if (y0 <= 1.5e-99) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (y0 <= 4.8e-51) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (y0 <= 1.45e+95) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (x * ((j * y1) - (y * c)))
    if (y0 <= (-5.8d+103)) then
        tmp = z * (y0 * ((b * k) - (c * y3)))
    else if (y0 <= (-1.15d+33)) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (y0 <= (-5.3d-76)) then
        tmp = t_1
    else if (y0 <= (-2.3d-147)) then
        tmp = (i * k) * (z * -y1)
    else if (y0 <= (-5.8d-192)) then
        tmp = t_1
    else if (y0 <= (-2d-261)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y0 <= 5.5d-209) then
        tmp = t_1
    else if (y0 <= 1.5d-99) then
        tmp = a * (y2 * ((t * y5) - (x * y1)))
    else if (y0 <= 4.8d-51) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (y0 <= 1.45d+95) then
        tmp = y * (y3 * ((c * y4) - (a * y5)))
    else
        tmp = y0 * (y5 * ((j * y3) - (k * y2)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (x * ((j * y1) - (y * c)));
	double tmp;
	if (y0 <= -5.8e+103) {
		tmp = z * (y0 * ((b * k) - (c * y3)));
	} else if (y0 <= -1.15e+33) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (y0 <= -5.3e-76) {
		tmp = t_1;
	} else if (y0 <= -2.3e-147) {
		tmp = (i * k) * (z * -y1);
	} else if (y0 <= -5.8e-192) {
		tmp = t_1;
	} else if (y0 <= -2e-261) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y0 <= 5.5e-209) {
		tmp = t_1;
	} else if (y0 <= 1.5e-99) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (y0 <= 4.8e-51) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (y0 <= 1.45e+95) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (x * ((j * y1) - (y * c)))
	tmp = 0
	if y0 <= -5.8e+103:
		tmp = z * (y0 * ((b * k) - (c * y3)))
	elif y0 <= -1.15e+33:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif y0 <= -5.3e-76:
		tmp = t_1
	elif y0 <= -2.3e-147:
		tmp = (i * k) * (z * -y1)
	elif y0 <= -5.8e-192:
		tmp = t_1
	elif y0 <= -2e-261:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y0 <= 5.5e-209:
		tmp = t_1
	elif y0 <= 1.5e-99:
		tmp = a * (y2 * ((t * y5) - (x * y1)))
	elif y0 <= 4.8e-51:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif y0 <= 1.45e+95:
		tmp = y * (y3 * ((c * y4) - (a * y5)))
	else:
		tmp = y0 * (y5 * ((j * y3) - (k * y2)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(x * Float64(Float64(j * y1) - Float64(y * c))))
	tmp = 0.0
	if (y0 <= -5.8e+103)
		tmp = Float64(z * Float64(y0 * Float64(Float64(b * k) - Float64(c * y3))));
	elseif (y0 <= -1.15e+33)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (y0 <= -5.3e-76)
		tmp = t_1;
	elseif (y0 <= -2.3e-147)
		tmp = Float64(Float64(i * k) * Float64(z * Float64(-y1)));
	elseif (y0 <= -5.8e-192)
		tmp = t_1;
	elseif (y0 <= -2e-261)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y0 <= 5.5e-209)
		tmp = t_1;
	elseif (y0 <= 1.5e-99)
		tmp = Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (y0 <= 4.8e-51)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (y0 <= 1.45e+95)
		tmp = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))));
	else
		tmp = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (x * ((j * y1) - (y * c)));
	tmp = 0.0;
	if (y0 <= -5.8e+103)
		tmp = z * (y0 * ((b * k) - (c * y3)));
	elseif (y0 <= -1.15e+33)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (y0 <= -5.3e-76)
		tmp = t_1;
	elseif (y0 <= -2.3e-147)
		tmp = (i * k) * (z * -y1);
	elseif (y0 <= -5.8e-192)
		tmp = t_1;
	elseif (y0 <= -2e-261)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y0 <= 5.5e-209)
		tmp = t_1;
	elseif (y0 <= 1.5e-99)
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	elseif (y0 <= 4.8e-51)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (y0 <= 1.45e+95)
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	else
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(x * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -5.8e+103], N[(z * N[(y0 * N[(N[(b * k), $MachinePrecision] - N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.15e+33], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -5.3e-76], t$95$1, If[LessEqual[y0, -2.3e-147], N[(N[(i * k), $MachinePrecision] * N[(z * (-y1)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -5.8e-192], t$95$1, If[LessEqual[y0, -2e-261], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 5.5e-209], t$95$1, If[LessEqual[y0, 1.5e-99], N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.8e-51], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.45e+95], N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y0 < -5.7999999999999997e103

   1. Initial program 16.7%

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

   3. Simplified 16.7%

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

   5. Taylor expanded in z around -inf 43.2%

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

   6. Taylor expanded in y0 around inf 55.2%

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

   if -5.7999999999999997e103 < y0 < -1.15000000000000005e33

   1. Initial program 46.2%

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

   3. Taylor expanded in y2 around inf 39.1%

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

   4. Taylor expanded in t around inf 55.3%

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

   if -1.15000000000000005e33 < y0 < -5.3e-76 or -2.2999999999999999e-147 < y0 < -5.80000000000000033e-192 or -1.99999999999999997e-261 < y0 < 5.5000000000000001e-209

   1. Initial program 34.6%

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

   3. Simplified 34.6%

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

   5. Taylor expanded in x around inf 53.0%

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

   6. Taylor expanded in i around -inf 58.9%

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

   if -5.3e-76 < y0 < -2.2999999999999999e-147

   1. Initial program 26.3%

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

   3. Simplified 26.3%

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

   5. Taylor expanded in i around -inf 47.6%

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

   6. Taylor expanded in c around 0 47.7%

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

   7. Taylor expanded in z around inf 32.5%

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

      1. associate-*r* 37.6%

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

   9. Simplified 37.6%

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

   if -5.80000000000000033e-192 < y0 < -1.99999999999999997e-261

   1. Initial program 17.0%

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

   3. Simplified 17.0%

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

   5. Taylor expanded in x around inf 46.4%

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

   6. Taylor expanded in y around inf 55.0%

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

   if 5.5000000000000001e-209 < y0 < 1.50000000000000003e-99

   1. Initial program 35.2%

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

   3. Taylor expanded in y2 around inf 46.4%

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

   4. Taylor expanded in a around -inf 53.8%

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

   if 1.50000000000000003e-99 < y0 < 4.8e-51

   1. Initial program 28.6%

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

   3. Simplified 28.6%

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

   5. Taylor expanded in i around -inf 35.9%

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

   6. Taylor expanded in y1 around inf 57.8%

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

   if 4.8e-51 < y0 < 1.45000000000000007e95

   1. Initial program 32.4%

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

   3. Taylor expanded in t around inf 30.9%

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

   4. Taylor expanded in y around inf 56.9%

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

   if 1.45000000000000007e95 < y0

   1. Initial program 18.9%

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

   3. Taylor expanded in t around inf 19.1%

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

   4. Taylor expanded in y0 around inf 57.0%

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

      1. mul-1-neg 57.0%

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

      2. distribute-rgt-neg-in 57.0%

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

      3. *-commutative 57.0%

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

   6. Simplified 57.0%

      \[\leadsto \color{blue}{y0 \cdot \left(-y5 \cdot \left(y2 \cdot k - j \cdot y3\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -5.8 \cdot 10^{+103}:\\ \;\;\;\;z \cdot \left(y0 \cdot \left(b \cdot k - c \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -1.15 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq -5.3 \cdot 10^{-76}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq -2.3 \cdot 10^{-147}:\\ \;\;\;\;\left(i \cdot k\right) \cdot \left(z \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;y0 \leq -5.8 \cdot 10^{-192}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq -2 \cdot 10^{-261}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 5.5 \cdot 10^{-209}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq 1.5 \cdot 10^{-99}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 4.8 \cdot 10^{-51}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 1.45 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ t_2 := y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{if}\;j \leq -4.6 \cdot 10^{+169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -4 \cdot 10^{+80}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{-195}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-193}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{-105}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+100}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 9 \cdot 10^{+163}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{+186}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{+248}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* j (- (* t y4) (* x y0)))))
        (t_2 (* y (* y3 (- (* c y4) (* a y5))))))
   (if (<= j -4.6e+169)
     t_1
     (if (<= j -4e+80)
       (* i (* j (* x y1)))
       (if (<= j -1.1e-195)
         (* b (* y (- (* x a) (* k y4))))
         (if (<= j 6.2e-193)
           t_2
           (if (<= j 1.15e-105)
             (* y0 (* y2 (- (* x c) (* k y5))))
             (if (<= j 4.5e+100)
               t_2
               (if (<= j 9e+163)
                 (* j (* x (- (* i y1) (* b y0))))
                 (if (<= j 7.5e+186)
                   (* t (* y2 (- (* a y5) (* c y4))))
                   (if (<= j 5.4e+248)
                     t_1
                     (* y1 (* y4 (- (* k y2) (* j y3)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (j * ((t * y4) - (x * y0)));
	double t_2 = y * (y3 * ((c * y4) - (a * y5)));
	double tmp;
	if (j <= -4.6e+169) {
		tmp = t_1;
	} else if (j <= -4e+80) {
		tmp = i * (j * (x * y1));
	} else if (j <= -1.1e-195) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (j <= 6.2e-193) {
		tmp = t_2;
	} else if (j <= 1.15e-105) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (j <= 4.5e+100) {
		tmp = t_2;
	} else if (j <= 9e+163) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (j <= 7.5e+186) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (j <= 5.4e+248) {
		tmp = t_1;
	} else {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (j * ((t * y4) - (x * y0)))
    t_2 = y * (y3 * ((c * y4) - (a * y5)))
    if (j <= (-4.6d+169)) then
        tmp = t_1
    else if (j <= (-4d+80)) then
        tmp = i * (j * (x * y1))
    else if (j <= (-1.1d-195)) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (j <= 6.2d-193) then
        tmp = t_2
    else if (j <= 1.15d-105) then
        tmp = y0 * (y2 * ((x * c) - (k * y5)))
    else if (j <= 4.5d+100) then
        tmp = t_2
    else if (j <= 9d+163) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (j <= 7.5d+186) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (j <= 5.4d+248) then
        tmp = t_1
    else
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (j * ((t * y4) - (x * y0)));
	double t_2 = y * (y3 * ((c * y4) - (a * y5)));
	double tmp;
	if (j <= -4.6e+169) {
		tmp = t_1;
	} else if (j <= -4e+80) {
		tmp = i * (j * (x * y1));
	} else if (j <= -1.1e-195) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (j <= 6.2e-193) {
		tmp = t_2;
	} else if (j <= 1.15e-105) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (j <= 4.5e+100) {
		tmp = t_2;
	} else if (j <= 9e+163) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (j <= 7.5e+186) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (j <= 5.4e+248) {
		tmp = t_1;
	} else {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (j * ((t * y4) - (x * y0)))
	t_2 = y * (y3 * ((c * y4) - (a * y5)))
	tmp = 0
	if j <= -4.6e+169:
		tmp = t_1
	elif j <= -4e+80:
		tmp = i * (j * (x * y1))
	elif j <= -1.1e-195:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif j <= 6.2e-193:
		tmp = t_2
	elif j <= 1.15e-105:
		tmp = y0 * (y2 * ((x * c) - (k * y5)))
	elif j <= 4.5e+100:
		tmp = t_2
	elif j <= 9e+163:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif j <= 7.5e+186:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif j <= 5.4e+248:
		tmp = t_1
	else:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))))
	t_2 = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))
	tmp = 0.0
	if (j <= -4.6e+169)
		tmp = t_1;
	elseif (j <= -4e+80)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (j <= -1.1e-195)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (j <= 6.2e-193)
		tmp = t_2;
	elseif (j <= 1.15e-105)
		tmp = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))));
	elseif (j <= 4.5e+100)
		tmp = t_2;
	elseif (j <= 9e+163)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (j <= 7.5e+186)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (j <= 5.4e+248)
		tmp = t_1;
	else
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (j * ((t * y4) - (x * y0)));
	t_2 = y * (y3 * ((c * y4) - (a * y5)));
	tmp = 0.0;
	if (j <= -4.6e+169)
		tmp = t_1;
	elseif (j <= -4e+80)
		tmp = i * (j * (x * y1));
	elseif (j <= -1.1e-195)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (j <= 6.2e-193)
		tmp = t_2;
	elseif (j <= 1.15e-105)
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	elseif (j <= 4.5e+100)
		tmp = t_2;
	elseif (j <= 9e+163)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (j <= 7.5e+186)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (j <= 5.4e+248)
		tmp = t_1;
	else
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4.6e+169], t$95$1, If[LessEqual[j, -4e+80], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.1e-195], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.2e-193], t$95$2, If[LessEqual[j, 1.15e-105], N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.5e+100], t$95$2, If[LessEqual[j, 9e+163], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.5e+186], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.4e+248], t$95$1, N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if j < -4.5999999999999999e169 or 7.4999999999999998e186 < j < 5.39999999999999977e248

   1. Initial program 17.3%

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

   3. Simplified 17.3%

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

   5. Taylor expanded in b around inf 43.1%

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

   6. Taylor expanded in j around inf 60.4%

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

   if -4.5999999999999999e169 < j < -4e80

   1. Initial program 23.8%

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

   3. Simplified 23.8%

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

   5. Taylor expanded in i around -inf 47.6%

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

   6. Taylor expanded in c around 0 53.5%

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

   7. Taylor expanded in x around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. distribute-rgt-neg-in 60.0%

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

      3. distribute-rgt-neg-in 60.0%

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

      4. *-commutative 60.0%

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

      5. distribute-rgt-neg-in 60.0%

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

   9. Simplified 60.0%

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

   if -4e80 < j < -1.10000000000000003e-195

   1. Initial program 24.7%

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

   3. Simplified 24.7%

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

   5. Taylor expanded in b around inf 40.3%

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

   6. Taylor expanded in y around inf 35.6%

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

      1. +-commutative 35.6%

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

      2. mul-1-neg 35.6%

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

      3. unsub-neg 35.6%

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

      4. *-commutative 35.6%

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

      5. *-commutative 35.6%

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

   8. Simplified 35.6%

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

   if -1.10000000000000003e-195 < j < 6.2000000000000004e-193 or 1.15e-105 < j < 4.50000000000000036e100

   1. Initial program 40.8%

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

   3. Taylor expanded in t around inf 37.5%

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

   4. Taylor expanded in y around inf 47.9%

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

   if 6.2000000000000004e-193 < j < 1.15e-105

   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 y2 around inf 53.5%

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

   4. Taylor expanded in y0 around inf 67.2%

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

      1. +-commutative 67.2%

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

      2. mul-1-neg 67.2%

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

      3. unsub-neg 67.2%

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

      4. *-commutative 67.2%

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

      5. *-commutative 67.2%

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

   6. Simplified 67.2%

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

   if 4.50000000000000036e100 < j < 8.99999999999999976e163

   1. Initial program 40.4%

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

   3. Simplified 40.4%

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

   5. Taylor expanded in x around inf 55.6%

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

   6. Taylor expanded in j around inf 56.8%

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

   if 8.99999999999999976e163 < j < 7.4999999999999998e186

   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 y2 around inf 50.0%

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

   4. Taylor expanded in t around inf 76.0%

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

   if 5.39999999999999977e248 < j

   1. Initial program 11.1%

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

   3. Taylor expanded in t around inf 22.2%

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

   4. Taylor expanded in y1 around inf 56.5%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.6 \cdot 10^{+169}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -4 \cdot 10^{+80}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{-195}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-193}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{-105}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+100}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 9 \cdot 10^{+163}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{+186}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{+248}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.6% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ t_2 := i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{if}\;y0 \leq -8.2 \cdot 10^{+76}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -4 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -26.5:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq -9.5 \cdot 10^{-194}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y0 \leq -4.2 \cdot 10^{-262}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 9.2 \cdot 10^{-210}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y0 \leq 1.6 \cdot 10^{-99}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 4.7 \cdot 10^{-48}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 1.5 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y (* y3 (- (* c y4) (* a y5)))))
        (t_2 (* i (* x (- (* j y1) (* y c))))))
   (if (<= y0 -8.2e+76)
     (* b (* j (- (* t y4) (* x y0))))
     (if (<= y0 -4e+34)
       t_1
       (if (<= y0 -26.5)
         (* y0 (* y2 (- (* x c) (* k y5))))
         (if (<= y0 -9.5e-194)
           t_2
           (if (<= y0 -4.2e-262)
             (* x (* y (- (* a b) (* c i))))
             (if (<= y0 9.2e-210)
               t_2
               (if (<= y0 1.6e-99)
                 (* a (* y2 (- (* t y5) (* x y1))))
                 (if (<= y0 4.7e-48)
                   (* i (* y1 (- (* x j) (* z k))))
                   (if (<= y0 1.5e+96)
                     t_1
                     (* y0 (* y5 (- (* j y3) (* k y2)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * (y3 * ((c * y4) - (a * y5)));
	double t_2 = i * (x * ((j * y1) - (y * c)));
	double tmp;
	if (y0 <= -8.2e+76) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y0 <= -4e+34) {
		tmp = t_1;
	} else if (y0 <= -26.5) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (y0 <= -9.5e-194) {
		tmp = t_2;
	} else if (y0 <= -4.2e-262) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y0 <= 9.2e-210) {
		tmp = t_2;
	} else if (y0 <= 1.6e-99) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (y0 <= 4.7e-48) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (y0 <= 1.5e+96) {
		tmp = t_1;
	} else {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (y3 * ((c * y4) - (a * y5)))
    t_2 = i * (x * ((j * y1) - (y * c)))
    if (y0 <= (-8.2d+76)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y0 <= (-4d+34)) then
        tmp = t_1
    else if (y0 <= (-26.5d0)) then
        tmp = y0 * (y2 * ((x * c) - (k * y5)))
    else if (y0 <= (-9.5d-194)) then
        tmp = t_2
    else if (y0 <= (-4.2d-262)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y0 <= 9.2d-210) then
        tmp = t_2
    else if (y0 <= 1.6d-99) then
        tmp = a * (y2 * ((t * y5) - (x * y1)))
    else if (y0 <= 4.7d-48) then
        tmp = i * (y1 * ((x * j) - (z * k)))
    else if (y0 <= 1.5d+96) then
        tmp = t_1
    else
        tmp = y0 * (y5 * ((j * y3) - (k * y2)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * (y3 * ((c * y4) - (a * y5)));
	double t_2 = i * (x * ((j * y1) - (y * c)));
	double tmp;
	if (y0 <= -8.2e+76) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y0 <= -4e+34) {
		tmp = t_1;
	} else if (y0 <= -26.5) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (y0 <= -9.5e-194) {
		tmp = t_2;
	} else if (y0 <= -4.2e-262) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y0 <= 9.2e-210) {
		tmp = t_2;
	} else if (y0 <= 1.6e-99) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (y0 <= 4.7e-48) {
		tmp = i * (y1 * ((x * j) - (z * k)));
	} else if (y0 <= 1.5e+96) {
		tmp = t_1;
	} else {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y * (y3 * ((c * y4) - (a * y5)))
	t_2 = i * (x * ((j * y1) - (y * c)))
	tmp = 0
	if y0 <= -8.2e+76:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y0 <= -4e+34:
		tmp = t_1
	elif y0 <= -26.5:
		tmp = y0 * (y2 * ((x * c) - (k * y5)))
	elif y0 <= -9.5e-194:
		tmp = t_2
	elif y0 <= -4.2e-262:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y0 <= 9.2e-210:
		tmp = t_2
	elif y0 <= 1.6e-99:
		tmp = a * (y2 * ((t * y5) - (x * y1)))
	elif y0 <= 4.7e-48:
		tmp = i * (y1 * ((x * j) - (z * k)))
	elif y0 <= 1.5e+96:
		tmp = t_1
	else:
		tmp = y0 * (y5 * ((j * y3) - (k * y2)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))
	t_2 = Float64(i * Float64(x * Float64(Float64(j * y1) - Float64(y * c))))
	tmp = 0.0
	if (y0 <= -8.2e+76)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y0 <= -4e+34)
		tmp = t_1;
	elseif (y0 <= -26.5)
		tmp = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))));
	elseif (y0 <= -9.5e-194)
		tmp = t_2;
	elseif (y0 <= -4.2e-262)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y0 <= 9.2e-210)
		tmp = t_2;
	elseif (y0 <= 1.6e-99)
		tmp = Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (y0 <= 4.7e-48)
		tmp = Float64(i * Float64(y1 * Float64(Float64(x * j) - Float64(z * k))));
	elseif (y0 <= 1.5e+96)
		tmp = t_1;
	else
		tmp = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y * (y3 * ((c * y4) - (a * y5)));
	t_2 = i * (x * ((j * y1) - (y * c)));
	tmp = 0.0;
	if (y0 <= -8.2e+76)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y0 <= -4e+34)
		tmp = t_1;
	elseif (y0 <= -26.5)
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	elseif (y0 <= -9.5e-194)
		tmp = t_2;
	elseif (y0 <= -4.2e-262)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y0 <= 9.2e-210)
		tmp = t_2;
	elseif (y0 <= 1.6e-99)
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	elseif (y0 <= 4.7e-48)
		tmp = i * (y1 * ((x * j) - (z * k)));
	elseif (y0 <= 1.5e+96)
		tmp = t_1;
	else
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(x * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -8.2e+76], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -4e+34], t$95$1, If[LessEqual[y0, -26.5], N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -9.5e-194], t$95$2, If[LessEqual[y0, -4.2e-262], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 9.2e-210], t$95$2, If[LessEqual[y0, 1.6e-99], N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.7e-48], N[(i * N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.5e+96], t$95$1, N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y0 < -8.1999999999999997e76

   1. Initial program 20.0%

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

   3. Simplified 20.0%

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

   5. Taylor expanded in b around inf 47.0%

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

   6. Taylor expanded in j around inf 51.8%

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

   if -8.1999999999999997e76 < y0 < -3.99999999999999978e34 or 4.6999999999999998e-48 < y0 < 1.5e96

   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 t around inf 34.5%

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

   4. Taylor expanded in y around inf 59.6%

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

   if -3.99999999999999978e34 < y0 < -26.5

   1. Initial program 16.7%

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

   3. Taylor expanded in y2 around inf 34.7%

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

   4. Taylor expanded in y0 around inf 68.0%

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

      1. +-commutative 68.0%

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

      2. mul-1-neg 68.0%

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

      3. unsub-neg 68.0%

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

      4. *-commutative 68.0%

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

      5. *-commutative 68.0%

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

   6. Simplified 68.0%

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

   if -26.5 < y0 < -9.50000000000000009e-194 or -4.1999999999999999e-262 < y0 < 9.2e-210

   1. Initial program 33.6%

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

   3. Simplified 33.6%

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

   5. Taylor expanded in x around inf 52.6%

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

   6. Taylor expanded in i around -inf 49.1%

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

   if -9.50000000000000009e-194 < y0 < -4.1999999999999999e-262

   1. Initial program 17.0%

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

   3. Simplified 17.0%

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

   5. Taylor expanded in x around inf 46.4%

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

   6. Taylor expanded in y around inf 55.0%

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

   if 9.2e-210 < y0 < 1.6e-99

   1. Initial program 35.2%

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

   3. Taylor expanded in y2 around inf 46.4%

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

   4. Taylor expanded in a around -inf 53.8%

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

   if 1.6e-99 < y0 < 4.6999999999999998e-48

   1. Initial program 28.6%

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

   3. Simplified 28.6%

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

   5. Taylor expanded in i around -inf 35.9%

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

   6. Taylor expanded in y1 around inf 57.8%

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

   if 1.5e96 < y0

   1. Initial program 18.9%

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

   3. Taylor expanded in t around inf 19.1%

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

   4. Taylor expanded in y0 around inf 57.0%

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

      1. mul-1-neg 57.0%

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

      2. distribute-rgt-neg-in 57.0%

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

      3. *-commutative 57.0%

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

   6. Simplified 57.0%

      \[\leadsto \color{blue}{y0 \cdot \left(-y5 \cdot \left(y2 \cdot k - j \cdot y3\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -8.2 \cdot 10^{+76}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -4 \cdot 10^{+34}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq -26.5:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq -9.5 \cdot 10^{-194}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq -4.2 \cdot 10^{-262}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 9.2 \cdot 10^{-210}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;y0 \leq 1.6 \cdot 10^{-99}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 4.7 \cdot 10^{-48}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y0 \leq 1.5 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 26.7% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{if}\;y2 \leq -1.58 \cdot 10^{+181}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -8.5 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -2.6 \cdot 10^{-266}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 2 \cdot 10^{-277}:\\ \;\;\;\;\left(i \cdot k\right) \cdot \left(z \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;y2 \leq 1.45 \cdot 10^{-249}:\\ \;\;\;\;i \cdot \left(t \cdot \left(j \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 5.2 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq 1.65 \cdot 10^{+82} \lor \neg \left(y2 \leq 6 \cdot 10^{+221}\right):\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* x (- (* y a) (* j y0))))))
   (if (<= y2 -1.58e+181)
     (* c (* y4 (* t (- y2))))
     (if (<= y2 -8.5e-213)
       t_1
       (if (<= y2 -2.6e-266)
         (* i (* j (* x y1)))
         (if (<= y2 2e-277)
           (* (* i k) (* z (- y1)))
           (if (<= y2 1.45e-249)
             (* i (* t (* j (- y5))))
             (if (<= y2 5.2e-91)
               t_1
               (if (or (<= y2 1.65e+82) (not (<= y2 6e+221)))
                 (* b (* j (- (* t y4) (* x y0))))
                 (* t (* y5 (* a y2))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (x * ((y * a) - (j * y0)));
	double tmp;
	if (y2 <= -1.58e+181) {
		tmp = c * (y4 * (t * -y2));
	} else if (y2 <= -8.5e-213) {
		tmp = t_1;
	} else if (y2 <= -2.6e-266) {
		tmp = i * (j * (x * y1));
	} else if (y2 <= 2e-277) {
		tmp = (i * k) * (z * -y1);
	} else if (y2 <= 1.45e-249) {
		tmp = i * (t * (j * -y5));
	} else if (y2 <= 5.2e-91) {
		tmp = t_1;
	} else if ((y2 <= 1.65e+82) || !(y2 <= 6e+221)) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = t * (y5 * (a * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (x * ((y * a) - (j * y0)))
    if (y2 <= (-1.58d+181)) then
        tmp = c * (y4 * (t * -y2))
    else if (y2 <= (-8.5d-213)) then
        tmp = t_1
    else if (y2 <= (-2.6d-266)) then
        tmp = i * (j * (x * y1))
    else if (y2 <= 2d-277) then
        tmp = (i * k) * (z * -y1)
    else if (y2 <= 1.45d-249) then
        tmp = i * (t * (j * -y5))
    else if (y2 <= 5.2d-91) then
        tmp = t_1
    else if ((y2 <= 1.65d+82) .or. (.not. (y2 <= 6d+221))) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else
        tmp = t * (y5 * (a * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (x * ((y * a) - (j * y0)));
	double tmp;
	if (y2 <= -1.58e+181) {
		tmp = c * (y4 * (t * -y2));
	} else if (y2 <= -8.5e-213) {
		tmp = t_1;
	} else if (y2 <= -2.6e-266) {
		tmp = i * (j * (x * y1));
	} else if (y2 <= 2e-277) {
		tmp = (i * k) * (z * -y1);
	} else if (y2 <= 1.45e-249) {
		tmp = i * (t * (j * -y5));
	} else if (y2 <= 5.2e-91) {
		tmp = t_1;
	} else if ((y2 <= 1.65e+82) || !(y2 <= 6e+221)) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = t * (y5 * (a * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (x * ((y * a) - (j * y0)))
	tmp = 0
	if y2 <= -1.58e+181:
		tmp = c * (y4 * (t * -y2))
	elif y2 <= -8.5e-213:
		tmp = t_1
	elif y2 <= -2.6e-266:
		tmp = i * (j * (x * y1))
	elif y2 <= 2e-277:
		tmp = (i * k) * (z * -y1)
	elif y2 <= 1.45e-249:
		tmp = i * (t * (j * -y5))
	elif y2 <= 5.2e-91:
		tmp = t_1
	elif (y2 <= 1.65e+82) or not (y2 <= 6e+221):
		tmp = b * (j * ((t * y4) - (x * y0)))
	else:
		tmp = t * (y5 * (a * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))))
	tmp = 0.0
	if (y2 <= -1.58e+181)
		tmp = Float64(c * Float64(y4 * Float64(t * Float64(-y2))));
	elseif (y2 <= -8.5e-213)
		tmp = t_1;
	elseif (y2 <= -2.6e-266)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (y2 <= 2e-277)
		tmp = Float64(Float64(i * k) * Float64(z * Float64(-y1)));
	elseif (y2 <= 1.45e-249)
		tmp = Float64(i * Float64(t * Float64(j * Float64(-y5))));
	elseif (y2 <= 5.2e-91)
		tmp = t_1;
	elseif ((y2 <= 1.65e+82) || !(y2 <= 6e+221))
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	else
		tmp = Float64(t * Float64(y5 * Float64(a * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (x * ((y * a) - (j * y0)));
	tmp = 0.0;
	if (y2 <= -1.58e+181)
		tmp = c * (y4 * (t * -y2));
	elseif (y2 <= -8.5e-213)
		tmp = t_1;
	elseif (y2 <= -2.6e-266)
		tmp = i * (j * (x * y1));
	elseif (y2 <= 2e-277)
		tmp = (i * k) * (z * -y1);
	elseif (y2 <= 1.45e-249)
		tmp = i * (t * (j * -y5));
	elseif (y2 <= 5.2e-91)
		tmp = t_1;
	elseif ((y2 <= 1.65e+82) || ~((y2 <= 6e+221)))
		tmp = b * (j * ((t * y4) - (x * y0)));
	else
		tmp = t * (y5 * (a * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.58e+181], N[(c * N[(y4 * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -8.5e-213], t$95$1, If[LessEqual[y2, -2.6e-266], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2e-277], N[(N[(i * k), $MachinePrecision] * N[(z * (-y1)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.45e-249], N[(i * N[(t * N[(j * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5.2e-91], t$95$1, If[Or[LessEqual[y2, 1.65e+82], N[Not[LessEqual[y2, 6e+221]], $MachinePrecision]], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y5 * N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y2 < -1.58000000000000002e181

   1. Initial program 13.5%

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

   3. Taylor expanded in y2 around inf 60.2%

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

   4. Taylor expanded in t around inf 54.4%

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

   5. Taylor expanded in a around 0 47.4%

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

      1. associate-*r* 47.4%

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

      2. neg-mul-1 47.4%

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

      3. associate-*r* 53.8%

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

   7. Simplified 53.8%

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

   if -1.58000000000000002e181 < y2 < -8.49999999999999994e-213 or 1.45000000000000011e-249 < y2 < 5.20000000000000028e-91

   1. Initial program 31.2%

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

   3. Simplified 32.1%

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

   5. Taylor expanded in x around inf 44.7%

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

   6. Taylor expanded in b around inf 39.4%

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

   if -8.49999999999999994e-213 < y2 < -2.6e-266

   1. Initial program 62.5%

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

   3. Simplified 62.5%

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

   5. Taylor expanded in i around -inf 62.6%

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

   6. Taylor expanded in c around 0 87.6%

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

   7. Taylor expanded in x around inf 62.9%

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

      1. mul-1-neg 62.9%

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

      2. distribute-rgt-neg-in 62.9%

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

      3. distribute-rgt-neg-in 62.9%

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

      4. *-commutative 62.9%

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

      5. distribute-rgt-neg-in 62.9%

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

   9. Simplified 62.9%

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

   if -2.6e-266 < y2 < 1.99999999999999994e-277

   1. Initial program 27.1%

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

   3. Simplified 27.1%

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

   5. Taylor expanded in i around -inf 63.7%

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

   6. Taylor expanded in c around 0 55.6%

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

   7. Taylor expanded in z around inf 28.6%

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

      1. associate-*r* 37.2%

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

   9. Simplified 37.2%

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

   if 1.99999999999999994e-277 < y2 < 1.45000000000000011e-249

   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 t around inf 34.4%

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

   4. Taylor expanded in i around inf 34.7%

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

   5. Taylor expanded in j around inf 50.8%

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

      1. mul-1-neg 50.8%

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

      2. *-commutative 50.8%

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

      3. distribute-lft-neg-in 50.8%

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

   7. Simplified 50.8%

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

   if 5.20000000000000028e-91 < y2 < 1.6499999999999999e82 or 6.0000000000000003e221 < y2

   1. Initial program 22.5%

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

   3. Simplified 22.5%

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

   5. Taylor expanded in b around inf 43.8%

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

   6. Taylor expanded in j around inf 51.2%

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

   if 1.6499999999999999e82 < y2 < 6.0000000000000003e221

   1. Initial program 24.4%

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

   3. Taylor expanded in y2 around inf 49.1%

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

   4. Taylor expanded in t around inf 37.4%

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

   5. Taylor expanded in a around inf 31.3%

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

      1. associate-*r* 40.0%

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

      2. *-commutative 40.0%

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

   7. Simplified 40.0%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.58 \cdot 10^{+181}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -8.5 \cdot 10^{-213}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq -2.6 \cdot 10^{-266}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 2 \cdot 10^{-277}:\\ \;\;\;\;\left(i \cdot k\right) \cdot \left(z \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;y2 \leq 1.45 \cdot 10^{-249}:\\ \;\;\;\;i \cdot \left(t \cdot \left(j \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 5.2 \cdot 10^{-91}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 1.65 \cdot 10^{+82} \lor \neg \left(y2 \leq 6 \cdot 10^{+221}\right):\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.6% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ t_2 := y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{if}\;j \leq -4 \cdot 10^{+169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -3.2 \cdot 10^{+80}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-194}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-170}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{+100}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{+178}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+249}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* j (- (* t y4) (* x y0)))))
        (t_2 (* y (* y3 (- (* c y4) (* a y5))))))
   (if (<= j -4e+169)
     t_1
     (if (<= j -3.2e+80)
       (* i (* j (* x y1)))
       (if (<= j -3.7e-194)
         (* b (* y (- (* x a) (* k y4))))
         (if (<= j 3.8e-170)
           t_2
           (if (<= j 1.35e-103)
             (* x (* y (- (* a b) (* c i))))
             (if (<= j 4e+100)
               t_2
               (if (<= j 1.15e+178)
                 (* j (* x (- (* i y1) (* b y0))))
                 (if (<= j 9.5e+249)
                   t_1
                   (* b (* x (- (* y a) (* j y0))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (j * ((t * y4) - (x * y0)));
	double t_2 = y * (y3 * ((c * y4) - (a * y5)));
	double tmp;
	if (j <= -4e+169) {
		tmp = t_1;
	} else if (j <= -3.2e+80) {
		tmp = i * (j * (x * y1));
	} else if (j <= -3.7e-194) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (j <= 3.8e-170) {
		tmp = t_2;
	} else if (j <= 1.35e-103) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (j <= 4e+100) {
		tmp = t_2;
	} else if (j <= 1.15e+178) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (j <= 9.5e+249) {
		tmp = t_1;
	} else {
		tmp = b * (x * ((y * a) - (j * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (j * ((t * y4) - (x * y0)))
    t_2 = y * (y3 * ((c * y4) - (a * y5)))
    if (j <= (-4d+169)) then
        tmp = t_1
    else if (j <= (-3.2d+80)) then
        tmp = i * (j * (x * y1))
    else if (j <= (-3.7d-194)) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (j <= 3.8d-170) then
        tmp = t_2
    else if (j <= 1.35d-103) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (j <= 4d+100) then
        tmp = t_2
    else if (j <= 1.15d+178) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (j <= 9.5d+249) then
        tmp = t_1
    else
        tmp = b * (x * ((y * a) - (j * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (j * ((t * y4) - (x * y0)));
	double t_2 = y * (y3 * ((c * y4) - (a * y5)));
	double tmp;
	if (j <= -4e+169) {
		tmp = t_1;
	} else if (j <= -3.2e+80) {
		tmp = i * (j * (x * y1));
	} else if (j <= -3.7e-194) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (j <= 3.8e-170) {
		tmp = t_2;
	} else if (j <= 1.35e-103) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (j <= 4e+100) {
		tmp = t_2;
	} else if (j <= 1.15e+178) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (j <= 9.5e+249) {
		tmp = t_1;
	} else {
		tmp = b * (x * ((y * a) - (j * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (j * ((t * y4) - (x * y0)))
	t_2 = y * (y3 * ((c * y4) - (a * y5)))
	tmp = 0
	if j <= -4e+169:
		tmp = t_1
	elif j <= -3.2e+80:
		tmp = i * (j * (x * y1))
	elif j <= -3.7e-194:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif j <= 3.8e-170:
		tmp = t_2
	elif j <= 1.35e-103:
		tmp = x * (y * ((a * b) - (c * i)))
	elif j <= 4e+100:
		tmp = t_2
	elif j <= 1.15e+178:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif j <= 9.5e+249:
		tmp = t_1
	else:
		tmp = b * (x * ((y * a) - (j * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))))
	t_2 = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))
	tmp = 0.0
	if (j <= -4e+169)
		tmp = t_1;
	elseif (j <= -3.2e+80)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (j <= -3.7e-194)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (j <= 3.8e-170)
		tmp = t_2;
	elseif (j <= 1.35e-103)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (j <= 4e+100)
		tmp = t_2;
	elseif (j <= 1.15e+178)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (j <= 9.5e+249)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (j * ((t * y4) - (x * y0)));
	t_2 = y * (y3 * ((c * y4) - (a * y5)));
	tmp = 0.0;
	if (j <= -4e+169)
		tmp = t_1;
	elseif (j <= -3.2e+80)
		tmp = i * (j * (x * y1));
	elseif (j <= -3.7e-194)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (j <= 3.8e-170)
		tmp = t_2;
	elseif (j <= 1.35e-103)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (j <= 4e+100)
		tmp = t_2;
	elseif (j <= 1.15e+178)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (j <= 9.5e+249)
		tmp = t_1;
	else
		tmp = b * (x * ((y * a) - (j * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4e+169], t$95$1, If[LessEqual[j, -3.2e+80], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.7e-194], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.8e-170], t$95$2, If[LessEqual[j, 1.35e-103], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4e+100], t$95$2, If[LessEqual[j, 1.15e+178], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9.5e+249], t$95$1, N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -3.99999999999999974e169 or 1.15e178 < j < 9.49999999999999925e249

   1. Initial program 15.9%

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

   3. Simplified 15.9%

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

   5. Taylor expanded in b around inf 41.7%

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

   6. Taylor expanded in j around inf 59.6%

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

   if -3.99999999999999974e169 < j < -3.1999999999999999e80

   1. Initial program 23.8%

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

   3. Simplified 23.8%

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

   5. Taylor expanded in i around -inf 47.6%

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

   6. Taylor expanded in c around 0 53.5%

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

   7. Taylor expanded in x around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. distribute-rgt-neg-in 60.0%

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

      3. distribute-rgt-neg-in 60.0%

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

      4. *-commutative 60.0%

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

      5. distribute-rgt-neg-in 60.0%

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

   9. Simplified 60.0%

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

   if -3.1999999999999999e80 < j < -3.70000000000000008e-194

   1. Initial program 24.7%

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

   3. Simplified 24.7%

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

   5. Taylor expanded in b around inf 40.3%

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

   6. Taylor expanded in y around inf 35.6%

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

      1. +-commutative 35.6%

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

      2. mul-1-neg 35.6%

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

      3. unsub-neg 35.6%

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

      4. *-commutative 35.6%

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

      5. *-commutative 35.6%

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

   8. Simplified 35.6%

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

   if -3.70000000000000008e-194 < j < 3.7999999999999998e-170 or 1.35000000000000005e-103 < j < 4.00000000000000006e100

   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 t around inf 36.9%

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

   4. Taylor expanded in y around inf 48.0%

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

   if 3.7999999999999998e-170 < j < 1.35000000000000005e-103

   1. Initial program 18.2%

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

   3. Simplified 18.2%

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

   5. Taylor expanded in x around inf 72.7%

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

   6. Taylor expanded in y around inf 55.6%

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

   if 4.00000000000000006e100 < j < 1.15e178

   1. Initial program 38.5%

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

   3. Simplified 38.5%

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

   5. Taylor expanded in x around inf 57.7%

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

   6. Taylor expanded in j around inf 58.8%

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

   if 9.49999999999999925e249 < j

   1. Initial program 11.8%

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

   3. Simplified 11.8%

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

   5. Taylor expanded in x around inf 35.5%

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

   6. Taylor expanded in b around inf 47.8%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4 \cdot 10^{+169}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -3.2 \cdot 10^{+80}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-194}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-170}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{+100}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{+178}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+249}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.7% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ t_2 := y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{if}\;j \leq -4.5 \cdot 10^{+170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{+80}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -5 \cdot 10^{-194}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{-193}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 5 \cdot 10^{-106}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 4.9 \cdot 10^{+101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{+167}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{+250}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* j (- (* t y4) (* x y0)))))
        (t_2 (* y (* y3 (- (* c y4) (* a y5))))))
   (if (<= j -4.5e+170)
     t_1
     (if (<= j -1.35e+80)
       (* i (* j (* x y1)))
       (if (<= j -5e-194)
         (* b (* y (- (* x a) (* k y4))))
         (if (<= j 1.9e-193)
           t_2
           (if (<= j 5e-106)
             (* y0 (* y2 (- (* x c) (* k y5))))
             (if (<= j 4.9e+101)
               t_2
               (if (<= j 1.65e+167)
                 (* j (* x (- (* i y1) (* b y0))))
                 (if (<= j 1.1e+250)
                   t_1
                   (* b (* x (- (* y a) (* j y0))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (j * ((t * y4) - (x * y0)));
	double t_2 = y * (y3 * ((c * y4) - (a * y5)));
	double tmp;
	if (j <= -4.5e+170) {
		tmp = t_1;
	} else if (j <= -1.35e+80) {
		tmp = i * (j * (x * y1));
	} else if (j <= -5e-194) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (j <= 1.9e-193) {
		tmp = t_2;
	} else if (j <= 5e-106) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (j <= 4.9e+101) {
		tmp = t_2;
	} else if (j <= 1.65e+167) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (j <= 1.1e+250) {
		tmp = t_1;
	} else {
		tmp = b * (x * ((y * a) - (j * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (j * ((t * y4) - (x * y0)))
    t_2 = y * (y3 * ((c * y4) - (a * y5)))
    if (j <= (-4.5d+170)) then
        tmp = t_1
    else if (j <= (-1.35d+80)) then
        tmp = i * (j * (x * y1))
    else if (j <= (-5d-194)) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (j <= 1.9d-193) then
        tmp = t_2
    else if (j <= 5d-106) then
        tmp = y0 * (y2 * ((x * c) - (k * y5)))
    else if (j <= 4.9d+101) then
        tmp = t_2
    else if (j <= 1.65d+167) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (j <= 1.1d+250) then
        tmp = t_1
    else
        tmp = b * (x * ((y * a) - (j * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (j * ((t * y4) - (x * y0)));
	double t_2 = y * (y3 * ((c * y4) - (a * y5)));
	double tmp;
	if (j <= -4.5e+170) {
		tmp = t_1;
	} else if (j <= -1.35e+80) {
		tmp = i * (j * (x * y1));
	} else if (j <= -5e-194) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (j <= 1.9e-193) {
		tmp = t_2;
	} else if (j <= 5e-106) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else if (j <= 4.9e+101) {
		tmp = t_2;
	} else if (j <= 1.65e+167) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (j <= 1.1e+250) {
		tmp = t_1;
	} else {
		tmp = b * (x * ((y * a) - (j * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (j * ((t * y4) - (x * y0)))
	t_2 = y * (y3 * ((c * y4) - (a * y5)))
	tmp = 0
	if j <= -4.5e+170:
		tmp = t_1
	elif j <= -1.35e+80:
		tmp = i * (j * (x * y1))
	elif j <= -5e-194:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif j <= 1.9e-193:
		tmp = t_2
	elif j <= 5e-106:
		tmp = y0 * (y2 * ((x * c) - (k * y5)))
	elif j <= 4.9e+101:
		tmp = t_2
	elif j <= 1.65e+167:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif j <= 1.1e+250:
		tmp = t_1
	else:
		tmp = b * (x * ((y * a) - (j * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))))
	t_2 = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))
	tmp = 0.0
	if (j <= -4.5e+170)
		tmp = t_1;
	elseif (j <= -1.35e+80)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (j <= -5e-194)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (j <= 1.9e-193)
		tmp = t_2;
	elseif (j <= 5e-106)
		tmp = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))));
	elseif (j <= 4.9e+101)
		tmp = t_2;
	elseif (j <= 1.65e+167)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (j <= 1.1e+250)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (j * ((t * y4) - (x * y0)));
	t_2 = y * (y3 * ((c * y4) - (a * y5)));
	tmp = 0.0;
	if (j <= -4.5e+170)
		tmp = t_1;
	elseif (j <= -1.35e+80)
		tmp = i * (j * (x * y1));
	elseif (j <= -5e-194)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (j <= 1.9e-193)
		tmp = t_2;
	elseif (j <= 5e-106)
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	elseif (j <= 4.9e+101)
		tmp = t_2;
	elseif (j <= 1.65e+167)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (j <= 1.1e+250)
		tmp = t_1;
	else
		tmp = b * (x * ((y * a) - (j * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4.5e+170], t$95$1, If[LessEqual[j, -1.35e+80], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -5e-194], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.9e-193], t$95$2, If[LessEqual[j, 5e-106], N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.9e+101], t$95$2, If[LessEqual[j, 1.65e+167], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.1e+250], t$95$1, N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -4.50000000000000022e170 or 1.65000000000000009e167 < j < 1.10000000000000007e250

   1. Initial program 15.9%

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

   3. Simplified 15.9%

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

   5. Taylor expanded in b around inf 41.7%

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

   6. Taylor expanded in j around inf 59.6%

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

   if -4.50000000000000022e170 < j < -1.34999999999999991e80

   1. Initial program 23.8%

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

   3. Simplified 23.8%

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

   5. Taylor expanded in i around -inf 47.6%

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

   6. Taylor expanded in c around 0 53.5%

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

   7. Taylor expanded in x around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. distribute-rgt-neg-in 60.0%

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

      3. distribute-rgt-neg-in 60.0%

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

      4. *-commutative 60.0%

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

      5. distribute-rgt-neg-in 60.0%

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

   9. Simplified 60.0%

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

   if -1.34999999999999991e80 < j < -5.0000000000000002e-194

   1. Initial program 24.7%

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

   3. Simplified 24.7%

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

   5. Taylor expanded in b around inf 40.3%

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

   6. Taylor expanded in y around inf 35.6%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 35.6%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 35.6%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 35.6%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

      4. *-commutative 35.6%

         \[\leadsto b \cdot \left(y \cdot \left(\color{blue}{x \cdot a} - k \cdot y4\right)\right) \]

      5. *-commutative 35.6%

         \[\leadsto b \cdot \left(y \cdot \left(x \cdot a - \color{blue}{y4 \cdot k}\right)\right) \]

   8. Simplified 35.6%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(x \cdot a - y4 \cdot k\right)\right)} \]

   if -5.0000000000000002e-194 < j < 1.90000000000000002e-193 or 4.99999999999999983e-106 < j < 4.89999999999999983e101

   1. Initial program 40.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 37.5%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in y around inf 47.9%

      \[\leadsto \color{blue}{y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   if 1.90000000000000002e-193 < j < 4.99999999999999983e-106

   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 y2 around inf 53.5%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in y0 around inf 67.2%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 67.2%

         \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(c \cdot x + -1 \cdot \left(k \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 67.2%

         \[\leadsto y0 \cdot \left(y2 \cdot \left(c \cdot x + \color{blue}{\left(-k \cdot y5\right)}\right)\right) \]

      3. unsub-neg 67.2%

         \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(c \cdot x - k \cdot y5\right)}\right) \]

      4. *-commutative 67.2%

         \[\leadsto y0 \cdot \left(y2 \cdot \left(\color{blue}{x \cdot c} - k \cdot y5\right)\right) \]

      5. *-commutative 67.2%

         \[\leadsto y0 \cdot \left(y2 \cdot \left(x \cdot c - \color{blue}{y5 \cdot k}\right)\right) \]

   6. Simplified 67.2%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(x \cdot c - y5 \cdot k\right)\right)} \]

   if 4.89999999999999983e101 < j < 1.65000000000000009e167

   1. Initial program 38.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 38.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 57.7%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in j around inf 58.8%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   if 1.10000000000000007e250 < j

   1. Initial program 11.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 11.8%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 35.5%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in b around inf 47.8%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.5 \cdot 10^{+170}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{+80}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;j \leq -5 \cdot 10^{-194}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{-193}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{-106}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 4.9 \cdot 10^{+101}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{+167}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{+250}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 27.4% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -8.1 \cdot 10^{+180}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -3.6 \cdot 10^{-212}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq -3.8 \cdot 10^{-263}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq -2.25 \cdot 10^{-305}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 4 \cdot 10^{-65}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 4.1 \cdot 10^{+84} \lor \neg \left(y2 \leq 1.2 \cdot 10^{+222}\right):\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -8.1e+180)
   (* c (* y4 (* t (- y2))))
   (if (<= y2 -3.6e-212)
     (* b (* x (- (* y a) (* j y0))))
     (if (<= y2 -3.8e-263)
       (* i (* j (* x y1)))
       (if (<= y2 -2.25e-305)
         (* b (* j (* t y4)))
         (if (<= y2 4e-65)
           (* b (* y (- (* x a) (* k y4))))
           (if (or (<= y2 4.1e+84) (not (<= y2 1.2e+222)))
             (* b (* j (- (* t y4) (* x y0))))
             (* t (* y5 (* a y2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -8.1e+180) {
		tmp = c * (y4 * (t * -y2));
	} else if (y2 <= -3.6e-212) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y2 <= -3.8e-263) {
		tmp = i * (j * (x * y1));
	} else if (y2 <= -2.25e-305) {
		tmp = b * (j * (t * y4));
	} else if (y2 <= 4e-65) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if ((y2 <= 4.1e+84) || !(y2 <= 1.2e+222)) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = t * (y5 * (a * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-8.1d+180)) then
        tmp = c * (y4 * (t * -y2))
    else if (y2 <= (-3.6d-212)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y2 <= (-3.8d-263)) then
        tmp = i * (j * (x * y1))
    else if (y2 <= (-2.25d-305)) then
        tmp = b * (j * (t * y4))
    else if (y2 <= 4d-65) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if ((y2 <= 4.1d+84) .or. (.not. (y2 <= 1.2d+222))) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else
        tmp = t * (y5 * (a * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -8.1e+180) {
		tmp = c * (y4 * (t * -y2));
	} else if (y2 <= -3.6e-212) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y2 <= -3.8e-263) {
		tmp = i * (j * (x * y1));
	} else if (y2 <= -2.25e-305) {
		tmp = b * (j * (t * y4));
	} else if (y2 <= 4e-65) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if ((y2 <= 4.1e+84) || !(y2 <= 1.2e+222)) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = t * (y5 * (a * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -8.1e+180:
		tmp = c * (y4 * (t * -y2))
	elif y2 <= -3.6e-212:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y2 <= -3.8e-263:
		tmp = i * (j * (x * y1))
	elif y2 <= -2.25e-305:
		tmp = b * (j * (t * y4))
	elif y2 <= 4e-65:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif (y2 <= 4.1e+84) or not (y2 <= 1.2e+222):
		tmp = b * (j * ((t * y4) - (x * y0)))
	else:
		tmp = t * (y5 * (a * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -8.1e+180)
		tmp = Float64(c * Float64(y4 * Float64(t * Float64(-y2))));
	elseif (y2 <= -3.6e-212)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y2 <= -3.8e-263)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (y2 <= -2.25e-305)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	elseif (y2 <= 4e-65)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif ((y2 <= 4.1e+84) || !(y2 <= 1.2e+222))
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	else
		tmp = Float64(t * Float64(y5 * Float64(a * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -8.1e+180)
		tmp = c * (y4 * (t * -y2));
	elseif (y2 <= -3.6e-212)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y2 <= -3.8e-263)
		tmp = i * (j * (x * y1));
	elseif (y2 <= -2.25e-305)
		tmp = b * (j * (t * y4));
	elseif (y2 <= 4e-65)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif ((y2 <= 4.1e+84) || ~((y2 <= 1.2e+222)))
		tmp = b * (j * ((t * y4) - (x * y0)));
	else
		tmp = t * (y5 * (a * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -8.1e+180], N[(c * N[(y4 * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -3.6e-212], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -3.8e-263], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.25e-305], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4e-65], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y2, 4.1e+84], N[Not[LessEqual[y2, 1.2e+222]], $MachinePrecision]], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y5 * N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y2 < -8.10000000000000003e180

   1. Initial program 13.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 60.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 54.4%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   5. Taylor expanded in a around 0 47.4%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 47.4%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

      2. neg-mul-1 47.4%

         \[\leadsto \color{blue}{\left(-c\right)} \cdot \left(t \cdot \left(y2 \cdot y4\right)\right) \]

      3. associate-*r* 53.8%

         \[\leadsto \left(-c\right) \cdot \color{blue}{\left(\left(t \cdot y2\right) \cdot y4\right)} \]

   7. Simplified 53.8%

      \[\leadsto \color{blue}{\left(-c\right) \cdot \left(\left(t \cdot y2\right) \cdot y4\right)} \]

   if -8.10000000000000003e180 < y2 < -3.6000000000000001e-212

   1. Initial program 25.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 42.9%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in b around inf 37.2%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if -3.6000000000000001e-212 < y2 < -3.80000000000000005e-263

   1. Initial program 62.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 62.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 62.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   6. Taylor expanded in c around 0 87.6%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   7. Taylor expanded in x around inf 62.9%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 62.9%

         \[\leadsto -1 \cdot \color{blue}{\left(-i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\right)} \]

      2. distribute-rgt-neg-in 62.9%

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(-j \cdot \left(x \cdot y1\right)\right)\right)} \]

      3. distribute-rgt-neg-in 62.9%

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(j \cdot \left(-x \cdot y1\right)\right)}\right) \]

      4. *-commutative 62.9%

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot \left(-\color{blue}{y1 \cdot x}\right)\right)\right) \]

      5. distribute-rgt-neg-in 62.9%

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot \left(-x\right)\right)}\right)\right) \]

   9. Simplified 62.9%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot \left(y1 \cdot \left(-x\right)\right)\right)\right)} \]

   if -3.80000000000000005e-263 < y2 < -2.2500000000000001e-305

   1. Initial program 16.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 16.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 17.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 18.2%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 34.9%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

   if -2.2500000000000001e-305 < y2 < 3.99999999999999969e-65

   1. Initial program 44.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 44.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y around inf 45.6%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 45.6%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 45.6%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 45.6%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

      4. *-commutative 45.6%

         \[\leadsto b \cdot \left(y \cdot \left(\color{blue}{x \cdot a} - k \cdot y4\right)\right) \]

      5. *-commutative 45.6%

         \[\leadsto b \cdot \left(y \cdot \left(x \cdot a - \color{blue}{y4 \cdot k}\right)\right) \]

   8. Simplified 45.6%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(x \cdot a - y4 \cdot k\right)\right)} \]

   if 3.99999999999999969e-65 < y2 < 4.1000000000000003e84 or 1.2000000000000001e222 < y2

   1. Initial program 23.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.8%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 42.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 52.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if 4.1000000000000003e84 < y2 < 1.2000000000000001e222

   1. Initial program 24.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 49.1%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 37.4%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   5. Taylor expanded in a around inf 31.3%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(y2 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 40.0%

         \[\leadsto t \cdot \color{blue}{\left(\left(a \cdot y2\right) \cdot y5\right)} \]

      2. *-commutative 40.0%

         \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(a \cdot y2\right)\right)} \]

   7. Simplified 40.0%

      \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(a \cdot y2\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -8.1 \cdot 10^{+180}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -3.6 \cdot 10^{-212}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq -3.8 \cdot 10^{-263}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq -2.25 \cdot 10^{-305}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 4 \cdot 10^{-65}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 4.1 \cdot 10^{+84} \lor \neg \left(y2 \leq 1.2 \cdot 10^{+222}\right):\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 28.7% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_2 := c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{if}\;t \leq -3 \cdot 10^{+194}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-113}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+94}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+171}:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* x (- (* i y1) (* b y0)))))
        (t_2 (* c (* y2 (- (* x y0) (* t y4))))))
   (if (<= t -3e+194)
     (* b (* j (- (* t y4) (* x y0))))
     (if (<= t -2.45e+132)
       t_1
       (if (<= t -3.5e-113)
         t_2
         (if (<= t 3.8e-77)
           t_1
           (if (<= t 4.2e+14)
             (* b (* x (- (* y a) (* j y0))))
             (if (<= t 5.5e+94)
               (* i (* j (* x y1)))
               (if (<= t 6.8e+171) (* i (* t (* z c))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (x * ((i * y1) - (b * y0)));
	double t_2 = c * (y2 * ((x * y0) - (t * y4)));
	double tmp;
	if (t <= -3e+194) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (t <= -2.45e+132) {
		tmp = t_1;
	} else if (t <= -3.5e-113) {
		tmp = t_2;
	} else if (t <= 3.8e-77) {
		tmp = t_1;
	} else if (t <= 4.2e+14) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (t <= 5.5e+94) {
		tmp = i * (j * (x * y1));
	} else if (t <= 6.8e+171) {
		tmp = i * (t * (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (x * ((i * y1) - (b * y0)))
    t_2 = c * (y2 * ((x * y0) - (t * y4)))
    if (t <= (-3d+194)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (t <= (-2.45d+132)) then
        tmp = t_1
    else if (t <= (-3.5d-113)) then
        tmp = t_2
    else if (t <= 3.8d-77) then
        tmp = t_1
    else if (t <= 4.2d+14) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (t <= 5.5d+94) then
        tmp = i * (j * (x * y1))
    else if (t <= 6.8d+171) then
        tmp = i * (t * (z * c))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (x * ((i * y1) - (b * y0)));
	double t_2 = c * (y2 * ((x * y0) - (t * y4)));
	double tmp;
	if (t <= -3e+194) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (t <= -2.45e+132) {
		tmp = t_1;
	} else if (t <= -3.5e-113) {
		tmp = t_2;
	} else if (t <= 3.8e-77) {
		tmp = t_1;
	} else if (t <= 4.2e+14) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (t <= 5.5e+94) {
		tmp = i * (j * (x * y1));
	} else if (t <= 6.8e+171) {
		tmp = i * (t * (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (x * ((i * y1) - (b * y0)))
	t_2 = c * (y2 * ((x * y0) - (t * y4)))
	tmp = 0
	if t <= -3e+194:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif t <= -2.45e+132:
		tmp = t_1
	elif t <= -3.5e-113:
		tmp = t_2
	elif t <= 3.8e-77:
		tmp = t_1
	elif t <= 4.2e+14:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif t <= 5.5e+94:
		tmp = i * (j * (x * y1))
	elif t <= 6.8e+171:
		tmp = i * (t * (z * c))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))))
	t_2 = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))))
	tmp = 0.0
	if (t <= -3e+194)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (t <= -2.45e+132)
		tmp = t_1;
	elseif (t <= -3.5e-113)
		tmp = t_2;
	elseif (t <= 3.8e-77)
		tmp = t_1;
	elseif (t <= 4.2e+14)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (t <= 5.5e+94)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (t <= 6.8e+171)
		tmp = Float64(i * Float64(t * Float64(z * c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * (x * ((i * y1) - (b * y0)));
	t_2 = c * (y2 * ((x * y0) - (t * y4)));
	tmp = 0.0;
	if (t <= -3e+194)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (t <= -2.45e+132)
		tmp = t_1;
	elseif (t <= -3.5e-113)
		tmp = t_2;
	elseif (t <= 3.8e-77)
		tmp = t_1;
	elseif (t <= 4.2e+14)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (t <= 5.5e+94)
		tmp = i * (j * (x * y1));
	elseif (t <= 6.8e+171)
		tmp = i * (t * (z * c));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3e+194], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.45e+132], t$95$1, If[LessEqual[t, -3.5e-113], t$95$2, If[LessEqual[t, 3.8e-77], t$95$1, If[LessEqual[t, 4.2e+14], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+94], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e+171], N[(i * N[(t * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -3.0000000000000003e194

   1. Initial program 22.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 22.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 45.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 59.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -3.0000000000000003e194 < t < -2.4500000000000001e132 or -3.50000000000000029e-113 < t < 3.7999999999999999e-77

   1. Initial program 31.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 49.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in j around inf 44.1%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   if -2.4500000000000001e132 < t < -3.50000000000000029e-113 or 6.8000000000000003e171 < t

   1. Initial program 21.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 39.9%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 46.7%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]

   if 3.7999999999999999e-77 < t < 4.2e14

   1. Initial program 38.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 38.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 43.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in b around inf 48.0%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if 4.2e14 < t < 5.4999999999999997e94

   1. Initial program 22.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 22.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 55.9%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   6. Taylor expanded in c around 0 50.7%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   7. Taylor expanded in x around inf 45.3%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 45.3%

         \[\leadsto -1 \cdot \color{blue}{\left(-i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\right)} \]

      2. distribute-rgt-neg-in 45.3%

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(-j \cdot \left(x \cdot y1\right)\right)\right)} \]

      3. distribute-rgt-neg-in 45.3%

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(j \cdot \left(-x \cdot y1\right)\right)}\right) \]

      4. *-commutative 45.3%

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot \left(-\color{blue}{y1 \cdot x}\right)\right)\right) \]

      5. distribute-rgt-neg-in 45.3%

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot \left(-x\right)\right)}\right)\right) \]

   9. Simplified 45.3%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot \left(y1 \cdot \left(-x\right)\right)\right)\right)} \]

   if 5.4999999999999997e94 < t < 6.8000000000000003e171

   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 t around inf 35.0%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in i around inf 50.7%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]

   5. Taylor expanded in j around 0 35.8%

      \[\leadsto i \cdot \color{blue}{\left(c \cdot \left(t \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 35.8%

         \[\leadsto i \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot c\right)} \]

      2. associate-*r* 36.0%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot \left(z \cdot c\right)\right)} \]

   7. Simplified 36.0%

      \[\leadsto i \cdot \color{blue}{\left(t \cdot \left(z \cdot c\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+194}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{+132}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-113}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-77}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+94}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+171}:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 30.6% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{+158}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-138}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-51}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+16}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+84}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(t \cdot \left(-z\right)\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y2 (- (* x y0) (* t y4))))))
   (if (<= x -7.8e+158)
     (* j (* x (- (* i y1) (* b y0))))
     (if (<= x -1.5e+84)
       t_1
       (if (<= x -1.25e-138)
         (* b (* j (- (* t y4) (* x y0))))
         (if (<= x 1.3e-51)
           (* t (* y2 (- (* a y5) (* c y4))))
           (if (<= x 1.45e+16)
             (* b (* y (- (* x a) (* k y4))))
             (if (<= x 7.2e+84)
               (* (* a b) (* t (- z)))
               (if (<= x 3.2e+140)
                 t_1
                 (* b (* x (- (* y a) (* j y0)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * ((x * y0) - (t * y4)));
	double tmp;
	if (x <= -7.8e+158) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (x <= -1.5e+84) {
		tmp = t_1;
	} else if (x <= -1.25e-138) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (x <= 1.3e-51) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (x <= 1.45e+16) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (x <= 7.2e+84) {
		tmp = (a * b) * (t * -z);
	} else if (x <= 3.2e+140) {
		tmp = t_1;
	} else {
		tmp = b * (x * ((y * a) - (j * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (y2 * ((x * y0) - (t * y4)))
    if (x <= (-7.8d+158)) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (x <= (-1.5d+84)) then
        tmp = t_1
    else if (x <= (-1.25d-138)) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (x <= 1.3d-51) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (x <= 1.45d+16) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (x <= 7.2d+84) then
        tmp = (a * b) * (t * -z)
    else if (x <= 3.2d+140) then
        tmp = t_1
    else
        tmp = b * (x * ((y * a) - (j * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * ((x * y0) - (t * y4)));
	double tmp;
	if (x <= -7.8e+158) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (x <= -1.5e+84) {
		tmp = t_1;
	} else if (x <= -1.25e-138) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (x <= 1.3e-51) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (x <= 1.45e+16) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (x <= 7.2e+84) {
		tmp = (a * b) * (t * -z);
	} else if (x <= 3.2e+140) {
		tmp = t_1;
	} else {
		tmp = b * (x * ((y * a) - (j * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y2 * ((x * y0) - (t * y4)))
	tmp = 0
	if x <= -7.8e+158:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif x <= -1.5e+84:
		tmp = t_1
	elif x <= -1.25e-138:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif x <= 1.3e-51:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif x <= 1.45e+16:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif x <= 7.2e+84:
		tmp = (a * b) * (t * -z)
	elif x <= 3.2e+140:
		tmp = t_1
	else:
		tmp = b * (x * ((y * a) - (j * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))))
	tmp = 0.0
	if (x <= -7.8e+158)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (x <= -1.5e+84)
		tmp = t_1;
	elseif (x <= -1.25e-138)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (x <= 1.3e-51)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (x <= 1.45e+16)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (x <= 7.2e+84)
		tmp = Float64(Float64(a * b) * Float64(t * Float64(-z)));
	elseif (x <= 3.2e+140)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y2 * ((x * y0) - (t * y4)));
	tmp = 0.0;
	if (x <= -7.8e+158)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (x <= -1.5e+84)
		tmp = t_1;
	elseif (x <= -1.25e-138)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (x <= 1.3e-51)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (x <= 1.45e+16)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (x <= 7.2e+84)
		tmp = (a * b) * (t * -z);
	elseif (x <= 3.2e+140)
		tmp = t_1;
	else
		tmp = b * (x * ((y * a) - (j * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.8e+158], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.5e+84], t$95$1, If[LessEqual[x, -1.25e-138], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e-51], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.45e+16], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.2e+84], N[(N[(a * b), $MachinePrecision] * N[(t * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e+140], t$95$1, N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -7.8e158

   1. Initial program 16.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 16.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 70.6%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in j around inf 57.2%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   if -7.8e158 < x < -1.49999999999999998e84 or 7.1999999999999999e84 < x < 3.20000000000000011e140

   1. Initial program 26.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 47.4%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 53.6%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]

   if -1.49999999999999998e84 < x < -1.24999999999999997e-138

   1. Initial program 33.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 36.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 37.0%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -1.24999999999999997e-138 < x < 1.3e-51

   1. Initial program 25.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 32.1%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 34.9%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   if 1.3e-51 < x < 1.45e16

   1. Initial program 44.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 44.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 50.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y around inf 45.5%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 45.5%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 45.5%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 45.5%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

      4. *-commutative 45.5%

         \[\leadsto b \cdot \left(y \cdot \left(\color{blue}{x \cdot a} - k \cdot y4\right)\right) \]

      5. *-commutative 45.5%

         \[\leadsto b \cdot \left(y \cdot \left(x \cdot a - \color{blue}{y4 \cdot k}\right)\right) \]

   8. Simplified 45.5%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(x \cdot a - y4 \cdot k\right)\right)} \]

   if 1.45e16 < x < 7.1999999999999999e84

   1. Initial program 21.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 36.3%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in z around inf 31.4%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 31.4%

         \[\leadsto \color{blue}{-t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. associate-*r* 37.7%

         \[\leadsto -\color{blue}{\left(t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)} \]

   6. Simplified 37.7%

      \[\leadsto \color{blue}{-\left(t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)} \]

   7. Taylor expanded in a around inf 38.8%

      \[\leadsto -\color{blue}{a \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 45.3%

         \[\leadsto -\color{blue}{\left(a \cdot b\right) \cdot \left(t \cdot z\right)} \]

      2. *-commutative 45.3%

         \[\leadsto -\color{blue}{\left(b \cdot a\right)} \cdot \left(t \cdot z\right) \]

      3. *-commutative 45.3%

         \[\leadsto -\color{blue}{\left(t \cdot z\right) \cdot \left(b \cdot a\right)} \]

   9. Simplified 45.3%

      \[\leadsto -\color{blue}{\left(t \cdot z\right) \cdot \left(b \cdot a\right)} \]

   if 3.20000000000000011e140 < x

   1. Initial program 32.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.4%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 75.0%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in b around inf 68.4%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+158}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+84}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-138}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-51}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+16}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+84}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(t \cdot \left(-z\right)\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+140}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 31.6% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{if}\;y2 \leq -2.05 \cdot 10^{+181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -1.85 \cdot 10^{-212}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq -8 \cdot 10^{-265}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq -7.6 \cdot 10^{-302}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 3.1 \cdot 10^{-66}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 3.4 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y2 (- (* x y0) (* t y4))))))
   (if (<= y2 -2.05e+181)
     t_1
     (if (<= y2 -1.85e-212)
       (* b (* x (- (* y a) (* j y0))))
       (if (<= y2 -8e-265)
         (* i (* j (* x y1)))
         (if (<= y2 -7.6e-302)
           (* b (* j (* t y4)))
           (if (<= y2 3.1e-66)
             (* b (* y (- (* x a) (* k y4))))
             (if (<= y2 3.4e+81) (* b (* j (- (* t y4) (* 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 = c * (y2 * ((x * y0) - (t * y4)));
	double tmp;
	if (y2 <= -2.05e+181) {
		tmp = t_1;
	} else if (y2 <= -1.85e-212) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y2 <= -8e-265) {
		tmp = i * (j * (x * y1));
	} else if (y2 <= -7.6e-302) {
		tmp = b * (j * (t * y4));
	} else if (y2 <= 3.1e-66) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y2 <= 3.4e+81) {
		tmp = b * (j * ((t * y4) - (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 = c * (y2 * ((x * y0) - (t * y4)))
    if (y2 <= (-2.05d+181)) then
        tmp = t_1
    else if (y2 <= (-1.85d-212)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y2 <= (-8d-265)) then
        tmp = i * (j * (x * y1))
    else if (y2 <= (-7.6d-302)) then
        tmp = b * (j * (t * y4))
    else if (y2 <= 3.1d-66) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (y2 <= 3.4d+81) then
        tmp = b * (j * ((t * y4) - (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 = c * (y2 * ((x * y0) - (t * y4)));
	double tmp;
	if (y2 <= -2.05e+181) {
		tmp = t_1;
	} else if (y2 <= -1.85e-212) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y2 <= -8e-265) {
		tmp = i * (j * (x * y1));
	} else if (y2 <= -7.6e-302) {
		tmp = b * (j * (t * y4));
	} else if (y2 <= 3.1e-66) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (y2 <= 3.4e+81) {
		tmp = b * (j * ((t * y4) - (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 = c * (y2 * ((x * y0) - (t * y4)))
	tmp = 0
	if y2 <= -2.05e+181:
		tmp = t_1
	elif y2 <= -1.85e-212:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y2 <= -8e-265:
		tmp = i * (j * (x * y1))
	elif y2 <= -7.6e-302:
		tmp = b * (j * (t * y4))
	elif y2 <= 3.1e-66:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif y2 <= 3.4e+81:
		tmp = b * (j * ((t * y4) - (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(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))))
	tmp = 0.0
	if (y2 <= -2.05e+181)
		tmp = t_1;
	elseif (y2 <= -1.85e-212)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y2 <= -8e-265)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (y2 <= -7.6e-302)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	elseif (y2 <= 3.1e-66)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (y2 <= 3.4e+81)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y2 * ((x * y0) - (t * y4)));
	tmp = 0.0;
	if (y2 <= -2.05e+181)
		tmp = t_1;
	elseif (y2 <= -1.85e-212)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y2 <= -8e-265)
		tmp = i * (j * (x * y1));
	elseif (y2 <= -7.6e-302)
		tmp = b * (j * (t * y4));
	elseif (y2 <= 3.1e-66)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (y2 <= 3.4e+81)
		tmp = b * (j * ((t * y4) - (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[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -2.05e+181], t$95$1, If[LessEqual[y2, -1.85e-212], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -8e-265], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -7.6e-302], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.1e-66], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.4e+81], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y2 < -2.05000000000000009e181 or 3.40000000000000003e81 < y2

   1. Initial program 19.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 54.5%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 49.2%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]

   if -2.05000000000000009e181 < y2 < -1.84999999999999995e-212

   1. Initial program 25.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 43.6%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in b around inf 36.8%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]

   if -1.84999999999999995e-212 < y2 < -7.99999999999999988e-265

   1. Initial program 62.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 62.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 62.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   6. Taylor expanded in c around 0 87.6%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   7. Taylor expanded in x around inf 62.9%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 62.9%

         \[\leadsto -1 \cdot \color{blue}{\left(-i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\right)} \]

      2. distribute-rgt-neg-in 62.9%

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(-j \cdot \left(x \cdot y1\right)\right)\right)} \]

      3. distribute-rgt-neg-in 62.9%

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(j \cdot \left(-x \cdot y1\right)\right)}\right) \]

      4. *-commutative 62.9%

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot \left(-\color{blue}{y1 \cdot x}\right)\right)\right) \]

      5. distribute-rgt-neg-in 62.9%

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot \left(-x\right)\right)}\right)\right) \]

   9. Simplified 62.9%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot \left(y1 \cdot \left(-x\right)\right)\right)\right)} \]

   if -7.99999999999999988e-265 < y2 < -7.5999999999999999e-302

   1. Initial program 16.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 16.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 17.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 18.2%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 34.9%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

   if -7.5999999999999999e-302 < y2 < 3.0999999999999997e-66

   1. Initial program 44.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 44.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y around inf 45.6%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 45.6%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 45.6%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 45.6%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

      4. *-commutative 45.6%

         \[\leadsto b \cdot \left(y \cdot \left(\color{blue}{x \cdot a} - k \cdot y4\right)\right) \]

      5. *-commutative 45.6%

         \[\leadsto b \cdot \left(y \cdot \left(x \cdot a - \color{blue}{y4 \cdot k}\right)\right) \]

   8. Simplified 45.6%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(x \cdot a - y4 \cdot k\right)\right)} \]

   if 3.0999999999999997e-66 < y2 < 3.40000000000000003e81

   1. Initial program 28.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 44.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 57.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2.05 \cdot 10^{+181}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -1.85 \cdot 10^{-212}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq -8 \cdot 10^{-265}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq -7.6 \cdot 10^{-302}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 3.1 \cdot 10^{-66}:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 3.4 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.6% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ t_2 := t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{if}\;i \leq -7.5 \cdot 10^{+199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1500000:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq -1.3 \cdot 10^{-13}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq -9.5 \cdot 10^{-58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{-129}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{+56}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* x (* y (- (* a b) (* c i)))))
        (t_2 (* t (* y2 (- (* a y5) (* c y4))))))
   (if (<= i -7.5e+199)
     t_1
     (if (<= i -1500000.0)
       (* b (* y (- (* x a) (* k y4))))
       (if (<= i -1.3e-13)
         (* j (* x (- (* i y1) (* b y0))))
         (if (<= i -9.5e-58)
           t_2
           (if (<= i 1.1e-129)
             (* b (* x (- (* y a) (* j y0))))
             (if (<= i 5.2e+56) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (y * ((a * b) - (c * i)));
	double t_2 = t * (y2 * ((a * y5) - (c * y4)));
	double tmp;
	if (i <= -7.5e+199) {
		tmp = t_1;
	} else if (i <= -1500000.0) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (i <= -1.3e-13) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (i <= -9.5e-58) {
		tmp = t_2;
	} else if (i <= 1.1e-129) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (i <= 5.2e+56) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y * ((a * b) - (c * i)))
    t_2 = t * (y2 * ((a * y5) - (c * y4)))
    if (i <= (-7.5d+199)) then
        tmp = t_1
    else if (i <= (-1500000.0d0)) then
        tmp = b * (y * ((x * a) - (k * y4)))
    else if (i <= (-1.3d-13)) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (i <= (-9.5d-58)) then
        tmp = t_2
    else if (i <= 1.1d-129) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (i <= 5.2d+56) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (y * ((a * b) - (c * i)));
	double t_2 = t * (y2 * ((a * y5) - (c * y4)));
	double tmp;
	if (i <= -7.5e+199) {
		tmp = t_1;
	} else if (i <= -1500000.0) {
		tmp = b * (y * ((x * a) - (k * y4)));
	} else if (i <= -1.3e-13) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (i <= -9.5e-58) {
		tmp = t_2;
	} else if (i <= 1.1e-129) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (i <= 5.2e+56) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = x * (y * ((a * b) - (c * i)))
	t_2 = t * (y2 * ((a * y5) - (c * y4)))
	tmp = 0
	if i <= -7.5e+199:
		tmp = t_1
	elif i <= -1500000.0:
		tmp = b * (y * ((x * a) - (k * y4)))
	elif i <= -1.3e-13:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif i <= -9.5e-58:
		tmp = t_2
	elif i <= 1.1e-129:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif i <= 5.2e+56:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))))
	t_2 = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))))
	tmp = 0.0
	if (i <= -7.5e+199)
		tmp = t_1;
	elseif (i <= -1500000.0)
		tmp = Float64(b * Float64(y * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (i <= -1.3e-13)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (i <= -9.5e-58)
		tmp = t_2;
	elseif (i <= 1.1e-129)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (i <= 5.2e+56)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = x * (y * ((a * b) - (c * i)));
	t_2 = t * (y2 * ((a * y5) - (c * y4)));
	tmp = 0.0;
	if (i <= -7.5e+199)
		tmp = t_1;
	elseif (i <= -1500000.0)
		tmp = b * (y * ((x * a) - (k * y4)));
	elseif (i <= -1.3e-13)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (i <= -9.5e-58)
		tmp = t_2;
	elseif (i <= 1.1e-129)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (i <= 5.2e+56)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -7.5e+199], t$95$1, If[LessEqual[i, -1500000.0], N[(b * N[(y * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.3e-13], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -9.5e-58], t$95$2, If[LessEqual[i, 1.1e-129], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.2e+56], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -7.49999999999999977e199 or 5.20000000000000022e56 < i

   1. Initial program 14.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 15.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 47.7%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in y around inf 46.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

   if -7.49999999999999977e199 < i < -1.5e6

   1. Initial program 30.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.1%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 43.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y around inf 43.4%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(-1 \cdot \left(k \cdot y4\right) + a \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 43.4%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x + -1 \cdot \left(k \cdot y4\right)\right)}\right) \]

      2. mul-1-neg 43.4%

         \[\leadsto b \cdot \left(y \cdot \left(a \cdot x + \color{blue}{\left(-k \cdot y4\right)}\right)\right) \]

      3. unsub-neg 43.4%

         \[\leadsto b \cdot \left(y \cdot \color{blue}{\left(a \cdot x - k \cdot y4\right)}\right) \]

      4. *-commutative 43.4%

         \[\leadsto b \cdot \left(y \cdot \left(\color{blue}{x \cdot a} - k \cdot y4\right)\right) \]

      5. *-commutative 43.4%

         \[\leadsto b \cdot \left(y \cdot \left(x \cdot a - \color{blue}{y4 \cdot k}\right)\right) \]

   8. Simplified 43.4%

      \[\leadsto \color{blue}{b \cdot \left(y \cdot \left(x \cdot a - y4 \cdot k\right)\right)} \]

   if -1.5e6 < i < -1.3e-13

   1. Initial program 1.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 1.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 50.0%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in j around inf 66.8%

      \[\leadsto \color{blue}{j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)} \]

   if -1.3e-13 < i < -9.4999999999999994e-58 or 1.10000000000000001e-129 < i < 5.20000000000000022e56

   1. Initial program 32.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 42.9%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 50.1%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   if -9.4999999999999994e-58 < i < 1.10000000000000001e-129

   1. Initial program 37.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 50.2%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   6. Taylor expanded in b around inf 37.2%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -7.5 \cdot 10^{+199}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;i \leq -1500000:\\ \;\;\;\;b \cdot \left(y \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq -1.3 \cdot 10^{-13}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq -9.5 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{-129}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{+56}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 26.3% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{if}\;y2 \leq -1.7 \cdot 10^{+188}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -9 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -3.3 \cdot 10^{-247}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 2.4 \cdot 10^{+82} \lor \neg \left(y2 \leq 8 \cdot 10^{+221}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* j (- (* t y4) (* x y0))))))
   (if (<= y2 -1.7e+188)
     (* c (* y4 (* t (- y2))))
     (if (<= y2 -9e-110)
       t_1
       (if (<= y2 -3.3e-247)
         (* i (* j (* x y1)))
         (if (or (<= y2 2.4e+82) (not (<= y2 8e+221)))
           t_1
           (* t (* y5 (* a y2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (j * ((t * y4) - (x * y0)));
	double tmp;
	if (y2 <= -1.7e+188) {
		tmp = c * (y4 * (t * -y2));
	} else if (y2 <= -9e-110) {
		tmp = t_1;
	} else if (y2 <= -3.3e-247) {
		tmp = i * (j * (x * y1));
	} else if ((y2 <= 2.4e+82) || !(y2 <= 8e+221)) {
		tmp = t_1;
	} else {
		tmp = t * (y5 * (a * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (j * ((t * y4) - (x * y0)))
    if (y2 <= (-1.7d+188)) then
        tmp = c * (y4 * (t * -y2))
    else if (y2 <= (-9d-110)) then
        tmp = t_1
    else if (y2 <= (-3.3d-247)) then
        tmp = i * (j * (x * y1))
    else if ((y2 <= 2.4d+82) .or. (.not. (y2 <= 8d+221))) then
        tmp = t_1
    else
        tmp = t * (y5 * (a * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (j * ((t * y4) - (x * y0)));
	double tmp;
	if (y2 <= -1.7e+188) {
		tmp = c * (y4 * (t * -y2));
	} else if (y2 <= -9e-110) {
		tmp = t_1;
	} else if (y2 <= -3.3e-247) {
		tmp = i * (j * (x * y1));
	} else if ((y2 <= 2.4e+82) || !(y2 <= 8e+221)) {
		tmp = t_1;
	} else {
		tmp = t * (y5 * (a * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (j * ((t * y4) - (x * y0)))
	tmp = 0
	if y2 <= -1.7e+188:
		tmp = c * (y4 * (t * -y2))
	elif y2 <= -9e-110:
		tmp = t_1
	elif y2 <= -3.3e-247:
		tmp = i * (j * (x * y1))
	elif (y2 <= 2.4e+82) or not (y2 <= 8e+221):
		tmp = t_1
	else:
		tmp = t * (y5 * (a * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))))
	tmp = 0.0
	if (y2 <= -1.7e+188)
		tmp = Float64(c * Float64(y4 * Float64(t * Float64(-y2))));
	elseif (y2 <= -9e-110)
		tmp = t_1;
	elseif (y2 <= -3.3e-247)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif ((y2 <= 2.4e+82) || !(y2 <= 8e+221))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(y5 * Float64(a * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (j * ((t * y4) - (x * y0)));
	tmp = 0.0;
	if (y2 <= -1.7e+188)
		tmp = c * (y4 * (t * -y2));
	elseif (y2 <= -9e-110)
		tmp = t_1;
	elseif (y2 <= -3.3e-247)
		tmp = i * (j * (x * y1));
	elseif ((y2 <= 2.4e+82) || ~((y2 <= 8e+221)))
		tmp = t_1;
	else
		tmp = t * (y5 * (a * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.7e+188], N[(c * N[(y4 * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -9e-110], t$95$1, If[LessEqual[y2, -3.3e-247], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y2, 2.4e+82], N[Not[LessEqual[y2, 8e+221]], $MachinePrecision]], t$95$1, N[(t * N[(y5 * N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -1.69999999999999998e188

   1. Initial program 15.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 59.5%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 56.7%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   5. Taylor expanded in a around 0 52.6%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 52.6%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

      2. neg-mul-1 52.6%

         \[\leadsto \color{blue}{\left(-c\right)} \cdot \left(t \cdot \left(y2 \cdot y4\right)\right) \]

      3. associate-*r* 59.6%

         \[\leadsto \left(-c\right) \cdot \color{blue}{\left(\left(t \cdot y2\right) \cdot y4\right)} \]

   7. Simplified 59.6%

      \[\leadsto \color{blue}{\left(-c\right) \cdot \left(\left(t \cdot y2\right) \cdot y4\right)} \]

   if -1.69999999999999998e188 < y2 < -9.0000000000000002e-110 or -3.29999999999999971e-247 < y2 < 2.39999999999999998e82 or 8.0000000000000004e221 < y2

   1. Initial program 29.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 38.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 36.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if -9.0000000000000002e-110 < y2 < -3.29999999999999971e-247

   1. Initial program 32.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.1%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 48.4%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   6. Taylor expanded in c around 0 52.4%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   7. Taylor expanded in x around inf 40.6%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 40.6%

         \[\leadsto -1 \cdot \color{blue}{\left(-i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\right)} \]

      2. distribute-rgt-neg-in 40.6%

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(-j \cdot \left(x \cdot y1\right)\right)\right)} \]

      3. distribute-rgt-neg-in 40.6%

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(j \cdot \left(-x \cdot y1\right)\right)}\right) \]

      4. *-commutative 40.6%

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot \left(-\color{blue}{y1 \cdot x}\right)\right)\right) \]

      5. distribute-rgt-neg-in 40.6%

         \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot \left(-x\right)\right)}\right)\right) \]

   9. Simplified 40.6%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(j \cdot \left(y1 \cdot \left(-x\right)\right)\right)\right)} \]

   if 2.39999999999999998e82 < y2 < 8.0000000000000004e221

   1. Initial program 24.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 49.1%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 37.4%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   5. Taylor expanded in a around inf 31.3%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(y2 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 40.0%

         \[\leadsto t \cdot \color{blue}{\left(\left(a \cdot y2\right) \cdot y5\right)} \]

      2. *-commutative 40.0%

         \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(a \cdot y2\right)\right)} \]

   7. Simplified 40.0%

      \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(a \cdot y2\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.7 \cdot 10^{+188}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -9 \cdot 10^{-110}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq -3.3 \cdot 10^{-247}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 2.4 \cdot 10^{+82} \lor \neg \left(y2 \leq 8 \cdot 10^{+221}\right):\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 22.1% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{if}\;y4 \leq -6.2 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq 2.1 \cdot 10^{-142}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 7.2 \cdot 10^{-59}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq 1.9 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq 3.4 \cdot 10^{+146}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* t (* j y4)))))
   (if (<= y4 -6.2e+28)
     t_1
     (if (<= y4 2.1e-142)
       (* a (* t (* y2 y5)))
       (if (<= y4 7.2e-59)
         (* c (* i (* z t)))
         (if (<= y4 1.9e+79)
           t_1
           (if (<= y4 3.4e+146)
             (* c (* x (* y0 y2)))
             (* b (* j (* t y4))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (t * (j * y4));
	double tmp;
	if (y4 <= -6.2e+28) {
		tmp = t_1;
	} else if (y4 <= 2.1e-142) {
		tmp = a * (t * (y2 * y5));
	} else if (y4 <= 7.2e-59) {
		tmp = c * (i * (z * t));
	} else if (y4 <= 1.9e+79) {
		tmp = t_1;
	} else if (y4 <= 3.4e+146) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = b * (j * (t * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t * (j * y4))
    if (y4 <= (-6.2d+28)) then
        tmp = t_1
    else if (y4 <= 2.1d-142) then
        tmp = a * (t * (y2 * y5))
    else if (y4 <= 7.2d-59) then
        tmp = c * (i * (z * t))
    else if (y4 <= 1.9d+79) then
        tmp = t_1
    else if (y4 <= 3.4d+146) then
        tmp = c * (x * (y0 * y2))
    else
        tmp = b * (j * (t * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (t * (j * y4));
	double tmp;
	if (y4 <= -6.2e+28) {
		tmp = t_1;
	} else if (y4 <= 2.1e-142) {
		tmp = a * (t * (y2 * y5));
	} else if (y4 <= 7.2e-59) {
		tmp = c * (i * (z * t));
	} else if (y4 <= 1.9e+79) {
		tmp = t_1;
	} else if (y4 <= 3.4e+146) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = b * (j * (t * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (t * (j * y4))
	tmp = 0
	if y4 <= -6.2e+28:
		tmp = t_1
	elif y4 <= 2.1e-142:
		tmp = a * (t * (y2 * y5))
	elif y4 <= 7.2e-59:
		tmp = c * (i * (z * t))
	elif y4 <= 1.9e+79:
		tmp = t_1
	elif y4 <= 3.4e+146:
		tmp = c * (x * (y0 * y2))
	else:
		tmp = b * (j * (t * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(t * Float64(j * y4)))
	tmp = 0.0
	if (y4 <= -6.2e+28)
		tmp = t_1;
	elseif (y4 <= 2.1e-142)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (y4 <= 7.2e-59)
		tmp = Float64(c * Float64(i * Float64(z * t)));
	elseif (y4 <= 1.9e+79)
		tmp = t_1;
	elseif (y4 <= 3.4e+146)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	else
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (t * (j * y4));
	tmp = 0.0;
	if (y4 <= -6.2e+28)
		tmp = t_1;
	elseif (y4 <= 2.1e-142)
		tmp = a * (t * (y2 * y5));
	elseif (y4 <= 7.2e-59)
		tmp = c * (i * (z * t));
	elseif (y4 <= 1.9e+79)
		tmp = t_1;
	elseif (y4 <= 3.4e+146)
		tmp = c * (x * (y0 * y2));
	else
		tmp = b * (j * (t * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -6.2e+28], t$95$1, If[LessEqual[y4, 2.1e-142], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 7.2e-59], N[(c * N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.9e+79], t$95$1, If[LessEqual[y4, 3.4e+146], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y4 < -6.2000000000000001e28 or 7.20000000000000001e-59 < y4 < 1.9000000000000001e79

   1. Initial program 22.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 32.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 34.7%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 31.8%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 31.8%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

      2. associate-*r* 32.8%

         \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot y4\right) \cdot t\right)} \]

   9. Simplified 32.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(j \cdot y4\right) \cdot t\right)} \]

   if -6.2000000000000001e28 < y4 < 2.0999999999999999e-142

   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 y2 around inf 34.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 26.3%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   5. Taylor expanded in a around inf 23.1%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]

   if 2.0999999999999999e-142 < y4 < 7.20000000000000001e-59

   1. Initial program 10.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 30.6%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in i around inf 40.8%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]

   5. Taylor expanded in j around 0 41.1%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]

   if 1.9000000000000001e79 < y4 < 3.39999999999999991e146

   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 y2 around inf 47.5%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in y0 around inf 48.0%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 48.0%

         \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(c \cdot x + -1 \cdot \left(k \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 48.0%

         \[\leadsto y0 \cdot \left(y2 \cdot \left(c \cdot x + \color{blue}{\left(-k \cdot y5\right)}\right)\right) \]

      3. unsub-neg 48.0%

         \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(c \cdot x - k \cdot y5\right)}\right) \]

      4. *-commutative 48.0%

         \[\leadsto y0 \cdot \left(y2 \cdot \left(\color{blue}{x \cdot c} - k \cdot y5\right)\right) \]

      5. *-commutative 48.0%

         \[\leadsto y0 \cdot \left(y2 \cdot \left(x \cdot c - \color{blue}{y5 \cdot k}\right)\right) \]

   6. Simplified 48.0%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(x \cdot c - y5 \cdot k\right)\right)} \]

   7. Taylor expanded in x around inf 32.8%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if 3.39999999999999991e146 < y4

   1. Initial program 29.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.4%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 50.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 59.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 50.6%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 32.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -6.2 \cdot 10^{+28}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 2.1 \cdot 10^{-142}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 7.2 \cdot 10^{-59}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;y4 \leq 1.9 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 3.4 \cdot 10^{+146}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 21.8% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -1.15 \cdot 10^{+155}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -2.5 \cdot 10^{+18}:\\ \;\;\;\;i \cdot \left(t \cdot \left(j \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -1.25 \cdot 10^{-125}:\\ \;\;\;\;k \cdot \left(z \cdot \left(i \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 1.85 \cdot 10^{-233}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 2 \cdot 10^{+160}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -1.15e+155)
   (* y0 (* y2 (* k (- y5))))
   (if (<= y5 -2.5e+18)
     (* i (* t (* j (- y5))))
     (if (<= y5 -1.25e-125)
       (* k (* z (* i (- y1))))
       (if (<= y5 1.85e-233)
         (* c (* y4 (* t (- y2))))
         (if (<= y5 2e+160) (* j (* b (* t y4))) (* t (* y2 (* a y5)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -1.15e+155) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (y5 <= -2.5e+18) {
		tmp = i * (t * (j * -y5));
	} else if (y5 <= -1.25e-125) {
		tmp = k * (z * (i * -y1));
	} else if (y5 <= 1.85e-233) {
		tmp = c * (y4 * (t * -y2));
	} else if (y5 <= 2e+160) {
		tmp = j * (b * (t * y4));
	} else {
		tmp = t * (y2 * (a * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y5 <= (-1.15d+155)) then
        tmp = y0 * (y2 * (k * -y5))
    else if (y5 <= (-2.5d+18)) then
        tmp = i * (t * (j * -y5))
    else if (y5 <= (-1.25d-125)) then
        tmp = k * (z * (i * -y1))
    else if (y5 <= 1.85d-233) then
        tmp = c * (y4 * (t * -y2))
    else if (y5 <= 2d+160) then
        tmp = j * (b * (t * y4))
    else
        tmp = t * (y2 * (a * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -1.15e+155) {
		tmp = y0 * (y2 * (k * -y5));
	} else if (y5 <= -2.5e+18) {
		tmp = i * (t * (j * -y5));
	} else if (y5 <= -1.25e-125) {
		tmp = k * (z * (i * -y1));
	} else if (y5 <= 1.85e-233) {
		tmp = c * (y4 * (t * -y2));
	} else if (y5 <= 2e+160) {
		tmp = j * (b * (t * y4));
	} else {
		tmp = t * (y2 * (a * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y5 <= -1.15e+155:
		tmp = y0 * (y2 * (k * -y5))
	elif y5 <= -2.5e+18:
		tmp = i * (t * (j * -y5))
	elif y5 <= -1.25e-125:
		tmp = k * (z * (i * -y1))
	elif y5 <= 1.85e-233:
		tmp = c * (y4 * (t * -y2))
	elif y5 <= 2e+160:
		tmp = j * (b * (t * y4))
	else:
		tmp = t * (y2 * (a * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -1.15e+155)
		tmp = Float64(y0 * Float64(y2 * Float64(k * Float64(-y5))));
	elseif (y5 <= -2.5e+18)
		tmp = Float64(i * Float64(t * Float64(j * Float64(-y5))));
	elseif (y5 <= -1.25e-125)
		tmp = Float64(k * Float64(z * Float64(i * Float64(-y1))));
	elseif (y5 <= 1.85e-233)
		tmp = Float64(c * Float64(y4 * Float64(t * Float64(-y2))));
	elseif (y5 <= 2e+160)
		tmp = Float64(j * Float64(b * Float64(t * y4)));
	else
		tmp = Float64(t * Float64(y2 * Float64(a * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y5 <= -1.15e+155)
		tmp = y0 * (y2 * (k * -y5));
	elseif (y5 <= -2.5e+18)
		tmp = i * (t * (j * -y5));
	elseif (y5 <= -1.25e-125)
		tmp = k * (z * (i * -y1));
	elseif (y5 <= 1.85e-233)
		tmp = c * (y4 * (t * -y2));
	elseif (y5 <= 2e+160)
		tmp = j * (b * (t * y4));
	else
		tmp = t * (y2 * (a * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y5, -1.15e+155], N[(y0 * N[(y2 * N[(k * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2.5e+18], N[(i * N[(t * N[(j * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.25e-125], N[(k * N[(z * N[(i * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.85e-233], N[(c * N[(y4 * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2e+160], N[(j * N[(b * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y2 * N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y5 < -1.14999999999999999e155

   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 y2 around inf 37.4%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in y0 around inf 57.6%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 57.6%

         \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(c \cdot x + -1 \cdot \left(k \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 57.6%

         \[\leadsto y0 \cdot \left(y2 \cdot \left(c \cdot x + \color{blue}{\left(-k \cdot y5\right)}\right)\right) \]

      3. unsub-neg 57.6%

         \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(c \cdot x - k \cdot y5\right)}\right) \]

      4. *-commutative 57.6%

         \[\leadsto y0 \cdot \left(y2 \cdot \left(\color{blue}{x \cdot c} - k \cdot y5\right)\right) \]

      5. *-commutative 57.6%

         \[\leadsto y0 \cdot \left(y2 \cdot \left(x \cdot c - \color{blue}{y5 \cdot k}\right)\right) \]

   6. Simplified 57.6%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(x \cdot c - y5 \cdot k\right)\right)} \]

   7. Taylor expanded in x around 0 47.8%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 47.8%

         \[\leadsto \color{blue}{\left(-1 \cdot k\right) \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right)} \]

      2. neg-mul-1 47.8%

         \[\leadsto \color{blue}{\left(-k\right)} \cdot \left(y0 \cdot \left(y2 \cdot y5\right)\right) \]

      3. *-commutative 47.8%

         \[\leadsto \left(-k\right) \cdot \color{blue}{\left(\left(y2 \cdot y5\right) \cdot y0\right)} \]

      4. associate-*r* 47.8%

         \[\leadsto \color{blue}{\left(\left(-k\right) \cdot \left(y2 \cdot y5\right)\right) \cdot y0} \]

      5. *-commutative 47.8%

         \[\leadsto \left(\left(-k\right) \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \cdot y0 \]

      6. associate-*r* 57.5%

         \[\leadsto \color{blue}{\left(\left(\left(-k\right) \cdot y5\right) \cdot y2\right)} \cdot y0 \]

      7. distribute-lft-neg-in 57.5%

         \[\leadsto \left(\color{blue}{\left(-k \cdot y5\right)} \cdot y2\right) \cdot y0 \]

      8. *-commutative 57.5%

         \[\leadsto \left(\left(-\color{blue}{y5 \cdot k}\right) \cdot y2\right) \cdot y0 \]

      9. distribute-lft-neg-in 57.5%

         \[\leadsto \left(\color{blue}{\left(\left(-y5\right) \cdot k\right)} \cdot y2\right) \cdot y0 \]

      10. *-commutative 57.5%

          \[\leadsto \left(\color{blue}{\left(k \cdot \left(-y5\right)\right)} \cdot y2\right) \cdot y0 \]

   9. Simplified 57.5%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(-y5\right)\right) \cdot y2\right) \cdot y0} \]

   if -1.14999999999999999e155 < y5 < -2.5e18

   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 t around inf 35.5%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in i around inf 35.9%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]

   5. Taylor expanded in j around inf 44.7%

      \[\leadsto i \cdot \left(t \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y5\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 44.7%

         \[\leadsto i \cdot \left(t \cdot \color{blue}{\left(-j \cdot y5\right)}\right) \]

      2. *-commutative 44.7%

         \[\leadsto i \cdot \left(t \cdot \left(-\color{blue}{y5 \cdot j}\right)\right) \]

      3. distribute-lft-neg-in 44.7%

         \[\leadsto i \cdot \left(t \cdot \color{blue}{\left(\left(-y5\right) \cdot j\right)}\right) \]

   7. Simplified 44.7%

      \[\leadsto i \cdot \left(t \cdot \color{blue}{\left(\left(-y5\right) \cdot j\right)}\right) \]

   if -2.5e18 < y5 < -1.24999999999999992e-125

   1. Initial program 34.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 48.9%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   6. Taylor expanded in c around 0 52.8%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   7. Taylor expanded in z around inf 35.7%

      \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(k \cdot \left(y1 \cdot z\right)\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 35.7%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(k \cdot \left(y1 \cdot z\right)\right) \cdot i\right)} \]

      2. associate-*l* 32.6%

         \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(\left(y1 \cdot z\right) \cdot i\right)\right)} \]

      3. *-commutative 32.6%

         \[\leadsto -1 \cdot \left(k \cdot \left(\color{blue}{\left(z \cdot y1\right)} \cdot i\right)\right) \]

      4. associate-*l* 35.9%

         \[\leadsto -1 \cdot \left(k \cdot \color{blue}{\left(z \cdot \left(y1 \cdot i\right)\right)}\right) \]

      5. *-commutative 35.9%

         \[\leadsto -1 \cdot \left(k \cdot \left(z \cdot \color{blue}{\left(i \cdot y1\right)}\right)\right) \]

   9. Simplified 35.9%

      \[\leadsto -1 \cdot \color{blue}{\left(k \cdot \left(z \cdot \left(i \cdot y1\right)\right)\right)} \]

   if -1.24999999999999992e-125 < y5 < 1.8499999999999999e-233

   1. Initial program 28.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 42.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 22.2%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   5. Taylor expanded in a around 0 25.8%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 25.8%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

      2. neg-mul-1 25.8%

         \[\leadsto \color{blue}{\left(-c\right)} \cdot \left(t \cdot \left(y2 \cdot y4\right)\right) \]

      3. associate-*r* 29.0%

         \[\leadsto \left(-c\right) \cdot \color{blue}{\left(\left(t \cdot y2\right) \cdot y4\right)} \]

   7. Simplified 29.0%

      \[\leadsto \color{blue}{\left(-c\right) \cdot \left(\left(t \cdot y2\right) \cdot y4\right)} \]

   if 1.8499999999999999e-233 < y5 < 2.00000000000000001e160

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 38.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 40.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 31.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. expm1-log1p-u 17.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\right)\right)} \]

      2. expm1-udef 17.8%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\right)} - 1} \]

      3. associate-*r* 15.3%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(b \cdot j\right) \cdot \left(t \cdot y4\right)}\right)} - 1 \]

   9. Applied egg-rr 15.3%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(b \cdot j\right) \cdot \left(t \cdot y4\right)\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 15.3%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(b \cdot j\right) \cdot \left(t \cdot y4\right)\right)\right)} \]

       2. expm1-log1p 27.4%

          \[\leadsto \color{blue}{\left(b \cdot j\right) \cdot \left(t \cdot y4\right)} \]

       3. *-commutative 27.4%

          \[\leadsto \color{blue}{\left(j \cdot b\right)} \cdot \left(t \cdot y4\right) \]

       4. associate-*l* 35.0%

          \[\leadsto \color{blue}{j \cdot \left(b \cdot \left(t \cdot y4\right)\right)} \]

   11. Simplified 35.0%

       \[\leadsto \color{blue}{j \cdot \left(b \cdot \left(t \cdot y4\right)\right)} \]

   if 2.00000000000000001e160 < y5

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 33.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 39.9%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   5. Taylor expanded in a around inf 37.5%

      \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(a \cdot y5\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative 37.5%

         \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot a\right)}\right) \]

   7. Simplified 37.5%

      \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(y5 \cdot a\right)}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.15 \cdot 10^{+155}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(k \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -2.5 \cdot 10^{+18}:\\ \;\;\;\;i \cdot \left(t \cdot \left(j \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -1.25 \cdot 10^{-125}:\\ \;\;\;\;k \cdot \left(z \cdot \left(i \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 1.85 \cdot 10^{-233}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 2 \cdot 10^{+160}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 22.1% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-54}:\\ \;\;\;\;a \cdot \left(b \cdot \left(t \cdot \left(-z\right)\right)\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-242}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(c \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+66}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t \cdot \left(a \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -6e+119)
   (* t (* y5 (* a y2)))
   (if (<= a -1.4e-54)
     (* a (* b (* t (- z))))
     (if (<= a -3e-242)
       (* t (* y2 (* c (- y4))))
       (if (<= a 5.5e+66) (* j (* b (* t y4))) (* z (- (* t (* a b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -6e+119) {
		tmp = t * (y5 * (a * y2));
	} else if (a <= -1.4e-54) {
		tmp = a * (b * (t * -z));
	} else if (a <= -3e-242) {
		tmp = t * (y2 * (c * -y4));
	} else if (a <= 5.5e+66) {
		tmp = j * (b * (t * y4));
	} else {
		tmp = z * -(t * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (a <= (-6d+119)) then
        tmp = t * (y5 * (a * y2))
    else if (a <= (-1.4d-54)) then
        tmp = a * (b * (t * -z))
    else if (a <= (-3d-242)) then
        tmp = t * (y2 * (c * -y4))
    else if (a <= 5.5d+66) then
        tmp = j * (b * (t * y4))
    else
        tmp = z * -(t * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -6e+119) {
		tmp = t * (y5 * (a * y2));
	} else if (a <= -1.4e-54) {
		tmp = a * (b * (t * -z));
	} else if (a <= -3e-242) {
		tmp = t * (y2 * (c * -y4));
	} else if (a <= 5.5e+66) {
		tmp = j * (b * (t * y4));
	} else {
		tmp = z * -(t * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if a <= -6e+119:
		tmp = t * (y5 * (a * y2))
	elif a <= -1.4e-54:
		tmp = a * (b * (t * -z))
	elif a <= -3e-242:
		tmp = t * (y2 * (c * -y4))
	elif a <= 5.5e+66:
		tmp = j * (b * (t * y4))
	else:
		tmp = z * -(t * (a * b))
	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 (a <= -6e+119)
		tmp = Float64(t * Float64(y5 * Float64(a * y2)));
	elseif (a <= -1.4e-54)
		tmp = Float64(a * Float64(b * Float64(t * Float64(-z))));
	elseif (a <= -3e-242)
		tmp = Float64(t * Float64(y2 * Float64(c * Float64(-y4))));
	elseif (a <= 5.5e+66)
		tmp = Float64(j * Float64(b * Float64(t * y4)));
	else
		tmp = Float64(z * Float64(-Float64(t * Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (a <= -6e+119)
		tmp = t * (y5 * (a * y2));
	elseif (a <= -1.4e-54)
		tmp = a * (b * (t * -z));
	elseif (a <= -3e-242)
		tmp = t * (y2 * (c * -y4));
	elseif (a <= 5.5e+66)
		tmp = j * (b * (t * y4));
	else
		tmp = z * -(t * (a * b));
	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[a, -6e+119], N[(t * N[(y5 * N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.4e-54], N[(a * N[(b * N[(t * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3e-242], N[(t * N[(y2 * N[(c * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e+66], N[(j * N[(b * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * (-N[(t * N[(a * b), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -6.00000000000000002e119

   1. Initial program 31.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 41.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 41.6%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   5. Taylor expanded in a around inf 31.8%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(y2 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 40.4%

         \[\leadsto t \cdot \color{blue}{\left(\left(a \cdot y2\right) \cdot y5\right)} \]

      2. *-commutative 40.4%

         \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(a \cdot y2\right)\right)} \]

   7. Simplified 40.4%

      \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(a \cdot y2\right)\right)} \]

   if -6.00000000000000002e119 < a < -1.4000000000000001e-54

   1. Initial program 16.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 29.6%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in z around inf 37.1%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 37.1%

         \[\leadsto \color{blue}{-t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. associate-*r* 39.7%

         \[\leadsto -\color{blue}{\left(t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)} \]

   6. Simplified 39.7%

      \[\leadsto \color{blue}{-\left(t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)} \]

   7. Taylor expanded in a around inf 42.8%

      \[\leadsto -\color{blue}{a \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 42.8%

         \[\leadsto -a \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot b\right)} \]

   9. Simplified 42.8%

      \[\leadsto -\color{blue}{a \cdot \left(\left(t \cdot z\right) \cdot b\right)} \]

   if -1.4000000000000001e-54 < a < -3e-242

   1. Initial program 29.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 37.7%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 38.3%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   5. Taylor expanded in a around 0 33.5%

      \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot y4\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 33.5%

         \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(-c \cdot y4\right)}\right) \]

      2. distribute-lft-neg-out 33.5%

         \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(\left(-c\right) \cdot y4\right)}\right) \]

      3. *-commutative 33.5%

         \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot \left(-c\right)\right)}\right) \]

   7. Simplified 33.5%

      \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(y4 \cdot \left(-c\right)\right)}\right) \]

   if -3e-242 < a < 5.5e66

   1. Initial program 31.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.4%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 42.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 30.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. expm1-log1p-u 13.5%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\right)\right)} \]

      2. expm1-udef 13.4%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\right)} - 1} \]

      3. associate-*r* 11.2%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(b \cdot j\right) \cdot \left(t \cdot y4\right)}\right)} - 1 \]

   9. Applied egg-rr 11.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(b \cdot j\right) \cdot \left(t \cdot y4\right)\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 11.3%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(b \cdot j\right) \cdot \left(t \cdot y4\right)\right)\right)} \]

       2. expm1-log1p 28.1%

          \[\leadsto \color{blue}{\left(b \cdot j\right) \cdot \left(t \cdot y4\right)} \]

       3. *-commutative 28.1%

          \[\leadsto \color{blue}{\left(j \cdot b\right)} \cdot \left(t \cdot y4\right) \]

       4. associate-*l* 32.4%

          \[\leadsto \color{blue}{j \cdot \left(b \cdot \left(t \cdot y4\right)\right)} \]

   11. Simplified 32.4%

       \[\leadsto \color{blue}{j \cdot \left(b \cdot \left(t \cdot y4\right)\right)} \]

   if 5.5e66 < a

   1. Initial program 22.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 35.0%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in z around inf 33.1%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 33.1%

         \[\leadsto \color{blue}{-t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. associate-*r* 29.4%

         \[\leadsto -\color{blue}{\left(t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)} \]

   6. Simplified 29.4%

      \[\leadsto \color{blue}{-\left(t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)} \]

   7. Taylor expanded in a around inf 22.3%

      \[\leadsto -\color{blue}{a \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 26.0%

         \[\leadsto -\color{blue}{\left(a \cdot b\right) \cdot \left(t \cdot z\right)} \]

      2. *-commutative 26.0%

         \[\leadsto -\color{blue}{\left(b \cdot a\right)} \cdot \left(t \cdot z\right) \]

      3. *-commutative 26.0%

         \[\leadsto -\color{blue}{\left(t \cdot z\right) \cdot \left(b \cdot a\right)} \]

   9. Simplified 26.0%

      \[\leadsto -\color{blue}{\left(t \cdot z\right) \cdot \left(b \cdot a\right)} \]

   10. Taylor expanded in t around 0 22.3%

       \[\leadsto -\color{blue}{a \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 22.3%

          \[\leadsto -\color{blue}{\left(b \cdot \left(t \cdot z\right)\right) \cdot a} \]

       2. *-commutative 22.3%

          \[\leadsto -\color{blue}{\left(\left(t \cdot z\right) \cdot b\right)} \cdot a \]

       3. associate-*r* 26.0%

          \[\leadsto -\color{blue}{\left(t \cdot z\right) \cdot \left(b \cdot a\right)} \]

       4. associate-*r* 31.4%

          \[\leadsto -\color{blue}{t \cdot \left(z \cdot \left(b \cdot a\right)\right)} \]

       5. *-commutative 31.4%

          \[\leadsto -\color{blue}{\left(z \cdot \left(b \cdot a\right)\right) \cdot t} \]

       6. associate-*l* 33.4%

          \[\leadsto -\color{blue}{z \cdot \left(\left(b \cdot a\right) \cdot t\right)} \]

       7. *-commutative 33.4%

          \[\leadsto -z \cdot \left(\color{blue}{\left(a \cdot b\right)} \cdot t\right) \]

   12. Simplified 33.4%

       \[\leadsto -\color{blue}{z \cdot \left(\left(a \cdot b\right) \cdot t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 35.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-54}:\\ \;\;\;\;a \cdot \left(b \cdot \left(t \cdot \left(-z\right)\right)\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-242}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(c \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+66}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t \cdot \left(a \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 21.6% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{if}\;j \leq -4 \cdot 10^{+141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{-79}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq -2.15 \cdot 10^{-107}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-113}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* t (* j y4)))))
   (if (<= j -4e+141)
     t_1
     (if (<= j -4.2e-79)
       (* c (* x (* y0 y2)))
       (if (<= j -2.15e-107)
         (* b (* j (* t y4)))
         (if (<= j 2.3e-113) (* c (* z (* t i))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (t * (j * y4));
	double tmp;
	if (j <= -4e+141) {
		tmp = t_1;
	} else if (j <= -4.2e-79) {
		tmp = c * (x * (y0 * y2));
	} else if (j <= -2.15e-107) {
		tmp = b * (j * (t * y4));
	} else if (j <= 2.3e-113) {
		tmp = c * (z * (t * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t * (j * y4))
    if (j <= (-4d+141)) then
        tmp = t_1
    else if (j <= (-4.2d-79)) then
        tmp = c * (x * (y0 * y2))
    else if (j <= (-2.15d-107)) then
        tmp = b * (j * (t * y4))
    else if (j <= 2.3d-113) then
        tmp = c * (z * (t * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (t * (j * y4));
	double tmp;
	if (j <= -4e+141) {
		tmp = t_1;
	} else if (j <= -4.2e-79) {
		tmp = c * (x * (y0 * y2));
	} else if (j <= -2.15e-107) {
		tmp = b * (j * (t * y4));
	} else if (j <= 2.3e-113) {
		tmp = c * (z * (t * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (t * (j * y4))
	tmp = 0
	if j <= -4e+141:
		tmp = t_1
	elif j <= -4.2e-79:
		tmp = c * (x * (y0 * y2))
	elif j <= -2.15e-107:
		tmp = b * (j * (t * y4))
	elif j <= 2.3e-113:
		tmp = c * (z * (t * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(t * Float64(j * y4)))
	tmp = 0.0
	if (j <= -4e+141)
		tmp = t_1;
	elseif (j <= -4.2e-79)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (j <= -2.15e-107)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	elseif (j <= 2.3e-113)
		tmp = Float64(c * Float64(z * Float64(t * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (t * (j * y4));
	tmp = 0.0;
	if (j <= -4e+141)
		tmp = t_1;
	elseif (j <= -4.2e-79)
		tmp = c * (x * (y0 * y2));
	elseif (j <= -2.15e-107)
		tmp = b * (j * (t * y4));
	elseif (j <= 2.3e-113)
		tmp = c * (z * (t * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4e+141], t$95$1, If[LessEqual[j, -4.2e-79], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.15e-107], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.3e-113], N[(c * N[(z * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -4.00000000000000007e141 or 2.30000000000000008e-113 < j

   1. Initial program 23.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 42.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 32.5%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 32.5%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

      2. associate-*r* 33.9%

         \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot y4\right) \cdot t\right)} \]

   9. Simplified 33.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(j \cdot y4\right) \cdot t\right)} \]

   if -4.00000000000000007e141 < j < -4.1999999999999999e-79

   1. Initial program 24.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 35.6%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in y0 around inf 33.5%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 33.5%

         \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(c \cdot x + -1 \cdot \left(k \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 33.5%

         \[\leadsto y0 \cdot \left(y2 \cdot \left(c \cdot x + \color{blue}{\left(-k \cdot y5\right)}\right)\right) \]

      3. unsub-neg 33.5%

         \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(c \cdot x - k \cdot y5\right)}\right) \]

      4. *-commutative 33.5%

         \[\leadsto y0 \cdot \left(y2 \cdot \left(\color{blue}{x \cdot c} - k \cdot y5\right)\right) \]

      5. *-commutative 33.5%

         \[\leadsto y0 \cdot \left(y2 \cdot \left(x \cdot c - \color{blue}{y5 \cdot k}\right)\right) \]

   6. Simplified 33.5%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(x \cdot c - y5 \cdot k\right)\right)} \]

   7. Taylor expanded in x around inf 30.9%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]

   if -4.1999999999999999e-79 < j < -2.1499999999999999e-107

   1. Initial program 40.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 40.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 41.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 21.5%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 21.4%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

   if -2.1499999999999999e-107 < j < 2.30000000000000008e-113

   1. Initial program 33.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 39.4%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in i around inf 28.4%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]

   5. Taylor expanded in j around 0 25.0%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 28.4%

         \[\leadsto c \cdot \color{blue}{\left(\left(i \cdot t\right) \cdot z\right)} \]

      2. *-commutative 28.4%

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(i \cdot t\right)\right)} \]

   7. Simplified 28.4%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(i \cdot t\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 31.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4 \cdot 10^{+141}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{-79}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq -2.15 \cdot 10^{-107}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-113}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 21.7% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+120}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(b \cdot \left(t \cdot \left(-z\right)\right)\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+66}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t \cdot \left(a \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -3.8e+120)
   (* t (* y5 (* a y2)))
   (if (<= a -4.2e-57)
     (* a (* b (* t (- z))))
     (if (<= a 2.6e+66) (* j (* b (* t y4))) (* z (- (* t (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -3.8e+120) {
		tmp = t * (y5 * (a * y2));
	} else if (a <= -4.2e-57) {
		tmp = a * (b * (t * -z));
	} else if (a <= 2.6e+66) {
		tmp = j * (b * (t * y4));
	} else {
		tmp = z * -(t * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (a <= (-3.8d+120)) then
        tmp = t * (y5 * (a * y2))
    else if (a <= (-4.2d-57)) then
        tmp = a * (b * (t * -z))
    else if (a <= 2.6d+66) then
        tmp = j * (b * (t * y4))
    else
        tmp = z * -(t * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (a <= -3.8e+120) {
		tmp = t * (y5 * (a * y2));
	} else if (a <= -4.2e-57) {
		tmp = a * (b * (t * -z));
	} else if (a <= 2.6e+66) {
		tmp = j * (b * (t * y4));
	} else {
		tmp = z * -(t * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if a <= -3.8e+120:
		tmp = t * (y5 * (a * y2))
	elif a <= -4.2e-57:
		tmp = a * (b * (t * -z))
	elif a <= 2.6e+66:
		tmp = j * (b * (t * y4))
	else:
		tmp = z * -(t * (a * b))
	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 (a <= -3.8e+120)
		tmp = Float64(t * Float64(y5 * Float64(a * y2)));
	elseif (a <= -4.2e-57)
		tmp = Float64(a * Float64(b * Float64(t * Float64(-z))));
	elseif (a <= 2.6e+66)
		tmp = Float64(j * Float64(b * Float64(t * y4)));
	else
		tmp = Float64(z * Float64(-Float64(t * Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (a <= -3.8e+120)
		tmp = t * (y5 * (a * y2));
	elseif (a <= -4.2e-57)
		tmp = a * (b * (t * -z));
	elseif (a <= 2.6e+66)
		tmp = j * (b * (t * y4));
	else
		tmp = z * -(t * (a * b));
	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[a, -3.8e+120], N[(t * N[(y5 * N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.2e-57], N[(a * N[(b * N[(t * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e+66], N[(j * N[(b * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * (-N[(t * N[(a * b), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.7999999999999998e120

   1. Initial program 31.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 41.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 41.6%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   5. Taylor expanded in a around inf 31.8%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(y2 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 40.4%

         \[\leadsto t \cdot \color{blue}{\left(\left(a \cdot y2\right) \cdot y5\right)} \]

      2. *-commutative 40.4%

         \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(a \cdot y2\right)\right)} \]

   7. Simplified 40.4%

      \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(a \cdot y2\right)\right)} \]

   if -3.7999999999999998e120 < a < -4.1999999999999999e-57

   1. Initial program 15.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 27.8%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in z around inf 34.9%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 34.9%

         \[\leadsto \color{blue}{-t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. associate-*r* 37.3%

         \[\leadsto -\color{blue}{\left(t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)} \]

   6. Simplified 37.3%

      \[\leadsto \color{blue}{-\left(t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)} \]

   7. Taylor expanded in a around inf 40.2%

      \[\leadsto -\color{blue}{a \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 40.2%

         \[\leadsto -a \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot b\right)} \]

   9. Simplified 40.2%

      \[\leadsto -\color{blue}{a \cdot \left(\left(t \cdot z\right) \cdot b\right)} \]

   if -4.1999999999999999e-57 < a < 2.60000000000000012e66

   1. Initial program 31.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 35.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 40.0%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 27.9%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. expm1-log1p-u 13.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\right)\right)} \]

      2. expm1-udef 13.7%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\right)} - 1} \]

      3. associate-*r* 11.4%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(b \cdot j\right) \cdot \left(t \cdot y4\right)}\right)} - 1 \]

   9. Applied egg-rr 11.4%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(b \cdot j\right) \cdot \left(t \cdot y4\right)\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 11.4%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(b \cdot j\right) \cdot \left(t \cdot y4\right)\right)\right)} \]

       2. expm1-log1p 25.6%

          \[\leadsto \color{blue}{\left(b \cdot j\right) \cdot \left(t \cdot y4\right)} \]

       3. *-commutative 25.6%

          \[\leadsto \color{blue}{\left(j \cdot b\right)} \cdot \left(t \cdot y4\right) \]

       4. associate-*l* 28.6%

          \[\leadsto \color{blue}{j \cdot \left(b \cdot \left(t \cdot y4\right)\right)} \]

   11. Simplified 28.6%

       \[\leadsto \color{blue}{j \cdot \left(b \cdot \left(t \cdot y4\right)\right)} \]

   if 2.60000000000000012e66 < a

   1. Initial program 22.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 35.0%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in z around inf 33.1%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 33.1%

         \[\leadsto \color{blue}{-t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. associate-*r* 29.4%

         \[\leadsto -\color{blue}{\left(t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)} \]

   6. Simplified 29.4%

      \[\leadsto \color{blue}{-\left(t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)} \]

   7. Taylor expanded in a around inf 22.3%

      \[\leadsto -\color{blue}{a \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 26.0%

         \[\leadsto -\color{blue}{\left(a \cdot b\right) \cdot \left(t \cdot z\right)} \]

      2. *-commutative 26.0%

         \[\leadsto -\color{blue}{\left(b \cdot a\right)} \cdot \left(t \cdot z\right) \]

      3. *-commutative 26.0%

         \[\leadsto -\color{blue}{\left(t \cdot z\right) \cdot \left(b \cdot a\right)} \]

   9. Simplified 26.0%

      \[\leadsto -\color{blue}{\left(t \cdot z\right) \cdot \left(b \cdot a\right)} \]

   10. Taylor expanded in t around 0 22.3%

       \[\leadsto -\color{blue}{a \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 22.3%

          \[\leadsto -\color{blue}{\left(b \cdot \left(t \cdot z\right)\right) \cdot a} \]

       2. *-commutative 22.3%

          \[\leadsto -\color{blue}{\left(\left(t \cdot z\right) \cdot b\right)} \cdot a \]

       3. associate-*r* 26.0%

          \[\leadsto -\color{blue}{\left(t \cdot z\right) \cdot \left(b \cdot a\right)} \]

       4. associate-*r* 31.4%

          \[\leadsto -\color{blue}{t \cdot \left(z \cdot \left(b \cdot a\right)\right)} \]

       5. *-commutative 31.4%

          \[\leadsto -\color{blue}{\left(z \cdot \left(b \cdot a\right)\right) \cdot t} \]

       6. associate-*l* 33.4%

          \[\leadsto -\color{blue}{z \cdot \left(\left(b \cdot a\right) \cdot t\right)} \]

       7. *-commutative 33.4%

          \[\leadsto -z \cdot \left(\color{blue}{\left(a \cdot b\right)} \cdot t\right) \]

   12. Simplified 33.4%

       \[\leadsto -\color{blue}{z \cdot \left(\left(a \cdot b\right) \cdot t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 33.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+120}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(b \cdot \left(t \cdot \left(-z\right)\right)\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+66}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t \cdot \left(a \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 22.3% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -1.32 \cdot 10^{+26}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 9.6 \cdot 10^{-142}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 9.5 \cdot 10^{-58}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -1.32e+26)
   (* b (* t (* j y4)))
   (if (<= y4 9.6e-142)
     (* a (* t (* y2 y5)))
     (if (<= y4 9.5e-58) (* c (* i (* z t))) (* b (* j (* t y4)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1.32e+26) {
		tmp = b * (t * (j * y4));
	} else if (y4 <= 9.6e-142) {
		tmp = a * (t * (y2 * y5));
	} else if (y4 <= 9.5e-58) {
		tmp = c * (i * (z * t));
	} else {
		tmp = b * (j * (t * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y4 <= (-1.32d+26)) then
        tmp = b * (t * (j * y4))
    else if (y4 <= 9.6d-142) then
        tmp = a * (t * (y2 * y5))
    else if (y4 <= 9.5d-58) then
        tmp = c * (i * (z * t))
    else
        tmp = b * (j * (t * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1.32e+26) {
		tmp = b * (t * (j * y4));
	} else if (y4 <= 9.6e-142) {
		tmp = a * (t * (y2 * y5));
	} else if (y4 <= 9.5e-58) {
		tmp = c * (i * (z * t));
	} else {
		tmp = b * (j * (t * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y4 <= -1.32e+26:
		tmp = b * (t * (j * y4))
	elif y4 <= 9.6e-142:
		tmp = a * (t * (y2 * y5))
	elif y4 <= 9.5e-58:
		tmp = c * (i * (z * t))
	else:
		tmp = b * (j * (t * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -1.32e+26)
		tmp = Float64(b * Float64(t * Float64(j * y4)));
	elseif (y4 <= 9.6e-142)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (y4 <= 9.5e-58)
		tmp = Float64(c * Float64(i * Float64(z * t)));
	else
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y4 <= -1.32e+26)
		tmp = b * (t * (j * y4));
	elseif (y4 <= 9.6e-142)
		tmp = a * (t * (y2 * y5));
	elseif (y4 <= 9.5e-58)
		tmp = c * (i * (z * t));
	else
		tmp = b * (j * (t * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -1.32e+26], N[(b * N[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 9.6e-142], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 9.5e-58], N[(c * N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y4 < -1.32e26

   1. Initial program 20.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 32.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 34.2%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 34.5%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 34.5%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

      2. associate-*r* 34.5%

         \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot y4\right) \cdot t\right)} \]

   9. Simplified 34.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(j \cdot y4\right) \cdot t\right)} \]

   if -1.32e26 < y4 < 9.59999999999999952e-142

   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 y2 around inf 34.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 26.3%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   5. Taylor expanded in a around inf 23.1%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]

   if 9.59999999999999952e-142 < y4 < 9.4999999999999994e-58

   1. Initial program 10.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 30.6%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in i around inf 40.8%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]

   5. Taylor expanded in j around 0 41.1%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]

   if 9.4999999999999994e-58 < y4

   1. Initial program 29.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 40.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 41.7%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 33.0%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 30.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.32 \cdot 10^{+26}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 9.6 \cdot 10^{-142}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 9.5 \cdot 10^{-58}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 22.4% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -1.3 \cdot 10^{+26}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 2 \cdot 10^{-141}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 2.45 \cdot 10^{-26}:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -1.3e+26)
   (* b (* t (* j y4)))
   (if (<= y4 2e-141)
     (* a (* t (* y2 y5)))
     (if (<= y4 2.45e-26) (* i (* t (* z c))) (* j (* b (* t y4)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1.3e+26) {
		tmp = b * (t * (j * y4));
	} else if (y4 <= 2e-141) {
		tmp = a * (t * (y2 * y5));
	} else if (y4 <= 2.45e-26) {
		tmp = i * (t * (z * c));
	} else {
		tmp = j * (b * (t * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y4 <= (-1.3d+26)) then
        tmp = b * (t * (j * y4))
    else if (y4 <= 2d-141) then
        tmp = a * (t * (y2 * y5))
    else if (y4 <= 2.45d-26) then
        tmp = i * (t * (z * c))
    else
        tmp = j * (b * (t * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1.3e+26) {
		tmp = b * (t * (j * y4));
	} else if (y4 <= 2e-141) {
		tmp = a * (t * (y2 * y5));
	} else if (y4 <= 2.45e-26) {
		tmp = i * (t * (z * c));
	} else {
		tmp = j * (b * (t * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y4 <= -1.3e+26:
		tmp = b * (t * (j * y4))
	elif y4 <= 2e-141:
		tmp = a * (t * (y2 * y5))
	elif y4 <= 2.45e-26:
		tmp = i * (t * (z * c))
	else:
		tmp = j * (b * (t * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -1.3e+26)
		tmp = Float64(b * Float64(t * Float64(j * y4)));
	elseif (y4 <= 2e-141)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (y4 <= 2.45e-26)
		tmp = Float64(i * Float64(t * Float64(z * c)));
	else
		tmp = Float64(j * Float64(b * Float64(t * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y4 <= -1.3e+26)
		tmp = b * (t * (j * y4));
	elseif (y4 <= 2e-141)
		tmp = a * (t * (y2 * y5));
	elseif (y4 <= 2.45e-26)
		tmp = i * (t * (z * c));
	else
		tmp = j * (b * (t * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -1.3e+26], N[(b * N[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2e-141], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2.45e-26], N[(i * N[(t * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(b * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y4 < -1.30000000000000001e26

   1. Initial program 20.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 32.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 34.2%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 34.5%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 34.5%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

      2. associate-*r* 34.5%

         \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot y4\right) \cdot t\right)} \]

   9. Simplified 34.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(j \cdot y4\right) \cdot t\right)} \]

   if -1.30000000000000001e26 < y4 < 2.0000000000000001e-141

   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 y2 around inf 34.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 26.3%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   5. Taylor expanded in a around inf 23.1%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]

   if 2.0000000000000001e-141 < y4 < 2.45e-26

   1. Initial program 19.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 41.5%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in i around inf 35.3%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]

   5. Taylor expanded in j around 0 32.3%

      \[\leadsto i \cdot \color{blue}{\left(c \cdot \left(t \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 32.3%

         \[\leadsto i \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot c\right)} \]

      2. associate-*r* 35.4%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot \left(z \cdot c\right)\right)} \]

   7. Simplified 35.4%

      \[\leadsto i \cdot \color{blue}{\left(t \cdot \left(z \cdot c\right)\right)} \]

   if 2.45e-26 < y4

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 42.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 44.8%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 34.8%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. expm1-log1p-u 21.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\right)\right)} \]

      2. expm1-udef 21.4%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\right)} - 1} \]

      3. associate-*r* 17.7%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(b \cdot j\right) \cdot \left(t \cdot y4\right)}\right)} - 1 \]

   9. Applied egg-rr 17.7%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(b \cdot j\right) \cdot \left(t \cdot y4\right)\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 17.7%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(b \cdot j\right) \cdot \left(t \cdot y4\right)\right)\right)} \]

       2. expm1-log1p 30.9%

          \[\leadsto \color{blue}{\left(b \cdot j\right) \cdot \left(t \cdot y4\right)} \]

       3. *-commutative 30.9%

          \[\leadsto \color{blue}{\left(j \cdot b\right)} \cdot \left(t \cdot y4\right) \]

       4. associate-*l* 36.0%

          \[\leadsto \color{blue}{j \cdot \left(b \cdot \left(t \cdot y4\right)\right)} \]

   11. Simplified 36.0%

       \[\leadsto \color{blue}{j \cdot \left(b \cdot \left(t \cdot y4\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 31.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.3 \cdot 10^{+26}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 2 \cdot 10^{-141}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 2.45 \cdot 10^{-26}:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 22.1% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -6.8 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 2.3 \cdot 10^{-141}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 4.6 \cdot 10^{-26}:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -6.8e+36)
   (* b (* t (* j y4)))
   (if (<= y4 2.3e-141)
     (* t (* a (* y2 y5)))
     (if (<= y4 4.6e-26) (* i (* t (* z c))) (* j (* b (* t y4)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -6.8e+36) {
		tmp = b * (t * (j * y4));
	} else if (y4 <= 2.3e-141) {
		tmp = t * (a * (y2 * y5));
	} else if (y4 <= 4.6e-26) {
		tmp = i * (t * (z * c));
	} else {
		tmp = j * (b * (t * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y4 <= (-6.8d+36)) then
        tmp = b * (t * (j * y4))
    else if (y4 <= 2.3d-141) then
        tmp = t * (a * (y2 * y5))
    else if (y4 <= 4.6d-26) then
        tmp = i * (t * (z * c))
    else
        tmp = j * (b * (t * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -6.8e+36) {
		tmp = b * (t * (j * y4));
	} else if (y4 <= 2.3e-141) {
		tmp = t * (a * (y2 * y5));
	} else if (y4 <= 4.6e-26) {
		tmp = i * (t * (z * c));
	} else {
		tmp = j * (b * (t * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y4 <= -6.8e+36:
		tmp = b * (t * (j * y4))
	elif y4 <= 2.3e-141:
		tmp = t * (a * (y2 * y5))
	elif y4 <= 4.6e-26:
		tmp = i * (t * (z * c))
	else:
		tmp = j * (b * (t * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -6.8e+36)
		tmp = Float64(b * Float64(t * Float64(j * y4)));
	elseif (y4 <= 2.3e-141)
		tmp = Float64(t * Float64(a * Float64(y2 * y5)));
	elseif (y4 <= 4.6e-26)
		tmp = Float64(i * Float64(t * Float64(z * c)));
	else
		tmp = Float64(j * Float64(b * Float64(t * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y4 <= -6.8e+36)
		tmp = b * (t * (j * y4));
	elseif (y4 <= 2.3e-141)
		tmp = t * (a * (y2 * y5));
	elseif (y4 <= 4.6e-26)
		tmp = i * (t * (z * c));
	else
		tmp = j * (b * (t * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -6.8e+36], N[(b * N[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2.3e-141], N[(t * N[(a * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 4.6e-26], N[(i * N[(t * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(b * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y4 < -6.7999999999999996e36

   1. Initial program 18.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 20.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 32.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 34.7%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 35.0%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 35.0%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

      2. associate-*r* 35.1%

         \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot y4\right) \cdot t\right)} \]

   9. Simplified 35.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(j \cdot y4\right) \cdot t\right)} \]

   if -6.7999999999999996e36 < y4 < 2.29999999999999995e-141

   1. Initial program 35.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 34.4%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 26.0%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   5. Taylor expanded in a around inf 25.0%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(y2 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 25.0%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{\left(y5 \cdot y2\right)}\right) \]

   7. Simplified 25.0%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(y5 \cdot y2\right)\right)} \]

   if 2.29999999999999995e-141 < y4 < 4.60000000000000018e-26

   1. Initial program 19.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 41.5%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in i around inf 35.3%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]

   5. Taylor expanded in j around 0 32.3%

      \[\leadsto i \cdot \color{blue}{\left(c \cdot \left(t \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 32.3%

         \[\leadsto i \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot c\right)} \]

      2. associate-*r* 35.4%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot \left(z \cdot c\right)\right)} \]

   7. Simplified 35.4%

      \[\leadsto i \cdot \color{blue}{\left(t \cdot \left(z \cdot c\right)\right)} \]

   if 4.60000000000000018e-26 < y4

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 42.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 44.8%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 34.8%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. expm1-log1p-u 21.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\right)\right)} \]

      2. expm1-udef 21.4%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\right)} - 1} \]

      3. associate-*r* 17.7%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(b \cdot j\right) \cdot \left(t \cdot y4\right)}\right)} - 1 \]

   9. Applied egg-rr 17.7%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(b \cdot j\right) \cdot \left(t \cdot y4\right)\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 17.7%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(b \cdot j\right) \cdot \left(t \cdot y4\right)\right)\right)} \]

       2. expm1-log1p 30.9%

          \[\leadsto \color{blue}{\left(b \cdot j\right) \cdot \left(t \cdot y4\right)} \]

       3. *-commutative 30.9%

          \[\leadsto \color{blue}{\left(j \cdot b\right)} \cdot \left(t \cdot y4\right) \]

       4. associate-*l* 36.0%

          \[\leadsto \color{blue}{j \cdot \left(b \cdot \left(t \cdot y4\right)\right)} \]

   11. Simplified 36.0%

       \[\leadsto \color{blue}{j \cdot \left(b \cdot \left(t \cdot y4\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 31.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -6.8 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 2.3 \cdot 10^{-141}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 4.6 \cdot 10^{-26}:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 34: 21.5% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-289}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+167}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (* y5 (* a y2)))))
   (if (<= a -1.45e+26)
     t_1
     (if (<= a -1.05e-289)
       (* y0 (* y2 (* x c)))
       (if (<= a 9.5e+167) (* j (* b (* t y4))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (y5 * (a * y2));
	double tmp;
	if (a <= -1.45e+26) {
		tmp = t_1;
	} else if (a <= -1.05e-289) {
		tmp = y0 * (y2 * (x * c));
	} else if (a <= 9.5e+167) {
		tmp = j * (b * (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y5 * (a * y2))
    if (a <= (-1.45d+26)) then
        tmp = t_1
    else if (a <= (-1.05d-289)) then
        tmp = y0 * (y2 * (x * c))
    else if (a <= 9.5d+167) then
        tmp = j * (b * (t * y4))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (y5 * (a * y2));
	double tmp;
	if (a <= -1.45e+26) {
		tmp = t_1;
	} else if (a <= -1.05e-289) {
		tmp = y0 * (y2 * (x * c));
	} else if (a <= 9.5e+167) {
		tmp = j * (b * (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = t * (y5 * (a * y2))
	tmp = 0
	if a <= -1.45e+26:
		tmp = t_1
	elif a <= -1.05e-289:
		tmp = y0 * (y2 * (x * c))
	elif a <= 9.5e+167:
		tmp = j * (b * (t * y4))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(t * Float64(y5 * Float64(a * y2)))
	tmp = 0.0
	if (a <= -1.45e+26)
		tmp = t_1;
	elseif (a <= -1.05e-289)
		tmp = Float64(y0 * Float64(y2 * Float64(x * c)));
	elseif (a <= 9.5e+167)
		tmp = Float64(j * Float64(b * Float64(t * y4)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = t * (y5 * (a * y2));
	tmp = 0.0;
	if (a <= -1.45e+26)
		tmp = t_1;
	elseif (a <= -1.05e-289)
		tmp = y0 * (y2 * (x * c));
	elseif (a <= 9.5e+167)
		tmp = j * (b * (t * y4));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(t * N[(y5 * N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.45e+26], t$95$1, If[LessEqual[a, -1.05e-289], N[(y0 * N[(y2 * N[(x * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+167], N[(j * N[(b * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.45e26 or 9.5000000000000006e167 < a

   1. Initial program 23.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 36.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 38.0%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   5. Taylor expanded in a around inf 29.3%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(y2 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 35.7%

         \[\leadsto t \cdot \color{blue}{\left(\left(a \cdot y2\right) \cdot y5\right)} \]

      2. *-commutative 35.7%

         \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(a \cdot y2\right)\right)} \]

   7. Simplified 35.7%

      \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(a \cdot y2\right)\right)} \]

   if -1.45e26 < a < -1.0499999999999999e-289

   1. Initial program 29.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 37.1%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in y0 around inf 38.6%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(-1 \cdot \left(k \cdot y5\right) + c \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 38.6%

         \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(c \cdot x + -1 \cdot \left(k \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 38.6%

         \[\leadsto y0 \cdot \left(y2 \cdot \left(c \cdot x + \color{blue}{\left(-k \cdot y5\right)}\right)\right) \]

      3. unsub-neg 38.6%

         \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(c \cdot x - k \cdot y5\right)}\right) \]

      4. *-commutative 38.6%

         \[\leadsto y0 \cdot \left(y2 \cdot \left(\color{blue}{x \cdot c} - k \cdot y5\right)\right) \]

      5. *-commutative 38.6%

         \[\leadsto y0 \cdot \left(y2 \cdot \left(x \cdot c - \color{blue}{y5 \cdot k}\right)\right) \]

   6. Simplified 38.6%

      \[\leadsto \color{blue}{y0 \cdot \left(y2 \cdot \left(x \cdot c - y5 \cdot k\right)\right)} \]

   7. Taylor expanded in x around inf 27.5%

      \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(c \cdot x\right)}\right) \]
   8. Step-by-step derivation

      1. *-commutative 27.5%

         \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(x \cdot c\right)}\right) \]

   9. Simplified 27.5%

      \[\leadsto y0 \cdot \left(y2 \cdot \color{blue}{\left(x \cdot c\right)}\right) \]

   if -1.0499999999999999e-289 < a < 9.5000000000000006e167

   1. Initial program 29.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.8%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 37.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 35.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 28.0%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. expm1-log1p-u 14.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\right)\right)} \]

      2. expm1-udef 14.4%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\right)} - 1} \]

      3. associate-*r* 12.5%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(b \cdot j\right) \cdot \left(t \cdot y4\right)}\right)} - 1 \]

   9. Applied egg-rr 12.5%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(b \cdot j\right) \cdot \left(t \cdot y4\right)\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 12.5%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(b \cdot j\right) \cdot \left(t \cdot y4\right)\right)\right)} \]

       2. expm1-log1p 26.1%

          \[\leadsto \color{blue}{\left(b \cdot j\right) \cdot \left(t \cdot y4\right)} \]

       3. *-commutative 26.1%

          \[\leadsto \color{blue}{\left(j \cdot b\right)} \cdot \left(t \cdot y4\right) \]

       4. associate-*l* 30.7%

          \[\leadsto \color{blue}{j \cdot \left(b \cdot \left(t \cdot y4\right)\right)} \]

   11. Simplified 30.7%

       \[\leadsto \color{blue}{j \cdot \left(b \cdot \left(t \cdot y4\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+26}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-289}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+167}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 35: 21.0% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-57}:\\ \;\;\;\;\left(z \cdot \left(t \cdot b\right)\right) \cdot \left(-a\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+172}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (* y5 (* a y2)))))
   (if (<= a -1.8e+120)
     t_1
     (if (<= a -4.2e-57)
       (* (* z (* t b)) (- a))
       (if (<= a 1.15e+172) (* j (* b (* t y4))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (y5 * (a * y2));
	double tmp;
	if (a <= -1.8e+120) {
		tmp = t_1;
	} else if (a <= -4.2e-57) {
		tmp = (z * (t * b)) * -a;
	} else if (a <= 1.15e+172) {
		tmp = j * (b * (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y5 * (a * y2))
    if (a <= (-1.8d+120)) then
        tmp = t_1
    else if (a <= (-4.2d-57)) then
        tmp = (z * (t * b)) * -a
    else if (a <= 1.15d+172) then
        tmp = j * (b * (t * y4))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (y5 * (a * y2));
	double tmp;
	if (a <= -1.8e+120) {
		tmp = t_1;
	} else if (a <= -4.2e-57) {
		tmp = (z * (t * b)) * -a;
	} else if (a <= 1.15e+172) {
		tmp = j * (b * (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = t * (y5 * (a * y2))
	tmp = 0
	if a <= -1.8e+120:
		tmp = t_1
	elif a <= -4.2e-57:
		tmp = (z * (t * b)) * -a
	elif a <= 1.15e+172:
		tmp = j * (b * (t * y4))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(t * Float64(y5 * Float64(a * y2)))
	tmp = 0.0
	if (a <= -1.8e+120)
		tmp = t_1;
	elseif (a <= -4.2e-57)
		tmp = Float64(Float64(z * Float64(t * b)) * Float64(-a));
	elseif (a <= 1.15e+172)
		tmp = Float64(j * Float64(b * Float64(t * y4)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = t * (y5 * (a * y2));
	tmp = 0.0;
	if (a <= -1.8e+120)
		tmp = t_1;
	elseif (a <= -4.2e-57)
		tmp = (z * (t * b)) * -a;
	elseif (a <= 1.15e+172)
		tmp = j * (b * (t * y4));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(t * N[(y5 * N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8e+120], t$95$1, If[LessEqual[a, -4.2e-57], N[(N[(z * N[(t * b), $MachinePrecision]), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[a, 1.15e+172], N[(j * N[(b * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.80000000000000008e120 or 1.15e172 < a

   1. Initial program 24.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 38.7%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 40.0%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   5. Taylor expanded in a around inf 31.9%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(y2 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 40.0%

         \[\leadsto t \cdot \color{blue}{\left(\left(a \cdot y2\right) \cdot y5\right)} \]

      2. *-commutative 40.0%

         \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(a \cdot y2\right)\right)} \]

   7. Simplified 40.0%

      \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(a \cdot y2\right)\right)} \]

   if -1.80000000000000008e120 < a < -4.1999999999999999e-57

   1. Initial program 15.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 27.8%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in z around inf 34.9%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 34.9%

         \[\leadsto \color{blue}{-t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. associate-*r* 37.3%

         \[\leadsto -\color{blue}{\left(t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)} \]

   6. Simplified 37.3%

      \[\leadsto \color{blue}{-\left(t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)} \]

   7. Taylor expanded in a around inf 40.2%

      \[\leadsto -\color{blue}{a \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 40.2%

         \[\leadsto -\color{blue}{\left(a \cdot b\right) \cdot \left(t \cdot z\right)} \]

      2. *-commutative 40.2%

         \[\leadsto -\color{blue}{\left(b \cdot a\right)} \cdot \left(t \cdot z\right) \]

      3. *-commutative 40.2%

         \[\leadsto -\color{blue}{\left(t \cdot z\right) \cdot \left(b \cdot a\right)} \]

   9. Simplified 40.2%

      \[\leadsto -\color{blue}{\left(t \cdot z\right) \cdot \left(b \cdot a\right)} \]

   10. Taylor expanded in t around 0 40.2%

       \[\leadsto -\color{blue}{a \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 34.7%

          \[\leadsto -a \cdot \color{blue}{\left(\left(b \cdot t\right) \cdot z\right)} \]

   12. Simplified 34.7%

       \[\leadsto -\color{blue}{a \cdot \left(\left(b \cdot t\right) \cdot z\right)} \]

   if -4.1999999999999999e-57 < a < 1.15e172

   1. Initial program 31.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 34.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 36.0%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 26.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. expm1-log1p-u 13.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\right)\right)} \]

      2. expm1-udef 13.2%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\right)} - 1} \]

      3. associate-*r* 11.3%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(b \cdot j\right) \cdot \left(t \cdot y4\right)}\right)} - 1 \]

   9. Applied egg-rr 11.3%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(b \cdot j\right) \cdot \left(t \cdot y4\right)\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 11.3%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(b \cdot j\right) \cdot \left(t \cdot y4\right)\right)\right)} \]

       2. expm1-log1p 24.3%

          \[\leadsto \color{blue}{\left(b \cdot j\right) \cdot \left(t \cdot y4\right)} \]

       3. *-commutative 24.3%

          \[\leadsto \color{blue}{\left(j \cdot b\right)} \cdot \left(t \cdot y4\right) \]

       4. associate-*l* 27.3%

          \[\leadsto \color{blue}{j \cdot \left(b \cdot \left(t \cdot y4\right)\right)} \]

   11. Simplified 27.3%

       \[\leadsto \color{blue}{j \cdot \left(b \cdot \left(t \cdot y4\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+120}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-57}:\\ \;\;\;\;\left(z \cdot \left(t \cdot b\right)\right) \cdot \left(-a\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+172}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 36: 20.9% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{+124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(b \cdot \left(t \cdot \left(-z\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+177}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (* y5 (* a y2)))))
   (if (<= a -4.2e+124)
     t_1
     (if (<= a -4.2e-57)
       (* a (* b (* t (- z))))
       (if (<= a 1.1e+177) (* j (* b (* t y4))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (y5 * (a * y2));
	double tmp;
	if (a <= -4.2e+124) {
		tmp = t_1;
	} else if (a <= -4.2e-57) {
		tmp = a * (b * (t * -z));
	} else if (a <= 1.1e+177) {
		tmp = j * (b * (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y5 * (a * y2))
    if (a <= (-4.2d+124)) then
        tmp = t_1
    else if (a <= (-4.2d-57)) then
        tmp = a * (b * (t * -z))
    else if (a <= 1.1d+177) then
        tmp = j * (b * (t * y4))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (y5 * (a * y2));
	double tmp;
	if (a <= -4.2e+124) {
		tmp = t_1;
	} else if (a <= -4.2e-57) {
		tmp = a * (b * (t * -z));
	} else if (a <= 1.1e+177) {
		tmp = j * (b * (t * y4));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = t * (y5 * (a * y2))
	tmp = 0
	if a <= -4.2e+124:
		tmp = t_1
	elif a <= -4.2e-57:
		tmp = a * (b * (t * -z))
	elif a <= 1.1e+177:
		tmp = j * (b * (t * y4))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(t * Float64(y5 * Float64(a * y2)))
	tmp = 0.0
	if (a <= -4.2e+124)
		tmp = t_1;
	elseif (a <= -4.2e-57)
		tmp = Float64(a * Float64(b * Float64(t * Float64(-z))));
	elseif (a <= 1.1e+177)
		tmp = Float64(j * Float64(b * Float64(t * y4)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = t * (y5 * (a * y2));
	tmp = 0.0;
	if (a <= -4.2e+124)
		tmp = t_1;
	elseif (a <= -4.2e-57)
		tmp = a * (b * (t * -z));
	elseif (a <= 1.1e+177)
		tmp = j * (b * (t * y4));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(t * N[(y5 * N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.2e+124], t$95$1, If[LessEqual[a, -4.2e-57], N[(a * N[(b * N[(t * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.1e+177], N[(j * N[(b * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.20000000000000023e124 or 1.0999999999999999e177 < a

   1. Initial program 24.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 38.7%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 40.0%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   5. Taylor expanded in a around inf 31.9%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(y2 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 40.0%

         \[\leadsto t \cdot \color{blue}{\left(\left(a \cdot y2\right) \cdot y5\right)} \]

      2. *-commutative 40.0%

         \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(a \cdot y2\right)\right)} \]

   7. Simplified 40.0%

      \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(a \cdot y2\right)\right)} \]

   if -4.20000000000000023e124 < a < -4.1999999999999999e-57

   1. Initial program 15.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 27.8%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in z around inf 34.9%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 34.9%

         \[\leadsto \color{blue}{-t \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right)} \]

      2. associate-*r* 37.3%

         \[\leadsto -\color{blue}{\left(t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)} \]

   6. Simplified 37.3%

      \[\leadsto \color{blue}{-\left(t \cdot z\right) \cdot \left(a \cdot b - c \cdot i\right)} \]

   7. Taylor expanded in a around inf 40.2%

      \[\leadsto -\color{blue}{a \cdot \left(b \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 40.2%

         \[\leadsto -a \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot b\right)} \]

   9. Simplified 40.2%

      \[\leadsto -\color{blue}{a \cdot \left(\left(t \cdot z\right) \cdot b\right)} \]

   if -4.1999999999999999e-57 < a < 1.0999999999999999e177

   1. Initial program 31.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 34.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 36.0%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 26.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. expm1-log1p-u 13.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\right)\right)} \]

      2. expm1-udef 13.2%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\right)} - 1} \]

      3. associate-*r* 11.3%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(b \cdot j\right) \cdot \left(t \cdot y4\right)}\right)} - 1 \]

   9. Applied egg-rr 11.3%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(b \cdot j\right) \cdot \left(t \cdot y4\right)\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 11.3%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(b \cdot j\right) \cdot \left(t \cdot y4\right)\right)\right)} \]

       2. expm1-log1p 24.3%

          \[\leadsto \color{blue}{\left(b \cdot j\right) \cdot \left(t \cdot y4\right)} \]

       3. *-commutative 24.3%

          \[\leadsto \color{blue}{\left(j \cdot b\right)} \cdot \left(t \cdot y4\right) \]

       4. associate-*l* 27.3%

          \[\leadsto \color{blue}{j \cdot \left(b \cdot \left(t \cdot y4\right)\right)} \]

   11. Simplified 27.3%

       \[\leadsto \color{blue}{j \cdot \left(b \cdot \left(t \cdot y4\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 32.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+124}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(b \cdot \left(t \cdot \left(-z\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+177}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 37: 22.0% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -3 \cdot 10^{+28} \lor \neg \left(y4 \leq 2.2 \cdot 10^{-73}\right):\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y4 -3e+28) (not (<= y4 2.2e-73)))
   (* b (* j (* t y4)))
   (* a (* t (* y2 y5)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y4 <= -3e+28) || !(y4 <= 2.2e-73)) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y4 <= (-3d+28)) .or. (.not. (y4 <= 2.2d-73))) then
        tmp = b * (j * (t * y4))
    else
        tmp = a * (t * (y2 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y4 <= -3e+28) || !(y4 <= 2.2e-73)) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y4 <= -3e+28) or not (y4 <= 2.2e-73):
		tmp = b * (j * (t * y4))
	else:
		tmp = a * (t * (y2 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y4 <= -3e+28) || !(y4 <= 2.2e-73))
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	else
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y4 <= -3e+28) || ~((y4 <= 2.2e-73)))
		tmp = b * (j * (t * y4));
	else
		tmp = a * (t * (y2 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y4, -3e+28], N[Not[LessEqual[y4, 2.2e-73]], $MachinePrecision]], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y4 < -3.0000000000000001e28 or 2.2e-73 < y4

   1. Initial program 25.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.8%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 36.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 37.7%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 32.7%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

   if -3.0000000000000001e28 < y4 < 2.2e-73

   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 35.3%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 26.3%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   5. Taylor expanded in a around inf 21.7%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 28.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -3 \cdot 10^{+28} \lor \neg \left(y4 \leq 2.2 \cdot 10^{-73}\right):\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 38: 21.2% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-57} \lor \neg \left(a \leq 1.45 \cdot 10^{+168}\right):\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= a -4.2e-57) (not (<= a 1.45e+168)))
   (* t (* y5 (* a y2)))
   (* j (* b (* t y4)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((a <= -4.2e-57) || !(a <= 1.45e+168)) {
		tmp = t * (y5 * (a * y2));
	} else {
		tmp = j * (b * (t * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((a <= (-4.2d-57)) .or. (.not. (a <= 1.45d+168))) then
        tmp = t * (y5 * (a * y2))
    else
        tmp = j * (b * (t * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((a <= -4.2e-57) || !(a <= 1.45e+168)) {
		tmp = t * (y5 * (a * y2));
	} else {
		tmp = j * (b * (t * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (a <= -4.2e-57) or not (a <= 1.45e+168):
		tmp = t * (y5 * (a * y2))
	else:
		tmp = j * (b * (t * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((a <= -4.2e-57) || !(a <= 1.45e+168))
		tmp = Float64(t * Float64(y5 * Float64(a * y2)));
	else
		tmp = Float64(j * Float64(b * Float64(t * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((a <= -4.2e-57) || ~((a <= 1.45e+168)))
		tmp = t * (y5 * (a * y2));
	else
		tmp = j * (b * (t * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[a, -4.2e-57], N[Not[LessEqual[a, 1.45e+168]], $MachinePrecision]], N[(t * N[(y5 * N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(b * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.1999999999999999e-57 or 1.45e168 < a

   1. Initial program 21.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y2 around inf 36.9%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 36.0%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   5. Taylor expanded in a around inf 27.8%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(y2 \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 33.1%

         \[\leadsto t \cdot \color{blue}{\left(\left(a \cdot y2\right) \cdot y5\right)} \]

      2. *-commutative 33.1%

         \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(a \cdot y2\right)\right)} \]

   7. Simplified 33.1%

      \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(a \cdot y2\right)\right)} \]

   if -4.1999999999999999e-57 < a < 1.45e168

   1. Initial program 31.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 34.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 36.0%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 26.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. expm1-log1p-u 13.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\right)\right)} \]

      2. expm1-udef 13.2%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\right)} - 1} \]

      3. associate-*r* 11.3%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(b \cdot j\right) \cdot \left(t \cdot y4\right)}\right)} - 1 \]

   9. Applied egg-rr 11.3%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(b \cdot j\right) \cdot \left(t \cdot y4\right)\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 11.3%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(b \cdot j\right) \cdot \left(t \cdot y4\right)\right)\right)} \]

       2. expm1-log1p 24.3%

          \[\leadsto \color{blue}{\left(b \cdot j\right) \cdot \left(t \cdot y4\right)} \]

       3. *-commutative 24.3%

          \[\leadsto \color{blue}{\left(j \cdot b\right)} \cdot \left(t \cdot y4\right) \]

       4. associate-*l* 27.3%

          \[\leadsto \color{blue}{j \cdot \left(b \cdot \left(t \cdot y4\right)\right)} \]

   11. Simplified 27.3%

       \[\leadsto \color{blue}{j \cdot \left(b \cdot \left(t \cdot y4\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-57} \lor \neg \left(a \leq 1.45 \cdot 10^{+168}\right):\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 39: 22.0% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -3.2 \cdot 10^{+31}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 2.95 \cdot 10^{-77}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -3.2e+31)
   (* b (* t (* j y4)))
   (if (<= y4 2.95e-77) (* a (* t (* y2 y5))) (* b (* j (* t y4))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -3.2e+31) {
		tmp = b * (t * (j * y4));
	} else if (y4 <= 2.95e-77) {
		tmp = a * (t * (y2 * y5));
	} else {
		tmp = b * (j * (t * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y4 <= (-3.2d+31)) then
        tmp = b * (t * (j * y4))
    else if (y4 <= 2.95d-77) then
        tmp = a * (t * (y2 * y5))
    else
        tmp = b * (j * (t * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -3.2e+31) {
		tmp = b * (t * (j * y4));
	} else if (y4 <= 2.95e-77) {
		tmp = a * (t * (y2 * y5));
	} else {
		tmp = b * (j * (t * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y4 <= -3.2e+31:
		tmp = b * (t * (j * y4))
	elif y4 <= 2.95e-77:
		tmp = a * (t * (y2 * y5))
	else:
		tmp = b * (j * (t * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -3.2e+31)
		tmp = Float64(b * Float64(t * Float64(j * y4)));
	elseif (y4 <= 2.95e-77)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	else
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y4 <= -3.2e+31)
		tmp = b * (t * (j * y4));
	elseif (y4 <= 2.95e-77)
		tmp = a * (t * (y2 * y5));
	else
		tmp = b * (j * (t * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -3.2e+31], N[(b * N[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 2.95e-77], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y4 < -3.2000000000000001e31

   1. Initial program 20.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 32.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 34.2%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 34.5%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 34.5%

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

      2. associate-*r* 34.5%

         \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot y4\right) \cdot t\right)} \]

   9. Simplified 34.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(j \cdot y4\right) \cdot t\right)} \]

   if -3.2000000000000001e31 < y4 < 2.94999999999999982e-77

   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 35.3%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 26.3%

      \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   5. Taylor expanded in a around inf 21.7%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]

   if 2.94999999999999982e-77 < y4

   1. Initial program 28.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 40.0%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   7. Taylor expanded in t around inf 31.6%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 28.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -3.2 \cdot 10^{+31}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 2.95 \cdot 10^{-77}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 40: 16.9% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* t (* y2 y5))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (t * (y2 * y5));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * (t * (y2 * y5))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (t * (y2 * y5));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (t * (y2 * y5))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(t * Float64(y2 * y5)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (t * (y2 * y5));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 27.5%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Add Preprocessing

3. Taylor expanded in y2 around inf 34.7%

   \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

4. Taylor expanded in t around inf 29.4%

   \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

5. Taylor expanded in a around inf 16.7%

   \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]

6. Final simplification 16.7%

   \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right) \]
7. Add Preprocessing

Alternative 41: 17.0% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* y5 (* t y2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y5 * (t * y2));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * (y5 * (t * y2))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y5 * (t * y2));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (y5 * (t * y2))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(y5 * Float64(t * y2)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (y5 * (t * y2));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 27.5%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Add Preprocessing

3. Taylor expanded in y2 around inf 34.7%

   \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

4. Taylor expanded in t around inf 29.4%

   \[\leadsto \color{blue}{t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

5. Taylor expanded in a around inf 16.7%

   \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)} \]
6. Step-by-step derivation

   1. associate-*r* 17.2%

      \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot y2\right) \cdot y5\right)} \]

7. Simplified 17.2%

   \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2\right) \cdot y5\right)} \]

8. Final simplification 17.2%

   \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right) \]
9. Add Preprocessing

Developer target: 27.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot c - y5 \cdot a\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := y2 \cdot t - y3 \cdot y\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := y4 \cdot b - y5 \cdot i\\ t_6 := \left(j \cdot t - k \cdot y\right) \cdot t_5\\ t_7 := b \cdot a - i \cdot c\\ t_8 := t_7 \cdot \left(y \cdot x - t \cdot z\right)\\ t_9 := j \cdot x - k \cdot z\\ t_10 := \left(b \cdot y0 - i \cdot y1\right) \cdot t_9\\ t_11 := t_9 \cdot \left(y0 \cdot b - i \cdot y1\right)\\ t_12 := y4 \cdot y1 - y5 \cdot y0\\ t_13 := t_4 \cdot t_12\\ t_14 := \left(y2 \cdot k - y3 \cdot j\right) \cdot t_12\\ t_15 := \left(\left(\left(\left(k \cdot y\right) \cdot \left(y5 \cdot i\right) - \left(y \cdot b\right) \cdot \left(y4 \cdot k\right)\right) - \left(y5 \cdot t\right) \cdot \left(i \cdot j\right)\right) - \left(t_3 \cdot t_1 - t_14\right)\right) + \left(t_8 - \left(t_11 - \left(y2 \cdot x - y3 \cdot z\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right)\right)\\ t_16 := \left(\left(t_6 - \left(y3 \cdot y\right) \cdot \left(y5 \cdot a - y4 \cdot c\right)\right) + \left(\left(y5 \cdot a\right) \cdot \left(t \cdot y2\right) + t_13\right)\right) + \left(t_2 \cdot \left(c \cdot y0 - a \cdot y1\right) - \left(t_10 - \left(y \cdot x - z \cdot t\right) \cdot t_7\right)\right)\\ t_17 := t \cdot y2 - y \cdot y3\\ \mathbf{if}\;y4 < -7.206256231996481 \cdot 10^{+60}:\\ \;\;\;\;\left(t_8 - \left(t_11 - t_6\right)\right) - \left(\frac{t_3}{\frac{1}{t_1}} - t_14\right)\\ \mathbf{elif}\;y4 < -3.364603505246317 \cdot 10^{-66}:\\ \;\;\;\;\left(\left(\left(\left(t \cdot c\right) \cdot \left(i \cdot z\right) - \left(a \cdot t\right) \cdot \left(b \cdot z\right)\right) - \left(y \cdot c\right) \cdot \left(i \cdot x\right)\right) - t_10\right) + \left(\left(y0 \cdot c - a \cdot y1\right) \cdot t_2 - \left(t_17 \cdot \left(y4 \cdot c - a \cdot y5\right) - \left(y1 \cdot y4 - y5 \cdot y0\right) \cdot t_4\right)\right)\\ \mathbf{elif}\;y4 < -1.2000065055686116 \cdot 10^{-105}:\\ \;\;\;\;t_16\\ \mathbf{elif}\;y4 < 6.718963124057495 \cdot 10^{-279}:\\ \;\;\;\;t_15\\ \mathbf{elif}\;y4 < 4.77962681403792 \cdot 10^{-222}:\\ \;\;\;\;t_16\\ \mathbf{elif}\;y4 < 2.2852241541266835 \cdot 10^{-175}:\\ \;\;\;\;t_15\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(k \cdot \left(i \cdot \left(z \cdot y1\right)\right) - \left(j \cdot \left(i \cdot \left(x \cdot y1\right)\right) + y0 \cdot \left(k \cdot \left(z \cdot b\right)\right)\right)\right)\right) + \left(z \cdot \left(y3 \cdot \left(a \cdot y1\right)\right) - \left(y2 \cdot \left(x \cdot \left(a \cdot y1\right)\right) + y0 \cdot \left(z \cdot \left(c \cdot y3\right)\right)\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot t_5\right) - t_17 \cdot t_1\right) + t_13\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y4 c) (* y5 a)))
        (t_2 (- (* x y2) (* z y3)))
        (t_3 (- (* y2 t) (* y3 y)))
        (t_4 (- (* k y2) (* j y3)))
        (t_5 (- (* y4 b) (* y5 i)))
        (t_6 (* (- (* j t) (* k y)) t_5))
        (t_7 (- (* b a) (* i c)))
        (t_8 (* t_7 (- (* y x) (* t z))))
        (t_9 (- (* j x) (* k z)))
        (t_10 (* (- (* b y0) (* i y1)) t_9))
        (t_11 (* t_9 (- (* y0 b) (* i y1))))
        (t_12 (- (* y4 y1) (* y5 y0)))
        (t_13 (* t_4 t_12))
        (t_14 (* (- (* y2 k) (* y3 j)) t_12))
        (t_15
         (+
          (-
           (-
            (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k)))
            (* (* y5 t) (* i j)))
           (- (* t_3 t_1) t_14))
          (- t_8 (- t_11 (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))))
        (t_16
         (+
          (+
           (- t_6 (* (* y3 y) (- (* y5 a) (* y4 c))))
           (+ (* (* y5 a) (* t y2)) t_13))
          (-
           (* t_2 (- (* c y0) (* a y1)))
           (- t_10 (* (- (* y x) (* z t)) t_7)))))
        (t_17 (- (* t y2) (* y y3))))
   (if (< y4 -7.206256231996481e+60)
     (- (- t_8 (- t_11 t_6)) (- (/ t_3 (/ 1.0 t_1)) t_14))
     (if (< y4 -3.364603505246317e-66)
       (+
        (-
         (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x)))
         t_10)
        (-
         (* (- (* y0 c) (* a y1)) t_2)
         (- (* t_17 (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) t_4))))
       (if (< y4 -1.2000065055686116e-105)
         t_16
         (if (< y4 6.718963124057495e-279)
           t_15
           (if (< y4 4.77962681403792e-222)
             t_16
             (if (< y4 2.2852241541266835e-175)
               t_15
               (+
                (-
                 (+
                  (+
                   (-
                    (* (- (* x y) (* z t)) (- (* a b) (* c i)))
                    (-
                     (* k (* i (* z y1)))
                     (+ (* j (* i (* x y1))) (* y0 (* k (* z b))))))
                   (-
                    (* z (* y3 (* a y1)))
                    (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3))))))
                  (* (- (* t j) (* y k)) t_5))
                 (* t_17 t_1))
                t_13)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_17
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (y4 * c) - (y5 * a)
    t_2 = (x * y2) - (z * y3)
    t_3 = (y2 * t) - (y3 * y)
    t_4 = (k * y2) - (j * y3)
    t_5 = (y4 * b) - (y5 * i)
    t_6 = ((j * t) - (k * y)) * t_5
    t_7 = (b * a) - (i * c)
    t_8 = t_7 * ((y * x) - (t * z))
    t_9 = (j * x) - (k * z)
    t_10 = ((b * y0) - (i * y1)) * t_9
    t_11 = t_9 * ((y0 * b) - (i * y1))
    t_12 = (y4 * y1) - (y5 * y0)
    t_13 = t_4 * t_12
    t_14 = ((y2 * k) - (y3 * j)) * t_12
    t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
    t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
    t_17 = (t * y2) - (y * y3)
    if (y4 < (-7.206256231996481d+60)) then
        tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0d0 / t_1)) - t_14)
    else if (y4 < (-3.364603505246317d-66)) then
        tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
    else if (y4 < (-1.2000065055686116d-105)) then
        tmp = t_16
    else if (y4 < 6.718963124057495d-279) then
        tmp = t_15
    else if (y4 < 4.77962681403792d-222) then
        tmp = t_16
    else if (y4 < 2.2852241541266835d-175) then
        tmp = t_15
    else
        tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y4 * c) - (y5 * a)
	t_2 = (x * y2) - (z * y3)
	t_3 = (y2 * t) - (y3 * y)
	t_4 = (k * y2) - (j * y3)
	t_5 = (y4 * b) - (y5 * i)
	t_6 = ((j * t) - (k * y)) * t_5
	t_7 = (b * a) - (i * c)
	t_8 = t_7 * ((y * x) - (t * z))
	t_9 = (j * x) - (k * z)
	t_10 = ((b * y0) - (i * y1)) * t_9
	t_11 = t_9 * ((y0 * b) - (i * y1))
	t_12 = (y4 * y1) - (y5 * y0)
	t_13 = t_4 * t_12
	t_14 = ((y2 * k) - (y3 * j)) * t_12
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
	t_17 = (t * y2) - (y * y3)
	tmp = 0
	if y4 < -7.206256231996481e+60:
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14)
	elif y4 < -3.364603505246317e-66:
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
	elif y4 < -1.2000065055686116e-105:
		tmp = t_16
	elif y4 < 6.718963124057495e-279:
		tmp = t_15
	elif y4 < 4.77962681403792e-222:
		tmp = t_16
	elif y4 < 2.2852241541266835e-175:
		tmp = t_15
	else:
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y4 * c) - Float64(y5 * a))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(Float64(y2 * t) - Float64(y3 * y))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(Float64(y4 * b) - Float64(y5 * i))
	t_6 = Float64(Float64(Float64(j * t) - Float64(k * y)) * t_5)
	t_7 = Float64(Float64(b * a) - Float64(i * c))
	t_8 = Float64(t_7 * Float64(Float64(y * x) - Float64(t * z)))
	t_9 = Float64(Float64(j * x) - Float64(k * z))
	t_10 = Float64(Float64(Float64(b * y0) - Float64(i * y1)) * t_9)
	t_11 = Float64(t_9 * Float64(Float64(y0 * b) - Float64(i * y1)))
	t_12 = Float64(Float64(y4 * y1) - Float64(y5 * y0))
	t_13 = Float64(t_4 * t_12)
	t_14 = Float64(Float64(Float64(y2 * k) - Float64(y3 * j)) * t_12)
	t_15 = Float64(Float64(Float64(Float64(Float64(Float64(k * y) * Float64(y5 * i)) - Float64(Float64(y * b) * Float64(y4 * k))) - Float64(Float64(y5 * t) * Float64(i * j))) - Float64(Float64(t_3 * t_1) - t_14)) + Float64(t_8 - Float64(t_11 - Float64(Float64(Float64(y2 * x) - Float64(y3 * z)) * Float64(Float64(c * y0) - Float64(y1 * a))))))
	t_16 = Float64(Float64(Float64(t_6 - Float64(Float64(y3 * y) * Float64(Float64(y5 * a) - Float64(y4 * c)))) + Float64(Float64(Float64(y5 * a) * Float64(t * y2)) + t_13)) + Float64(Float64(t_2 * Float64(Float64(c * y0) - Float64(a * y1))) - Float64(t_10 - Float64(Float64(Float64(y * x) - Float64(z * t)) * t_7))))
	t_17 = Float64(Float64(t * y2) - Float64(y * y3))
	tmp = 0.0
	if (y4 < -7.206256231996481e+60)
		tmp = Float64(Float64(t_8 - Float64(t_11 - t_6)) - Float64(Float64(t_3 / Float64(1.0 / t_1)) - t_14));
	elseif (y4 < -3.364603505246317e-66)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(t * c) * Float64(i * z)) - Float64(Float64(a * t) * Float64(b * z))) - Float64(Float64(y * c) * Float64(i * x))) - t_10) + Float64(Float64(Float64(Float64(y0 * c) - Float64(a * y1)) * t_2) - Float64(Float64(t_17 * Float64(Float64(y4 * c) - Float64(a * y5))) - Float64(Float64(Float64(y1 * y4) - Float64(y5 * y0)) * t_4))));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * Float64(Float64(a * b) - Float64(c * i))) - Float64(Float64(k * Float64(i * Float64(z * y1))) - Float64(Float64(j * Float64(i * Float64(x * y1))) + Float64(y0 * Float64(k * Float64(z * b)))))) + Float64(Float64(z * Float64(y3 * Float64(a * y1))) - Float64(Float64(y2 * Float64(x * Float64(a * y1))) + Float64(y0 * Float64(z * Float64(c * y3)))))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * t_5)) - Float64(t_17 * t_1)) + t_13);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y4 * c) - (y5 * a);
	t_2 = (x * y2) - (z * y3);
	t_3 = (y2 * t) - (y3 * y);
	t_4 = (k * y2) - (j * y3);
	t_5 = (y4 * b) - (y5 * i);
	t_6 = ((j * t) - (k * y)) * t_5;
	t_7 = (b * a) - (i * c);
	t_8 = t_7 * ((y * x) - (t * z));
	t_9 = (j * x) - (k * z);
	t_10 = ((b * y0) - (i * y1)) * t_9;
	t_11 = t_9 * ((y0 * b) - (i * y1));
	t_12 = (y4 * y1) - (y5 * y0);
	t_13 = t_4 * t_12;
	t_14 = ((y2 * k) - (y3 * j)) * t_12;
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	t_17 = (t * y2) - (y * y3);
	tmp = 0.0;
	if (y4 < -7.206256231996481e+60)
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	elseif (y4 < -3.364603505246317e-66)
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y4 * b), $MachinePrecision] - N[(y5 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$7 * N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * t$95$9), $MachinePrecision]}, Block[{t$95$11 = N[(t$95$9 * N[(N[(y0 * b), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$12 = N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$13 = N[(t$95$4 * t$95$12), $MachinePrecision]}, Block[{t$95$14 = N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * t$95$12), $MachinePrecision]}, Block[{t$95$15 = N[(N[(N[(N[(N[(N[(k * y), $MachinePrecision] * N[(y5 * i), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] * N[(y4 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y5 * t), $MachinePrecision] * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 * t$95$1), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision] + N[(t$95$8 - N[(t$95$11 - N[(N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$16 = N[(N[(N[(t$95$6 - N[(N[(y3 * y), $MachinePrecision] * N[(N[(y5 * a), $MachinePrecision] - N[(y4 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y5 * a), $MachinePrecision] * N[(t * y2), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$10 - N[(N[(N[(y * x), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$17 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, If[Less[y4, -7.206256231996481e+60], N[(N[(t$95$8 - N[(t$95$11 - t$95$6), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 / N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision], If[Less[y4, -3.364603505246317e-66], N[(N[(N[(N[(N[(N[(t * c), $MachinePrecision] * N[(i * z), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * c), $MachinePrecision] * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$10), $MachinePrecision] + N[(N[(N[(N[(y0 * c), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] - N[(N[(t$95$17 * N[(N[(y4 * c), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y1 * y4), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y4, -1.2000065055686116e-105], t$95$16, If[Less[y4, 6.718963124057495e-279], t$95$15, If[Less[y4, 4.77962681403792e-222], t$95$16, If[Less[y4, 2.2852241541266835e-175], t$95$15, N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(k * N[(i * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(k * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(y3 * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y2 * N[(x * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(z * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(t$95$17 * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024010 
(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :name "Linear.Matrix:det44 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< y4 -7.206256231996481e+60) (- (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))))) (- (/ (- (* y2 t) (* y3 y)) (/ 1.0 (- (* y4 c) (* y5 a)))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (if (< y4 -3.364603505246317e-66) (+ (- (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x))) (* (- (* b y0) (* i y1)) (- (* j x) (* k z)))) (- (* (- (* y0 c) (* a y1)) (- (* x y2) (* z y3))) (- (* (- (* t y2) (* y y3)) (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) (- (* k y2) (* j y3)))))) (if (< y4 -1.2000065055686116e-105) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 6.718963124057495e-279) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (if (< y4 4.77962681403792e-222) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 2.2852241541266835e-175) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (- (* k (* i (* z y1))) (+ (* j (* i (* x y1))) (* y0 (* k (* z b)))))) (- (* z (* y3 (* a y1))) (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3)))))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))))))))

  (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (* (- (* x j) (* z k)) (- (* y0 b) (* y1 i)))) (* (- (* x y2) (* z y3)) (- (* y0 c) (* y1 a)))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))