Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 29.9% → 42.1%

Time: 1.6min

Alternatives: 34

Speedup: 4.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 29.9% 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: 42.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot y4 - i \cdot y5\\ t_2 := a \cdot y5 - c \cdot y4\\ t_3 := i \cdot y1 - b \cdot y0\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := t_4 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot t_2\\ t_6 := y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right) + \left(y4 \cdot t_4 + i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ t_7 := j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(t \cdot t_1 + x \cdot t_3\right)\right)\\ t_8 := y \cdot y3 - t \cdot y2\\ t_9 := t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(j \cdot t_1 + y2 \cdot t_2\right)\right)\\ \mathbf{if}\;y1 \leq -5.3 \cdot 10^{+125}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y1 \leq -4.3 \cdot 10^{+53}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right) + t_5\\ \mathbf{elif}\;y1 \leq -1.55 \cdot 10^{-49}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;y1 \leq -1.9 \cdot 10^{-108}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot t_8\right)\right)\\ \mathbf{elif}\;y1 \leq -3.3 \cdot 10^{-227}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;y1 \leq -3 \cdot 10^{-282}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right) - z \cdot t_3\right) + t_5\\ \mathbf{elif}\;y1 \leq 120000:\\ \;\;\;\;t_9\\ \mathbf{elif}\;y1 \leq 10^{+75}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) - \left(y0 \cdot t_4 + a \cdot t_8\right)\right)\\ \mathbf{elif}\;y1 \leq 8.4 \cdot 10^{+136}:\\ \;\;\;\;t_9\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* b y4) (* i y5)))
        (t_2 (- (* a y5) (* c y4)))
        (t_3 (- (* i y1) (* b y0)))
        (t_4 (- (* k y2) (* j y3)))
        (t_5 (+ (* t_4 (- (* y1 y4) (* y0 y5))) (* (- (* t y2) (* y y3)) t_2)))
        (t_6
         (*
          y1
          (+
           (* a (- (* z y3) (* x y2)))
           (+ (* y4 t_4) (* i (- (* x j) (* z k)))))))
        (t_7 (* j (+ (* y3 (- (* y0 y5) (* y1 y4))) (+ (* t t_1) (* x t_3)))))
        (t_8 (- (* y y3) (* t y2)))
        (t_9 (* t (+ (* z (- (* c i) (* a b))) (+ (* j t_1) (* y2 t_2))))))
   (if (<= y1 -5.3e+125)
     t_6
     (if (<= y1 -4.3e+53)
       (+
        (*
         b
         (+
          (+ (* a (- (* x y) (* z t))) (* y4 (- (* t j) (* y k))))
          (* y0 (- (* z k) (* x j)))))
        t_5)
       (if (<= y1 -1.55e-49)
         t_7
         (if (<= y1 -1.9e-108)
           (*
            c
            (+
             (* i (- (* z t) (* x y)))
             (+ (* y0 (- (* x y2) (* z y3))) (* y4 t_8))))
           (if (<= y1 -3.3e-227)
             t_7
             (if (<= y1 -3e-282)
               (+ (* k (- (* y (- (* i y5) (* b y4))) (* z t_3))) t_5)
               (if (<= y1 120000.0)
                 t_9
                 (if (<= y1 1e+75)
                   (*
                    y5
                    (- (* i (- (* y k) (* t j))) (+ (* y0 t_4) (* a t_8))))
                   (if (<= y1 8.4e+136) t_9 t_6)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y4) - (i * y5);
	double t_2 = (a * y5) - (c * y4);
	double t_3 = (i * y1) - (b * y0);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (t_4 * ((y1 * y4) - (y0 * y5))) + (((t * y2) - (y * y3)) * t_2);
	double t_6 = y1 * ((a * ((z * y3) - (x * y2))) + ((y4 * t_4) + (i * ((x * j) - (z * k)))));
	double t_7 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((t * t_1) + (x * t_3)));
	double t_8 = (y * y3) - (t * y2);
	double t_9 = t * ((z * ((c * i) - (a * b))) + ((j * t_1) + (y2 * t_2)));
	double tmp;
	if (y1 <= -5.3e+125) {
		tmp = t_6;
	} else if (y1 <= -4.3e+53) {
		tmp = (b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))) + t_5;
	} else if (y1 <= -1.55e-49) {
		tmp = t_7;
	} else if (y1 <= -1.9e-108) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_8)));
	} else if (y1 <= -3.3e-227) {
		tmp = t_7;
	} else if (y1 <= -3e-282) {
		tmp = (k * ((y * ((i * y5) - (b * y4))) - (z * t_3))) + t_5;
	} else if (y1 <= 120000.0) {
		tmp = t_9;
	} else if (y1 <= 1e+75) {
		tmp = y5 * ((i * ((y * k) - (t * j))) - ((y0 * t_4) + (a * t_8)));
	} else if (y1 <= 8.4e+136) {
		tmp = t_9;
	} 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_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 * y4) - (i * y5)
    t_2 = (a * y5) - (c * y4)
    t_3 = (i * y1) - (b * y0)
    t_4 = (k * y2) - (j * y3)
    t_5 = (t_4 * ((y1 * y4) - (y0 * y5))) + (((t * y2) - (y * y3)) * t_2)
    t_6 = y1 * ((a * ((z * y3) - (x * y2))) + ((y4 * t_4) + (i * ((x * j) - (z * k)))))
    t_7 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((t * t_1) + (x * t_3)))
    t_8 = (y * y3) - (t * y2)
    t_9 = t * ((z * ((c * i) - (a * b))) + ((j * t_1) + (y2 * t_2)))
    if (y1 <= (-5.3d+125)) then
        tmp = t_6
    else if (y1 <= (-4.3d+53)) then
        tmp = (b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))) + t_5
    else if (y1 <= (-1.55d-49)) then
        tmp = t_7
    else if (y1 <= (-1.9d-108)) then
        tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_8)))
    else if (y1 <= (-3.3d-227)) then
        tmp = t_7
    else if (y1 <= (-3d-282)) then
        tmp = (k * ((y * ((i * y5) - (b * y4))) - (z * t_3))) + t_5
    else if (y1 <= 120000.0d0) then
        tmp = t_9
    else if (y1 <= 1d+75) then
        tmp = y5 * ((i * ((y * k) - (t * j))) - ((y0 * t_4) + (a * t_8)))
    else if (y1 <= 8.4d+136) then
        tmp = t_9
    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 * y4) - (i * y5);
	double t_2 = (a * y5) - (c * y4);
	double t_3 = (i * y1) - (b * y0);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (t_4 * ((y1 * y4) - (y0 * y5))) + (((t * y2) - (y * y3)) * t_2);
	double t_6 = y1 * ((a * ((z * y3) - (x * y2))) + ((y4 * t_4) + (i * ((x * j) - (z * k)))));
	double t_7 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((t * t_1) + (x * t_3)));
	double t_8 = (y * y3) - (t * y2);
	double t_9 = t * ((z * ((c * i) - (a * b))) + ((j * t_1) + (y2 * t_2)));
	double tmp;
	if (y1 <= -5.3e+125) {
		tmp = t_6;
	} else if (y1 <= -4.3e+53) {
		tmp = (b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))) + t_5;
	} else if (y1 <= -1.55e-49) {
		tmp = t_7;
	} else if (y1 <= -1.9e-108) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_8)));
	} else if (y1 <= -3.3e-227) {
		tmp = t_7;
	} else if (y1 <= -3e-282) {
		tmp = (k * ((y * ((i * y5) - (b * y4))) - (z * t_3))) + t_5;
	} else if (y1 <= 120000.0) {
		tmp = t_9;
	} else if (y1 <= 1e+75) {
		tmp = y5 * ((i * ((y * k) - (t * j))) - ((y0 * t_4) + (a * t_8)));
	} else if (y1 <= 8.4e+136) {
		tmp = t_9;
	} 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 * y4) - (i * y5)
	t_2 = (a * y5) - (c * y4)
	t_3 = (i * y1) - (b * y0)
	t_4 = (k * y2) - (j * y3)
	t_5 = (t_4 * ((y1 * y4) - (y0 * y5))) + (((t * y2) - (y * y3)) * t_2)
	t_6 = y1 * ((a * ((z * y3) - (x * y2))) + ((y4 * t_4) + (i * ((x * j) - (z * k)))))
	t_7 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((t * t_1) + (x * t_3)))
	t_8 = (y * y3) - (t * y2)
	t_9 = t * ((z * ((c * i) - (a * b))) + ((j * t_1) + (y2 * t_2)))
	tmp = 0
	if y1 <= -5.3e+125:
		tmp = t_6
	elif y1 <= -4.3e+53:
		tmp = (b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))) + t_5
	elif y1 <= -1.55e-49:
		tmp = t_7
	elif y1 <= -1.9e-108:
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_8)))
	elif y1 <= -3.3e-227:
		tmp = t_7
	elif y1 <= -3e-282:
		tmp = (k * ((y * ((i * y5) - (b * y4))) - (z * t_3))) + t_5
	elif y1 <= 120000.0:
		tmp = t_9
	elif y1 <= 1e+75:
		tmp = y5 * ((i * ((y * k) - (t * j))) - ((y0 * t_4) + (a * t_8)))
	elif y1 <= 8.4e+136:
		tmp = t_9
	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(Float64(b * y4) - Float64(i * y5))
	t_2 = Float64(Float64(a * y5) - Float64(c * y4))
	t_3 = Float64(Float64(i * y1) - Float64(b * y0))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(Float64(t_4 * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(Float64(Float64(t * y2) - Float64(y * y3)) * t_2))
	t_6 = Float64(y1 * Float64(Float64(a * Float64(Float64(z * y3) - Float64(x * y2))) + Float64(Float64(y4 * t_4) + Float64(i * Float64(Float64(x * j) - Float64(z * k))))))
	t_7 = Float64(j * Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(Float64(t * t_1) + Float64(x * t_3))))
	t_8 = Float64(Float64(y * y3) - Float64(t * y2))
	t_9 = Float64(t * Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(Float64(j * t_1) + Float64(y2 * t_2))))
	tmp = 0.0
	if (y1 <= -5.3e+125)
		tmp = t_6;
	elseif (y1 <= -4.3e+53)
		tmp = Float64(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_5);
	elseif (y1 <= -1.55e-49)
		tmp = t_7;
	elseif (y1 <= -1.9e-108)
		tmp = Float64(c * Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y4 * t_8))));
	elseif (y1 <= -3.3e-227)
		tmp = t_7;
	elseif (y1 <= -3e-282)
		tmp = Float64(Float64(k * Float64(Float64(y * Float64(Float64(i * y5) - Float64(b * y4))) - Float64(z * t_3))) + t_5);
	elseif (y1 <= 120000.0)
		tmp = t_9;
	elseif (y1 <= 1e+75)
		tmp = Float64(y5 * Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) - Float64(Float64(y0 * t_4) + Float64(a * t_8))));
	elseif (y1 <= 8.4e+136)
		tmp = t_9;
	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 * y4) - (i * y5);
	t_2 = (a * y5) - (c * y4);
	t_3 = (i * y1) - (b * y0);
	t_4 = (k * y2) - (j * y3);
	t_5 = (t_4 * ((y1 * y4) - (y0 * y5))) + (((t * y2) - (y * y3)) * t_2);
	t_6 = y1 * ((a * ((z * y3) - (x * y2))) + ((y4 * t_4) + (i * ((x * j) - (z * k)))));
	t_7 = j * ((y3 * ((y0 * y5) - (y1 * y4))) + ((t * t_1) + (x * t_3)));
	t_8 = (y * y3) - (t * y2);
	t_9 = t * ((z * ((c * i) - (a * b))) + ((j * t_1) + (y2 * t_2)));
	tmp = 0.0;
	if (y1 <= -5.3e+125)
		tmp = t_6;
	elseif (y1 <= -4.3e+53)
		tmp = (b * (((a * ((x * y) - (z * t))) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))) + t_5;
	elseif (y1 <= -1.55e-49)
		tmp = t_7;
	elseif (y1 <= -1.9e-108)
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_8)));
	elseif (y1 <= -3.3e-227)
		tmp = t_7;
	elseif (y1 <= -3e-282)
		tmp = (k * ((y * ((i * y5) - (b * y4))) - (z * t_3))) + t_5;
	elseif (y1 <= 120000.0)
		tmp = t_9;
	elseif (y1 <= 1e+75)
		tmp = y5 * ((i * ((y * k) - (t * j))) - ((y0 * t_4) + (a * t_8)));
	elseif (y1 <= 8.4e+136)
		tmp = t_9;
	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[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$4 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(y1 * N[(N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y4 * t$95$4), $MachinePrecision] + N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(j * N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * t$95$1), $MachinePrecision] + N[(x * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(t * N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * t$95$1), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -5.3e+125], t$95$6, If[LessEqual[y1, -4.3e+53], N[(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] + t$95$5), $MachinePrecision], If[LessEqual[y1, -1.55e-49], t$95$7, If[LessEqual[y1, -1.9e-108], N[(c * N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3.3e-227], t$95$7, If[LessEqual[y1, -3e-282], N[(N[(k * N[(N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision], If[LessEqual[y1, 120000.0], t$95$9, If[LessEqual[y1, 1e+75], N[(y5 * N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y0 * t$95$4), $MachinePrecision] + N[(a * t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 8.4e+136], t$95$9, t$95$6]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y1 < -5.3000000000000003e125 or 8.3999999999999996e136 < y1

   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 25.8%

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

   4. Taylor expanded in y1 around inf 63.5%

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

      1. mul-1-neg 63.5%

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

      2. *-commutative 63.5%

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

      3. *-commutative 63.5%

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

      4. *-commutative 63.5%

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

      5. mul-1-neg 63.5%

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

      6. *-commutative 63.5%

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

   6. Simplified 63.5%

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

   if -5.3000000000000003e125 < y1 < -4.2999999999999998e53

   1. Initial program 36.2%

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

   3. Simplified 36.2%

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

   4. Taylor expanded in b around inf 64.0%

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

   if -4.2999999999999998e53 < y1 < -1.55e-49 or -1.89999999999999987e-108 < y1 < -3.2999999999999999e-227

   1. Initial program 26.3%

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

   3. Simplified 26.3%

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

   4. Taylor expanded in j around inf 66.1%

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

      1. associate--l+ 66.1%

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

      2. mul-1-neg 66.1%

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

      3. *-commutative 66.1%

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

      4. *-commutative 66.1%

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

      5. *-commutative 66.1%

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

   6. Simplified 66.1%

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

   if -1.55e-49 < y1 < -1.89999999999999987e-108

   1. Initial program 46.3%

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

   3. Simplified 46.3%

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

   4. Taylor expanded in c around inf 55.1%

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

      1. associate--l+ 55.1%

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

      2. mul-1-neg 55.1%

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

      3. *-commutative 55.1%

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

   6. Simplified 55.1%

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

   if -3.2999999999999999e-227 < y1 < -3.0000000000000001e-282

   1. Initial program 49.3%

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

   3. Simplified 49.3%

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

   4. Taylor expanded in k around -inf 66.5%

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

      1. associate-*r* 66.5%

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

      2. sub-neg 66.5%

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

      3. mul-1-neg 66.5%

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

      4. *-commutative 66.5%

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

      5. associate-*r* 66.5%

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

      6. mul-1-neg 66.5%

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

      7. mul-1-neg 66.5%

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

      8. *-commutative 66.5%

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

      9. sub-neg 66.5%

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

   6. Simplified 66.5%

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

   if -3.0000000000000001e-282 < y1 < 1.2e5 or 9.99999999999999927e74 < y1 < 8.3999999999999996e136

   1. Initial program 45.0%

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

   3. Simplified 45.0%

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

   4. Taylor expanded in t around inf 62.1%

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

      1. associate--l+ 62.1%

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

      2. mul-1-neg 62.1%

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

      3. *-commutative 62.1%

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

      4. *-commutative 62.1%

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

      5. *-commutative 62.1%

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

      6. *-commutative 62.1%

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

      7. *-commutative 62.1%

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

   6. Simplified 62.1%

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

   if 1.2e5 < y1 < 9.99999999999999927e74

   1. Initial program 12.5%

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

   3. Simplified 12.5%

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

   4. Taylor expanded in y5 around -inf 62.5%

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

      1. mul-1-neg 62.5%

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

      2. associate--l+ 62.5%

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

      3. *-commutative 62.5%

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

   6. Simplified 62.5%

      \[\leadsto \color{blue}{-y5 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot i + \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -5.3 \cdot 10^{+125}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -4.3 \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) + \left(\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -1.55 \cdot 10^{-49}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -1.9 \cdot 10^{-108}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -3.3 \cdot 10^{-227}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y1 \leq -3 \cdot 10^{-282}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right) - z \cdot \left(i \cdot y1 - b \cdot y0\right)\right) + \left(\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 120000:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 10^{+75}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) - \left(y0 \cdot \left(k \cdot y2 - j \cdot y3\right) + a \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 8.4 \cdot 10^{+136}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \end{array} \]

Alternative 2: 53.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot y0 - a \cdot y1\right) \cdot \left(x \cdot y2 - z \cdot y3\right)\\ t_2 := y \cdot y3 - t \cdot y2\\ t_3 := b \cdot y0 - i \cdot y1\\ t_4 := a \cdot b - c \cdot i\\ t_5 := z \cdot k - x \cdot j\\ t_6 := x \cdot y - z \cdot t\\ t_7 := t \cdot j - y \cdot k\\ t_8 := k \cdot y2 - j \cdot y3\\ t_9 := b \cdot y4 - i \cdot y5\\ t_10 := y1 \cdot y4 - y0 \cdot y5\\ \mathbf{if}\;\left(\left(\left(\left(t_4 \cdot t_6 + t_3 \cdot t_5\right) + t_1\right) + t_7 \cdot t_9\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right) + t_8 \cdot t_10 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(t_8, t_10, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, t_2, \mathsf{fma}\left(t_6, t_4, \mathsf{fma}\left(t_3, t_5, \mathsf{fma}\left(t_7, t_9, t_1\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t_7 + y1 \cdot t_8\right) + c \cdot t_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (- (* c y0) (* a y1)) (- (* x y2) (* z y3))))
        (t_2 (- (* y y3) (* t y2)))
        (t_3 (- (* b y0) (* i y1)))
        (t_4 (- (* a b) (* c i)))
        (t_5 (- (* z k) (* x j)))
        (t_6 (- (* x y) (* z t)))
        (t_7 (- (* t j) (* y k)))
        (t_8 (- (* k y2) (* j y3)))
        (t_9 (- (* b y4) (* i y5)))
        (t_10 (- (* y1 y4) (* y0 y5))))
   (if (<=
        (+
         (+
          (+ (+ (+ (* t_4 t_6) (* t_3 t_5)) t_1) (* t_7 t_9))
          (* (- (* t y2) (* y y3)) (- (* a y5) (* c y4))))
         (* t_8 t_10))
        INFINITY)
     (fma
      t_8
      t_10
      (fma
       (- (* c y4) (* a y5))
       t_2
       (fma t_6 t_4 (fma t_3 t_5 (fma t_7 t_9 t_1)))))
     (* y4 (+ (+ (* b t_7) (* y1 t_8)) (* 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 = ((c * y0) - (a * y1)) * ((x * y2) - (z * y3));
	double t_2 = (y * y3) - (t * y2);
	double t_3 = (b * y0) - (i * y1);
	double t_4 = (a * b) - (c * i);
	double t_5 = (z * k) - (x * j);
	double t_6 = (x * y) - (z * t);
	double t_7 = (t * j) - (y * k);
	double t_8 = (k * y2) - (j * y3);
	double t_9 = (b * y4) - (i * y5);
	double t_10 = (y1 * y4) - (y0 * y5);
	double tmp;
	if (((((((t_4 * t_6) + (t_3 * t_5)) + t_1) + (t_7 * t_9)) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (t_8 * t_10)) <= ((double) INFINITY)) {
		tmp = fma(t_8, t_10, fma(((c * y4) - (a * y5)), t_2, fma(t_6, t_4, fma(t_3, t_5, fma(t_7, t_9, t_1)))));
	} else {
		tmp = y4 * (((b * t_7) + (y1 * t_8)) + (c * 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(Float64(c * y0) - Float64(a * y1)) * Float64(Float64(x * y2) - Float64(z * y3)))
	t_2 = Float64(Float64(y * y3) - Float64(t * y2))
	t_3 = Float64(Float64(b * y0) - Float64(i * y1))
	t_4 = Float64(Float64(a * b) - Float64(c * i))
	t_5 = Float64(Float64(z * k) - Float64(x * j))
	t_6 = Float64(Float64(x * y) - Float64(z * t))
	t_7 = Float64(Float64(t * j) - Float64(y * k))
	t_8 = Float64(Float64(k * y2) - Float64(j * y3))
	t_9 = Float64(Float64(b * y4) - Float64(i * y5))
	t_10 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(t_4 * t_6) + Float64(t_3 * t_5)) + t_1) + Float64(t_7 * t_9)) + Float64(Float64(Float64(t * y2) - Float64(y * y3)) * Float64(Float64(a * y5) - Float64(c * y4)))) + Float64(t_8 * t_10)) <= Inf)
		tmp = fma(t_8, t_10, fma(Float64(Float64(c * y4) - Float64(a * y5)), t_2, fma(t_6, t_4, fma(t_3, t_5, fma(t_7, t_9, t_1)))));
	else
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_7) + Float64(y1 * t_8)) + Float64(c * t_2)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(N[(N[(t$95$4 * t$95$6), $MachinePrecision] + N[(t$95$3 * t$95$5), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(t$95$7 * t$95$9), $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[(t$95$8 * t$95$10), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$8 * t$95$10 + N[(N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision] * t$95$2 + N[(t$95$6 * t$95$4 + N[(t$95$3 * t$95$5 + N[(t$95$7 * t$95$9 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(N[(N[(b * t$95$7), $MachinePrecision] + N[(y1 * t$95$8), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$2), $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 92.4%

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

   3. Simplified 92.4%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in y4 around inf 42.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.1%

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

Alternative 3: 53.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(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[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, Infinity], t$95$3, N[(y4 * N[(N[(N[(b * t$95$1), $MachinePrecision] + N[(y1 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $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 92.4%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in y4 around inf 42.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.0%

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

Alternative 4: 41.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot y5 - c \cdot y4\\ t_2 := y \cdot y3 - t \cdot y2\\ t_3 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t_2\right)\\ t_4 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_5 := c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot t_2\right)\right)\\ t_6 := y2 \cdot \left(t \cdot t_1 - \left(x \cdot \left(a \cdot y1 - c \cdot y0\right) + k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ \mathbf{if}\;y4 \leq -1.25 \cdot 10^{+105}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y4 \leq -1.26 \cdot 10^{-104}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y4 \leq -6.8 \cdot 10^{-148}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y4 \leq -1.1 \cdot 10^{-185}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y4 \leq 1.15 \cdot 10^{-160}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y4 \leq 1.12 \cdot 10^{-70}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y4 \leq 4.1 \cdot 10^{-13}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y4 \leq 1.6 \cdot 10^{+88}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y4 \leq 5.8 \cdot 10^{+107}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y4 \leq 5.6 \cdot 10^{+172} \lor \neg \left(y4 \leq 4.9 \cdot 10^{+207}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot y2\right) \cdot t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a y5) (* c y4)))
        (t_2 (- (* y y3) (* t y2)))
        (t_3
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c t_2))))
        (t_4
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
           (* j (- (* i y1) (* b y0))))))
        (t_5
         (*
          c
          (+
           (* i (- (* z t) (* x y)))
           (+ (* y0 (- (* x y2) (* z y3))) (* y4 t_2)))))
        (t_6
         (*
          y2
          (-
           (* t t_1)
           (+ (* x (- (* a y1) (* c y0))) (* k (- (* y0 y5) (* y1 y4))))))))
   (if (<= y4 -1.25e+105)
     t_3
     (if (<= y4 -1.26e-104)
       t_6
       (if (<= y4 -6.8e-148)
         t_3
         (if (<= y4 -1.1e-185)
           t_6
           (if (<= y4 1.15e-160)
             t_4
             (if (<= y4 1.12e-70)
               t_5
               (if (<= y4 4.1e-13)
                 t_6
                 (if (<= y4 1.6e+88)
                   t_5
                   (if (<= y4 5.8e+107)
                     t_4
                     (if (or (<= y4 5.6e+172) (not (<= y4 4.9e+207)))
                       t_3
                       (* (* t y2) t_1)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y5) - (c * y4);
	double t_2 = (y * y3) - (t * y2);
	double t_3 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2));
	double t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double t_5 = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_2)));
	double t_6 = y2 * ((t * t_1) - ((x * ((a * y1) - (c * y0))) + (k * ((y0 * y5) - (y1 * y4)))));
	double tmp;
	if (y4 <= -1.25e+105) {
		tmp = t_3;
	} else if (y4 <= -1.26e-104) {
		tmp = t_6;
	} else if (y4 <= -6.8e-148) {
		tmp = t_3;
	} else if (y4 <= -1.1e-185) {
		tmp = t_6;
	} else if (y4 <= 1.15e-160) {
		tmp = t_4;
	} else if (y4 <= 1.12e-70) {
		tmp = t_5;
	} else if (y4 <= 4.1e-13) {
		tmp = t_6;
	} else if (y4 <= 1.6e+88) {
		tmp = t_5;
	} else if (y4 <= 5.8e+107) {
		tmp = t_4;
	} else if ((y4 <= 5.6e+172) || !(y4 <= 4.9e+207)) {
		tmp = t_3;
	} else {
		tmp = (t * y2) * t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = (a * y5) - (c * y4)
    t_2 = (y * y3) - (t * y2)
    t_3 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2))
    t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    t_5 = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_2)))
    t_6 = y2 * ((t * t_1) - ((x * ((a * y1) - (c * y0))) + (k * ((y0 * y5) - (y1 * y4)))))
    if (y4 <= (-1.25d+105)) then
        tmp = t_3
    else if (y4 <= (-1.26d-104)) then
        tmp = t_6
    else if (y4 <= (-6.8d-148)) then
        tmp = t_3
    else if (y4 <= (-1.1d-185)) then
        tmp = t_6
    else if (y4 <= 1.15d-160) then
        tmp = t_4
    else if (y4 <= 1.12d-70) then
        tmp = t_5
    else if (y4 <= 4.1d-13) then
        tmp = t_6
    else if (y4 <= 1.6d+88) then
        tmp = t_5
    else if (y4 <= 5.8d+107) then
        tmp = t_4
    else if ((y4 <= 5.6d+172) .or. (.not. (y4 <= 4.9d+207))) then
        tmp = t_3
    else
        tmp = (t * y2) * t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y5) - (c * y4);
	double t_2 = (y * y3) - (t * y2);
	double t_3 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2));
	double t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double t_5 = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_2)));
	double t_6 = y2 * ((t * t_1) - ((x * ((a * y1) - (c * y0))) + (k * ((y0 * y5) - (y1 * y4)))));
	double tmp;
	if (y4 <= -1.25e+105) {
		tmp = t_3;
	} else if (y4 <= -1.26e-104) {
		tmp = t_6;
	} else if (y4 <= -6.8e-148) {
		tmp = t_3;
	} else if (y4 <= -1.1e-185) {
		tmp = t_6;
	} else if (y4 <= 1.15e-160) {
		tmp = t_4;
	} else if (y4 <= 1.12e-70) {
		tmp = t_5;
	} else if (y4 <= 4.1e-13) {
		tmp = t_6;
	} else if (y4 <= 1.6e+88) {
		tmp = t_5;
	} else if (y4 <= 5.8e+107) {
		tmp = t_4;
	} else if ((y4 <= 5.6e+172) || !(y4 <= 4.9e+207)) {
		tmp = t_3;
	} else {
		tmp = (t * y2) * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (a * y5) - (c * y4)
	t_2 = (y * y3) - (t * y2)
	t_3 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2))
	t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	t_5 = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_2)))
	t_6 = y2 * ((t * t_1) - ((x * ((a * y1) - (c * y0))) + (k * ((y0 * y5) - (y1 * y4)))))
	tmp = 0
	if y4 <= -1.25e+105:
		tmp = t_3
	elif y4 <= -1.26e-104:
		tmp = t_6
	elif y4 <= -6.8e-148:
		tmp = t_3
	elif y4 <= -1.1e-185:
		tmp = t_6
	elif y4 <= 1.15e-160:
		tmp = t_4
	elif y4 <= 1.12e-70:
		tmp = t_5
	elif y4 <= 4.1e-13:
		tmp = t_6
	elif y4 <= 1.6e+88:
		tmp = t_5
	elif y4 <= 5.8e+107:
		tmp = t_4
	elif (y4 <= 5.6e+172) or not (y4 <= 4.9e+207):
		tmp = t_3
	else:
		tmp = (t * y2) * t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(a * y5) - Float64(c * y4))
	t_2 = Float64(Float64(y * y3) - Float64(t * y2))
	t_3 = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * t_2)))
	t_4 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_5 = Float64(c * Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y4 * t_2))))
	t_6 = Float64(y2 * Float64(Float64(t * t_1) - Float64(Float64(x * Float64(Float64(a * y1) - Float64(c * y0))) + Float64(k * Float64(Float64(y0 * y5) - Float64(y1 * y4))))))
	tmp = 0.0
	if (y4 <= -1.25e+105)
		tmp = t_3;
	elseif (y4 <= -1.26e-104)
		tmp = t_6;
	elseif (y4 <= -6.8e-148)
		tmp = t_3;
	elseif (y4 <= -1.1e-185)
		tmp = t_6;
	elseif (y4 <= 1.15e-160)
		tmp = t_4;
	elseif (y4 <= 1.12e-70)
		tmp = t_5;
	elseif (y4 <= 4.1e-13)
		tmp = t_6;
	elseif (y4 <= 1.6e+88)
		tmp = t_5;
	elseif (y4 <= 5.8e+107)
		tmp = t_4;
	elseif ((y4 <= 5.6e+172) || !(y4 <= 4.9e+207))
		tmp = t_3;
	else
		tmp = Float64(Float64(t * y2) * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (a * y5) - (c * y4);
	t_2 = (y * y3) - (t * y2);
	t_3 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2));
	t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	t_5 = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_2)));
	t_6 = y2 * ((t * t_1) - ((x * ((a * y1) - (c * y0))) + (k * ((y0 * y5) - (y1 * y4)))));
	tmp = 0.0;
	if (y4 <= -1.25e+105)
		tmp = t_3;
	elseif (y4 <= -1.26e-104)
		tmp = t_6;
	elseif (y4 <= -6.8e-148)
		tmp = t_3;
	elseif (y4 <= -1.1e-185)
		tmp = t_6;
	elseif (y4 <= 1.15e-160)
		tmp = t_4;
	elseif (y4 <= 1.12e-70)
		tmp = t_5;
	elseif (y4 <= 4.1e-13)
		tmp = t_6;
	elseif (y4 <= 1.6e+88)
		tmp = t_5;
	elseif (y4 <= 5.8e+107)
		tmp = t_4;
	elseif ((y4 <= 5.6e+172) || ~((y4 <= 4.9e+207)))
		tmp = t_3;
	else
		tmp = (t * y2) * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(c * N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(y2 * N[(N[(t * t$95$1), $MachinePrecision] - N[(N[(x * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -1.25e+105], t$95$3, If[LessEqual[y4, -1.26e-104], t$95$6, If[LessEqual[y4, -6.8e-148], t$95$3, If[LessEqual[y4, -1.1e-185], t$95$6, If[LessEqual[y4, 1.15e-160], t$95$4, If[LessEqual[y4, 1.12e-70], t$95$5, If[LessEqual[y4, 4.1e-13], t$95$6, If[LessEqual[y4, 1.6e+88], t$95$5, If[LessEqual[y4, 5.8e+107], t$95$4, If[Or[LessEqual[y4, 5.6e+172], N[Not[LessEqual[y4, 4.9e+207]], $MachinePrecision]], t$95$3, N[(N[(t * y2), $MachinePrecision] * t$95$1), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y4 < -1.25000000000000011e105 or -1.26e-104 < y4 < -6.8000000000000005e-148 or 5.79999999999999975e107 < y4 < 5.5999999999999999e172 or 4.9e207 < y4

   1. Initial program 29.1%

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

   3. Simplified 29.1%

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

   4. Taylor expanded in y4 around inf 69.6%

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

   if -1.25000000000000011e105 < y4 < -1.26e-104 or -6.8000000000000005e-148 < y4 < -1.1e-185 or 1.12e-70 < y4 < 4.1000000000000002e-13

   1. Initial program 37.1%

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

   3. Simplified 37.1%

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

   4. Taylor expanded in y2 around inf 54.7%

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

   if -1.1e-185 < y4 < 1.14999999999999992e-160 or 1.5999999999999999e88 < y4 < 5.79999999999999975e107

   1. Initial program 34.0%

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

   3. Simplified 34.0%

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

   4. Taylor expanded in x around inf 58.8%

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

   if 1.14999999999999992e-160 < y4 < 1.12e-70 or 4.1000000000000002e-13 < y4 < 1.5999999999999999e88

   1. Initial program 31.0%

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

   3. Simplified 31.0%

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

   4. Taylor expanded in c around inf 59.1%

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

      1. associate--l+ 59.1%

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

      2. mul-1-neg 59.1%

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

      3. *-commutative 59.1%

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

   6. Simplified 59.1%

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

   if 5.5999999999999999e172 < y4 < 4.9e207

   1. Initial program 14.3%

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

   3. Simplified 14.3%

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

   4. Taylor expanded in t around inf 85.8%

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

      1. associate--l+ 85.8%

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

      2. mul-1-neg 85.8%

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

      3. *-commutative 85.8%

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

      4. *-commutative 85.8%

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

      5. *-commutative 85.8%

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

      6. *-commutative 85.8%

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

      7. *-commutative 85.8%

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

   6. Simplified 85.8%

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

   7. Taylor expanded in y2 around inf 72.5%

      \[\leadsto \color{blue}{\left(a \cdot y5 - c \cdot y4\right) \cdot \left(t \cdot y2\right)} \]
   8. Step-by-step derivation

      1. *-commutative 72.5%

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

      2. *-commutative 72.5%

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

   9. Simplified 72.5%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.25 \cdot 10^{+105}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -1.26 \cdot 10^{-104}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right) - \left(x \cdot \left(a \cdot y1 - c \cdot y0\right) + k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -6.8 \cdot 10^{-148}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -1.1 \cdot 10^{-185}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right) - \left(x \cdot \left(a \cdot y1 - c \cdot y0\right) + k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 1.15 \cdot 10^{-160}:\\ \;\;\;\;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}\;y4 \leq 1.12 \cdot 10^{-70}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 4.1 \cdot 10^{-13}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right) - \left(x \cdot \left(a \cdot y1 - c \cdot y0\right) + k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 1.6 \cdot 10^{+88}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 5.8 \cdot 10^{+107}:\\ \;\;\;\;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}\;y4 \leq 5.6 \cdot 10^{+172} \lor \neg \left(y4 \leq 4.9 \cdot 10^{+207}\right):\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot y2\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\\ \end{array} \]

Alternative 5: 41.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot y5 - c \cdot y4\\ t_2 := i \cdot y1 - b \cdot y0\\ t_3 := y \cdot y3 - t \cdot y2\\ t_4 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t_3\right)\\ t_5 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot t_2\right)\\ t_6 := c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot t_3\right)\right)\\ t_7 := y0 \cdot y5 - y1 \cdot y4\\ t_8 := y2 \cdot \left(t \cdot t_1 - \left(x \cdot \left(a \cdot y1 - c \cdot y0\right) + k \cdot t_7\right)\right)\\ \mathbf{if}\;y4 \leq -1.5 \cdot 10^{+105}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y4 \leq -4.1 \cdot 10^{-103}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;y4 \leq -4.8 \cdot 10^{-142}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y4 \leq -2 \cdot 10^{-185}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;y4 \leq 2.05 \cdot 10^{-160}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y4 \leq 8.2 \cdot 10^{-79}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y4 \leq 7.9 \cdot 10^{-13}:\\ \;\;\;\;j \cdot \left(y3 \cdot t_7 + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + x \cdot t_2\right)\right)\\ \mathbf{elif}\;y4 \leq 1.95 \cdot 10^{+89}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y4 \leq 9.2 \cdot 10^{+107}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y4 \leq 3.2 \cdot 10^{+172} \lor \neg \left(y4 \leq 4.1 \cdot 10^{+207}\right):\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot y2\right) \cdot t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a y5) (* c y4)))
        (t_2 (- (* i y1) (* b y0)))
        (t_3 (- (* y y3) (* t y2)))
        (t_4
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c t_3))))
        (t_5
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
           (* j t_2))))
        (t_6
         (*
          c
          (+
           (* i (- (* z t) (* x y)))
           (+ (* y0 (- (* x y2) (* z y3))) (* y4 t_3)))))
        (t_7 (- (* y0 y5) (* y1 y4)))
        (t_8 (* y2 (- (* t t_1) (+ (* x (- (* a y1) (* c y0))) (* k t_7))))))
   (if (<= y4 -1.5e+105)
     t_4
     (if (<= y4 -4.1e-103)
       t_8
       (if (<= y4 -4.8e-142)
         t_4
         (if (<= y4 -2e-185)
           t_8
           (if (<= y4 2.05e-160)
             t_5
             (if (<= y4 8.2e-79)
               t_6
               (if (<= y4 7.9e-13)
                 (* j (+ (* y3 t_7) (+ (* t (- (* b y4) (* i y5))) (* x t_2))))
                 (if (<= y4 1.95e+89)
                   t_6
                   (if (<= y4 9.2e+107)
                     t_5
                     (if (or (<= y4 3.2e+172) (not (<= y4 4.1e+207)))
                       t_4
                       (* (* t y2) t_1)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y5) - (c * y4);
	double t_2 = (i * y1) - (b * y0);
	double t_3 = (y * y3) - (t * y2);
	double t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3));
	double t_5 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_2));
	double t_6 = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_3)));
	double t_7 = (y0 * y5) - (y1 * y4);
	double t_8 = y2 * ((t * t_1) - ((x * ((a * y1) - (c * y0))) + (k * t_7)));
	double tmp;
	if (y4 <= -1.5e+105) {
		tmp = t_4;
	} else if (y4 <= -4.1e-103) {
		tmp = t_8;
	} else if (y4 <= -4.8e-142) {
		tmp = t_4;
	} else if (y4 <= -2e-185) {
		tmp = t_8;
	} else if (y4 <= 2.05e-160) {
		tmp = t_5;
	} else if (y4 <= 8.2e-79) {
		tmp = t_6;
	} else if (y4 <= 7.9e-13) {
		tmp = j * ((y3 * t_7) + ((t * ((b * y4) - (i * y5))) + (x * t_2)));
	} else if (y4 <= 1.95e+89) {
		tmp = t_6;
	} else if (y4 <= 9.2e+107) {
		tmp = t_5;
	} else if ((y4 <= 3.2e+172) || !(y4 <= 4.1e+207)) {
		tmp = t_4;
	} else {
		tmp = (t * y2) * t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_1 = (a * y5) - (c * y4)
    t_2 = (i * y1) - (b * y0)
    t_3 = (y * y3) - (t * y2)
    t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3))
    t_5 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_2))
    t_6 = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_3)))
    t_7 = (y0 * y5) - (y1 * y4)
    t_8 = y2 * ((t * t_1) - ((x * ((a * y1) - (c * y0))) + (k * t_7)))
    if (y4 <= (-1.5d+105)) then
        tmp = t_4
    else if (y4 <= (-4.1d-103)) then
        tmp = t_8
    else if (y4 <= (-4.8d-142)) then
        tmp = t_4
    else if (y4 <= (-2d-185)) then
        tmp = t_8
    else if (y4 <= 2.05d-160) then
        tmp = t_5
    else if (y4 <= 8.2d-79) then
        tmp = t_6
    else if (y4 <= 7.9d-13) then
        tmp = j * ((y3 * t_7) + ((t * ((b * y4) - (i * y5))) + (x * t_2)))
    else if (y4 <= 1.95d+89) then
        tmp = t_6
    else if (y4 <= 9.2d+107) then
        tmp = t_5
    else if ((y4 <= 3.2d+172) .or. (.not. (y4 <= 4.1d+207))) then
        tmp = t_4
    else
        tmp = (t * y2) * t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y5) - (c * y4);
	double t_2 = (i * y1) - (b * y0);
	double t_3 = (y * y3) - (t * y2);
	double t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3));
	double t_5 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_2));
	double t_6 = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_3)));
	double t_7 = (y0 * y5) - (y1 * y4);
	double t_8 = y2 * ((t * t_1) - ((x * ((a * y1) - (c * y0))) + (k * t_7)));
	double tmp;
	if (y4 <= -1.5e+105) {
		tmp = t_4;
	} else if (y4 <= -4.1e-103) {
		tmp = t_8;
	} else if (y4 <= -4.8e-142) {
		tmp = t_4;
	} else if (y4 <= -2e-185) {
		tmp = t_8;
	} else if (y4 <= 2.05e-160) {
		tmp = t_5;
	} else if (y4 <= 8.2e-79) {
		tmp = t_6;
	} else if (y4 <= 7.9e-13) {
		tmp = j * ((y3 * t_7) + ((t * ((b * y4) - (i * y5))) + (x * t_2)));
	} else if (y4 <= 1.95e+89) {
		tmp = t_6;
	} else if (y4 <= 9.2e+107) {
		tmp = t_5;
	} else if ((y4 <= 3.2e+172) || !(y4 <= 4.1e+207)) {
		tmp = t_4;
	} else {
		tmp = (t * y2) * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (a * y5) - (c * y4)
	t_2 = (i * y1) - (b * y0)
	t_3 = (y * y3) - (t * y2)
	t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3))
	t_5 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_2))
	t_6 = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_3)))
	t_7 = (y0 * y5) - (y1 * y4)
	t_8 = y2 * ((t * t_1) - ((x * ((a * y1) - (c * y0))) + (k * t_7)))
	tmp = 0
	if y4 <= -1.5e+105:
		tmp = t_4
	elif y4 <= -4.1e-103:
		tmp = t_8
	elif y4 <= -4.8e-142:
		tmp = t_4
	elif y4 <= -2e-185:
		tmp = t_8
	elif y4 <= 2.05e-160:
		tmp = t_5
	elif y4 <= 8.2e-79:
		tmp = t_6
	elif y4 <= 7.9e-13:
		tmp = j * ((y3 * t_7) + ((t * ((b * y4) - (i * y5))) + (x * t_2)))
	elif y4 <= 1.95e+89:
		tmp = t_6
	elif y4 <= 9.2e+107:
		tmp = t_5
	elif (y4 <= 3.2e+172) or not (y4 <= 4.1e+207):
		tmp = t_4
	else:
		tmp = (t * y2) * t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(a * y5) - Float64(c * y4))
	t_2 = Float64(Float64(i * y1) - Float64(b * y0))
	t_3 = Float64(Float64(y * y3) - Float64(t * y2))
	t_4 = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * t_3)))
	t_5 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * t_2)))
	t_6 = Float64(c * Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y4 * t_3))))
	t_7 = Float64(Float64(y0 * y5) - Float64(y1 * y4))
	t_8 = Float64(y2 * Float64(Float64(t * t_1) - Float64(Float64(x * Float64(Float64(a * y1) - Float64(c * y0))) + Float64(k * t_7))))
	tmp = 0.0
	if (y4 <= -1.5e+105)
		tmp = t_4;
	elseif (y4 <= -4.1e-103)
		tmp = t_8;
	elseif (y4 <= -4.8e-142)
		tmp = t_4;
	elseif (y4 <= -2e-185)
		tmp = t_8;
	elseif (y4 <= 2.05e-160)
		tmp = t_5;
	elseif (y4 <= 8.2e-79)
		tmp = t_6;
	elseif (y4 <= 7.9e-13)
		tmp = Float64(j * Float64(Float64(y3 * t_7) + Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(x * t_2))));
	elseif (y4 <= 1.95e+89)
		tmp = t_6;
	elseif (y4 <= 9.2e+107)
		tmp = t_5;
	elseif ((y4 <= 3.2e+172) || !(y4 <= 4.1e+207))
		tmp = t_4;
	else
		tmp = Float64(Float64(t * y2) * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (a * y5) - (c * y4);
	t_2 = (i * y1) - (b * y0);
	t_3 = (y * y3) - (t * y2);
	t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3));
	t_5 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_2));
	t_6 = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_3)));
	t_7 = (y0 * y5) - (y1 * y4);
	t_8 = y2 * ((t * t_1) - ((x * ((a * y1) - (c * y0))) + (k * t_7)));
	tmp = 0.0;
	if (y4 <= -1.5e+105)
		tmp = t_4;
	elseif (y4 <= -4.1e-103)
		tmp = t_8;
	elseif (y4 <= -4.8e-142)
		tmp = t_4;
	elseif (y4 <= -2e-185)
		tmp = t_8;
	elseif (y4 <= 2.05e-160)
		tmp = t_5;
	elseif (y4 <= 8.2e-79)
		tmp = t_6;
	elseif (y4 <= 7.9e-13)
		tmp = j * ((y3 * t_7) + ((t * ((b * y4) - (i * y5))) + (x * t_2)));
	elseif (y4 <= 1.95e+89)
		tmp = t_6;
	elseif (y4 <= 9.2e+107)
		tmp = t_5;
	elseif ((y4 <= 3.2e+172) || ~((y4 <= 4.1e+207)))
		tmp = t_4;
	else
		tmp = (t * y2) * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(c * N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(y2 * N[(N[(t * t$95$1), $MachinePrecision] - N[(N[(x * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -1.5e+105], t$95$4, If[LessEqual[y4, -4.1e-103], t$95$8, If[LessEqual[y4, -4.8e-142], t$95$4, If[LessEqual[y4, -2e-185], t$95$8, If[LessEqual[y4, 2.05e-160], t$95$5, If[LessEqual[y4, 8.2e-79], t$95$6, If[LessEqual[y4, 7.9e-13], N[(j * N[(N[(y3 * t$95$7), $MachinePrecision] + N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.95e+89], t$95$6, If[LessEqual[y4, 9.2e+107], t$95$5, If[Or[LessEqual[y4, 3.2e+172], N[Not[LessEqual[y4, 4.1e+207]], $MachinePrecision]], t$95$4, N[(N[(t * y2), $MachinePrecision] * t$95$1), $MachinePrecision]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y4 < -1.5e105 or -4.09999999999999996e-103 < y4 < -4.79999999999999976e-142 or 9.2000000000000001e107 < y4 < 3.19999999999999985e172 or 4.1e207 < y4

   1. Initial program 29.1%

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

   3. Simplified 29.1%

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

   4. Taylor expanded in y4 around inf 69.6%

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

   if -1.5e105 < y4 < -4.09999999999999996e-103 or -4.79999999999999976e-142 < y4 < -2e-185

   1. Initial program 42.6%

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

   3. Simplified 42.6%

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

   4. Taylor expanded in y2 around inf 54.1%

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

   if -2e-185 < y4 < 2.05000000000000001e-160 or 1.95000000000000005e89 < y4 < 9.2000000000000001e107

   1. Initial program 34.0%

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

   3. Simplified 34.0%

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

   4. Taylor expanded in x around inf 58.8%

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

   if 2.05000000000000001e-160 < y4 < 8.19999999999999987e-79 or 7.89999999999999966e-13 < y4 < 1.95000000000000005e89

   1. Initial program 33.3%

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

   3. Simplified 33.3%

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

   4. Taylor expanded in c around inf 59.6%

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

      1. associate--l+ 59.6%

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

      2. mul-1-neg 59.6%

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

      3. *-commutative 59.6%

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

   6. Simplified 59.6%

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

   if 8.19999999999999987e-79 < y4 < 7.89999999999999966e-13

   1. Initial program 13.2%

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

   3. Simplified 13.2%

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

   4. Taylor expanded in j around inf 63.0%

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

      1. associate--l+ 63.0%

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

      2. mul-1-neg 63.0%

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

      3. *-commutative 63.0%

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

      4. *-commutative 63.0%

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

      5. *-commutative 63.0%

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

   6. Simplified 63.0%

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

   if 3.19999999999999985e172 < y4 < 4.1e207

   1. Initial program 14.3%

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

   3. Simplified 14.3%

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

   4. Taylor expanded in t around inf 85.8%

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

      1. associate--l+ 85.8%

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

      2. mul-1-neg 85.8%

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

      3. *-commutative 85.8%

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

      4. *-commutative 85.8%

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

      5. *-commutative 85.8%

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

      6. *-commutative 85.8%

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

      7. *-commutative 85.8%

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

   6. Simplified 85.8%

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

   7. Taylor expanded in y2 around inf 72.5%

      \[\leadsto \color{blue}{\left(a \cdot y5 - c \cdot y4\right) \cdot \left(t \cdot y2\right)} \]
   8. Step-by-step derivation

      1. *-commutative 72.5%

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

      2. *-commutative 72.5%

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

   9. Simplified 72.5%

      \[\leadsto \color{blue}{\left(y5 \cdot a - y4 \cdot c\right) \cdot \left(t \cdot y2\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.5 \cdot 10^{+105}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -4.1 \cdot 10^{-103}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right) - \left(x \cdot \left(a \cdot y1 - c \cdot y0\right) + k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -4.8 \cdot 10^{-142}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -2 \cdot 10^{-185}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right) - \left(x \cdot \left(a \cdot y1 - c \cdot y0\right) + k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 2.05 \cdot 10^{-160}:\\ \;\;\;\;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}\;y4 \leq 8.2 \cdot 10^{-79}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 7.9 \cdot 10^{-13}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 1.95 \cdot 10^{+89}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 9.2 \cdot 10^{+107}:\\ \;\;\;\;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}\;y4 \leq 3.2 \cdot 10^{+172} \lor \neg \left(y4 \leq 4.1 \cdot 10^{+207}\right):\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot y2\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\\ \end{array} \]

Alternative 6: 41.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot y3 - t \cdot y2\\ t_2 := a \cdot y5 - c \cdot y4\\ t_3 := i \cdot y1 - b \cdot y0\\ t_4 := y0 \cdot y5 - y1 \cdot y4\\ t_5 := b \cdot y4 - i \cdot y5\\ t_6 := t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(j \cdot t_5 + y2 \cdot t_2\right)\right)\\ t_7 := x \cdot y2 - z \cdot y3\\ t_8 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right) + \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) - y1 \cdot t_7\right)\right)\\ t_9 := y2 \cdot \left(t \cdot t_2 - \left(x \cdot \left(a \cdot y1 - c \cdot y0\right) + k \cdot t_4\right)\right)\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+117}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{+63}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{+55}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-24}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-197}:\\ \;\;\;\;j \cdot \left(y3 \cdot t_4 + \left(t \cdot t_5 + x \cdot t_3\right)\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-273}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot t_3\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-152}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t_1\right)\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-66}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+33}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot t_7 + y4 \cdot t_1\right)\right)\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+215}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_8\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y y3) (* t y2)))
        (t_2 (- (* a y5) (* c y4)))
        (t_3 (- (* i y1) (* b y0)))
        (t_4 (- (* y0 y5) (* y1 y4)))
        (t_5 (- (* b y4) (* i y5)))
        (t_6 (* t (+ (* z (- (* c i) (* a b))) (+ (* j t_5) (* y2 t_2)))))
        (t_7 (- (* x y2) (* z y3)))
        (t_8
         (*
          a
          (+
           (* b (- (* x y) (* z t)))
           (- (* y5 (- (* t y2) (* y y3))) (* y1 t_7)))))
        (t_9 (* y2 (- (* t t_2) (+ (* x (- (* a y1) (* c y0))) (* k t_4))))))
   (if (<= a -1.9e+117)
     t_8
     (if (<= a -1.55e+63)
       (* y0 (* k (- (* z b) (* y2 y5))))
       (if (<= a -8.2e+55)
         t_9
         (if (<= a -4.4e-24)
           t_6
           (if (<= a -4.8e-197)
             (* j (+ (* y3 t_4) (+ (* t t_5) (* x t_3))))
             (if (<= a 1.05e-273)
               (*
                x
                (+
                 (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
                 (* j t_3)))
               (if (<= a 1.45e-152)
                 (*
                  y4
                  (+
                   (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
                   (* c t_1)))
                 (if (<= a 1.12e-66)
                   t_9
                   (if (<= a 7e+33)
                     (*
                      c
                      (+ (* i (- (* z t) (* x y))) (+ (* y0 t_7) (* y4 t_1))))
                     (if (<= a 8.8e+215) t_6 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 = (y * y3) - (t * y2);
	double t_2 = (a * y5) - (c * y4);
	double t_3 = (i * y1) - (b * y0);
	double t_4 = (y0 * y5) - (y1 * y4);
	double t_5 = (b * y4) - (i * y5);
	double t_6 = t * ((z * ((c * i) - (a * b))) + ((j * t_5) + (y2 * t_2)));
	double t_7 = (x * y2) - (z * y3);
	double t_8 = a * ((b * ((x * y) - (z * t))) + ((y5 * ((t * y2) - (y * y3))) - (y1 * t_7)));
	double t_9 = y2 * ((t * t_2) - ((x * ((a * y1) - (c * y0))) + (k * t_4)));
	double tmp;
	if (a <= -1.9e+117) {
		tmp = t_8;
	} else if (a <= -1.55e+63) {
		tmp = y0 * (k * ((z * b) - (y2 * y5)));
	} else if (a <= -8.2e+55) {
		tmp = t_9;
	} else if (a <= -4.4e-24) {
		tmp = t_6;
	} else if (a <= -4.8e-197) {
		tmp = j * ((y3 * t_4) + ((t * t_5) + (x * t_3)));
	} else if (a <= 1.05e-273) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_3));
	} else if (a <= 1.45e-152) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1));
	} else if (a <= 1.12e-66) {
		tmp = t_9;
	} else if (a <= 7e+33) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_7) + (y4 * t_1)));
	} else if (a <= 8.8e+215) {
		tmp = t_6;
	} 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 = (y * y3) - (t * y2)
    t_2 = (a * y5) - (c * y4)
    t_3 = (i * y1) - (b * y0)
    t_4 = (y0 * y5) - (y1 * y4)
    t_5 = (b * y4) - (i * y5)
    t_6 = t * ((z * ((c * i) - (a * b))) + ((j * t_5) + (y2 * t_2)))
    t_7 = (x * y2) - (z * y3)
    t_8 = a * ((b * ((x * y) - (z * t))) + ((y5 * ((t * y2) - (y * y3))) - (y1 * t_7)))
    t_9 = y2 * ((t * t_2) - ((x * ((a * y1) - (c * y0))) + (k * t_4)))
    if (a <= (-1.9d+117)) then
        tmp = t_8
    else if (a <= (-1.55d+63)) then
        tmp = y0 * (k * ((z * b) - (y2 * y5)))
    else if (a <= (-8.2d+55)) then
        tmp = t_9
    else if (a <= (-4.4d-24)) then
        tmp = t_6
    else if (a <= (-4.8d-197)) then
        tmp = j * ((y3 * t_4) + ((t * t_5) + (x * t_3)))
    else if (a <= 1.05d-273) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_3))
    else if (a <= 1.45d-152) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1))
    else if (a <= 1.12d-66) then
        tmp = t_9
    else if (a <= 7d+33) then
        tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_7) + (y4 * t_1)))
    else if (a <= 8.8d+215) then
        tmp = t_6
    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 = (y * y3) - (t * y2);
	double t_2 = (a * y5) - (c * y4);
	double t_3 = (i * y1) - (b * y0);
	double t_4 = (y0 * y5) - (y1 * y4);
	double t_5 = (b * y4) - (i * y5);
	double t_6 = t * ((z * ((c * i) - (a * b))) + ((j * t_5) + (y2 * t_2)));
	double t_7 = (x * y2) - (z * y3);
	double t_8 = a * ((b * ((x * y) - (z * t))) + ((y5 * ((t * y2) - (y * y3))) - (y1 * t_7)));
	double t_9 = y2 * ((t * t_2) - ((x * ((a * y1) - (c * y0))) + (k * t_4)));
	double tmp;
	if (a <= -1.9e+117) {
		tmp = t_8;
	} else if (a <= -1.55e+63) {
		tmp = y0 * (k * ((z * b) - (y2 * y5)));
	} else if (a <= -8.2e+55) {
		tmp = t_9;
	} else if (a <= -4.4e-24) {
		tmp = t_6;
	} else if (a <= -4.8e-197) {
		tmp = j * ((y3 * t_4) + ((t * t_5) + (x * t_3)));
	} else if (a <= 1.05e-273) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_3));
	} else if (a <= 1.45e-152) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1));
	} else if (a <= 1.12e-66) {
		tmp = t_9;
	} else if (a <= 7e+33) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_7) + (y4 * t_1)));
	} else if (a <= 8.8e+215) {
		tmp = t_6;
	} 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 = (y * y3) - (t * y2)
	t_2 = (a * y5) - (c * y4)
	t_3 = (i * y1) - (b * y0)
	t_4 = (y0 * y5) - (y1 * y4)
	t_5 = (b * y4) - (i * y5)
	t_6 = t * ((z * ((c * i) - (a * b))) + ((j * t_5) + (y2 * t_2)))
	t_7 = (x * y2) - (z * y3)
	t_8 = a * ((b * ((x * y) - (z * t))) + ((y5 * ((t * y2) - (y * y3))) - (y1 * t_7)))
	t_9 = y2 * ((t * t_2) - ((x * ((a * y1) - (c * y0))) + (k * t_4)))
	tmp = 0
	if a <= -1.9e+117:
		tmp = t_8
	elif a <= -1.55e+63:
		tmp = y0 * (k * ((z * b) - (y2 * y5)))
	elif a <= -8.2e+55:
		tmp = t_9
	elif a <= -4.4e-24:
		tmp = t_6
	elif a <= -4.8e-197:
		tmp = j * ((y3 * t_4) + ((t * t_5) + (x * t_3)))
	elif a <= 1.05e-273:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_3))
	elif a <= 1.45e-152:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1))
	elif a <= 1.12e-66:
		tmp = t_9
	elif a <= 7e+33:
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_7) + (y4 * t_1)))
	elif a <= 8.8e+215:
		tmp = t_6
	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(y * y3) - Float64(t * y2))
	t_2 = Float64(Float64(a * y5) - Float64(c * y4))
	t_3 = Float64(Float64(i * y1) - Float64(b * y0))
	t_4 = Float64(Float64(y0 * y5) - Float64(y1 * y4))
	t_5 = Float64(Float64(b * y4) - Float64(i * y5))
	t_6 = Float64(t * Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(Float64(j * t_5) + Float64(y2 * t_2))))
	t_7 = Float64(Float64(x * y2) - Float64(z * y3))
	t_8 = Float64(a * Float64(Float64(b * Float64(Float64(x * y) - Float64(z * t))) + Float64(Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))) - Float64(y1 * t_7))))
	t_9 = Float64(y2 * Float64(Float64(t * t_2) - Float64(Float64(x * Float64(Float64(a * y1) - Float64(c * y0))) + Float64(k * t_4))))
	tmp = 0.0
	if (a <= -1.9e+117)
		tmp = t_8;
	elseif (a <= -1.55e+63)
		tmp = Float64(y0 * Float64(k * Float64(Float64(z * b) - Float64(y2 * y5))));
	elseif (a <= -8.2e+55)
		tmp = t_9;
	elseif (a <= -4.4e-24)
		tmp = t_6;
	elseif (a <= -4.8e-197)
		tmp = Float64(j * Float64(Float64(y3 * t_4) + Float64(Float64(t * t_5) + Float64(x * t_3))));
	elseif (a <= 1.05e-273)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * t_3)));
	elseif (a <= 1.45e-152)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * t_1)));
	elseif (a <= 1.12e-66)
		tmp = t_9;
	elseif (a <= 7e+33)
		tmp = Float64(c * Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y0 * t_7) + Float64(y4 * t_1))));
	elseif (a <= 8.8e+215)
		tmp = t_6;
	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 = (y * y3) - (t * y2);
	t_2 = (a * y5) - (c * y4);
	t_3 = (i * y1) - (b * y0);
	t_4 = (y0 * y5) - (y1 * y4);
	t_5 = (b * y4) - (i * y5);
	t_6 = t * ((z * ((c * i) - (a * b))) + ((j * t_5) + (y2 * t_2)));
	t_7 = (x * y2) - (z * y3);
	t_8 = a * ((b * ((x * y) - (z * t))) + ((y5 * ((t * y2) - (y * y3))) - (y1 * t_7)));
	t_9 = y2 * ((t * t_2) - ((x * ((a * y1) - (c * y0))) + (k * t_4)));
	tmp = 0.0;
	if (a <= -1.9e+117)
		tmp = t_8;
	elseif (a <= -1.55e+63)
		tmp = y0 * (k * ((z * b) - (y2 * y5)));
	elseif (a <= -8.2e+55)
		tmp = t_9;
	elseif (a <= -4.4e-24)
		tmp = t_6;
	elseif (a <= -4.8e-197)
		tmp = j * ((y3 * t_4) + ((t * t_5) + (x * t_3)));
	elseif (a <= 1.05e-273)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_3));
	elseif (a <= 1.45e-152)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1));
	elseif (a <= 1.12e-66)
		tmp = t_9;
	elseif (a <= 7e+33)
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_7) + (y4 * t_1)));
	elseif (a <= 8.8e+215)
		tmp = t_6;
	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[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t * N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * t$95$5), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(a * N[(N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y1 * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(y2 * N[(N[(t * t$95$2), $MachinePrecision] - N[(N[(x * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.9e+117], t$95$8, If[LessEqual[a, -1.55e+63], N[(y0 * N[(k * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.2e+55], t$95$9, If[LessEqual[a, -4.4e-24], t$95$6, If[LessEqual[a, -4.8e-197], N[(j * N[(N[(y3 * t$95$4), $MachinePrecision] + N[(N[(t * t$95$5), $MachinePrecision] + N[(x * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e-273], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.45e-152], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.12e-66], t$95$9, If[LessEqual[a, 7e+33], N[(c * N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * t$95$7), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.8e+215], t$95$6, t$95$8]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -1.9000000000000001e117 or 8.8000000000000006e215 < a

   1. Initial program 24.0%

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

   3. Simplified 24.0%

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

   4. Taylor expanded in a around inf 65.8%

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

      1. *-commutative 65.8%

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

      2. associate--l+ 65.8%

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

      3. mul-1-neg 65.8%

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

      4. *-commutative 65.8%

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

      5. mul-1-neg 65.8%

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

      6. *-commutative 65.8%

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

   6. Simplified 65.8%

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

   if -1.9000000000000001e117 < a < -1.55e63

   1. Initial program 30.0%

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

   3. Simplified 30.0%

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

   4. Taylor expanded in y0 around inf 20.2%

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

      1. *-commutative 20.2%

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

      2. *-commutative 20.2%

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

      3. mul-1-neg 20.2%

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

      4. *-commutative 20.2%

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

      5. *-commutative 20.2%

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

   6. Simplified 20.2%

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

   7. Taylor expanded in k around inf 60.3%

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

   if -1.55e63 < a < -8.19999999999999962e55 or 1.4500000000000001e-152 < a < 1.12000000000000004e-66

   1. Initial program 41.1%

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

   3. Simplified 41.1%

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

   4. Taylor expanded in y2 around inf 73.2%

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

   if -8.19999999999999962e55 < a < -4.40000000000000003e-24 or 7.0000000000000002e33 < a < 8.8000000000000006e215

   1. Initial program 35.8%

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

   3. Simplified 35.8%

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

   4. Taylor expanded in t around inf 62.9%

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

      1. associate--l+ 62.9%

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

      2. mul-1-neg 62.9%

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

      3. *-commutative 62.9%

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

      4. *-commutative 62.9%

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

      5. *-commutative 62.9%

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

      6. *-commutative 62.9%

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

      7. *-commutative 62.9%

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

   6. Simplified 62.9%

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

   if -4.40000000000000003e-24 < a < -4.8000000000000002e-197

   1. Initial program 29.1%

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

   3. Simplified 29.1%

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

   4. Taylor expanded in j around inf 60.8%

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

      1. associate--l+ 60.8%

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

      2. mul-1-neg 60.8%

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

      3. *-commutative 60.8%

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

      4. *-commutative 60.8%

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

      5. *-commutative 60.8%

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

   6. Simplified 60.8%

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

   if -4.8000000000000002e-197 < a < 1.0500000000000001e-273

   1. Initial program 29.7%

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

   3. Simplified 29.7%

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

   4. Taylor expanded in x around inf 54.9%

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

   if 1.0500000000000001e-273 < a < 1.4500000000000001e-152

   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%

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

   4. Taylor expanded in y4 around inf 59.4%

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

   if 1.12000000000000004e-66 < a < 7.0000000000000002e33

   1. Initial program 30.1%

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

   3. Simplified 30.1%

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

   4. Taylor expanded in c around inf 65.9%

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

      1. associate--l+ 65.9%

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

      2. mul-1-neg 65.9%

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

      3. *-commutative 65.9%

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

   6. Simplified 65.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+117}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right) + \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\right)\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{+63}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{+55}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right) - \left(x \cdot \left(a \cdot y1 - c \cdot y0\right) + k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-24}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-197}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-273}:\\ \;\;\;\;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}\;a \leq 1.45 \cdot 10^{-152}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-66}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right) - \left(x \cdot \left(a \cdot y1 - c \cdot y0\right) + k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+33}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+215}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right) + \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\right)\\ \end{array} \]

Alternative 7: 41.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot y5 - y1 \cdot y4\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right) + \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) - y1 \cdot t_2\right)\right)\\ t_4 := c \cdot i - a \cdot b\\ t_5 := y \cdot y3 - t \cdot y2\\ t_6 := a \cdot y5 - c \cdot y4\\ t_7 := i \cdot y1 - b \cdot y0\\ t_8 := k \cdot y2 - j \cdot y3\\ t_9 := b \cdot y4 - i \cdot y5\\ t_10 := t \cdot \left(z \cdot t_4 + \left(j \cdot t_9 + y2 \cdot t_6\right)\right)\\ \mathbf{if}\;a \leq -1.6 \cdot 10^{+118}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \left(k \cdot \left(i \cdot y5 - b \cdot y4\right) - \left(y3 \cdot t_6 + x \cdot t_4\right)\right)\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{+55}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right) + \left(y4 \cdot t_8 + i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-22}:\\ \;\;\;\;t_10\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-197}:\\ \;\;\;\;j \cdot \left(y3 \cdot t_1 + \left(t \cdot t_9 + x \cdot t_7\right)\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-274}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot t_7\right)\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-153}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot t_8\right) + c \cdot t_5\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-66}:\\ \;\;\;\;y2 \cdot \left(t \cdot t_6 - \left(x \cdot \left(a \cdot y1 - c \cdot y0\right) + k \cdot t_1\right)\right)\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+33}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot t_2 + y4 \cdot t_5\right)\right)\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+214}:\\ \;\;\;\;t_10\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y0 y5) (* y1 y4)))
        (t_2 (- (* x y2) (* z y3)))
        (t_3
         (*
          a
          (+
           (* b (- (* x y) (* z t)))
           (- (* y5 (- (* t y2) (* y y3))) (* y1 t_2)))))
        (t_4 (- (* c i) (* a b)))
        (t_5 (- (* y y3) (* t y2)))
        (t_6 (- (* a y5) (* c y4)))
        (t_7 (- (* i y1) (* b y0)))
        (t_8 (- (* k y2) (* j y3)))
        (t_9 (- (* b y4) (* i y5)))
        (t_10 (* t (+ (* z t_4) (+ (* j t_9) (* y2 t_6))))))
   (if (<= a -1.6e+118)
     t_3
     (if (<= a -4.2e+86)
       (* y (- (* k (- (* i y5) (* b y4))) (+ (* y3 t_6) (* x t_4))))
       (if (<= a -6.2e+55)
         (*
          y1
          (+
           (* a (- (* z y3) (* x y2)))
           (+ (* y4 t_8) (* i (- (* x j) (* z k))))))
         (if (<= a -3.9e-22)
           t_10
           (if (<= a -1.9e-197)
             (* j (+ (* y3 t_1) (+ (* t t_9) (* x t_7))))
             (if (<= a 3.5e-274)
               (*
                x
                (+
                 (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
                 (* j t_7)))
               (if (<= a 9.2e-153)
                 (* y4 (+ (+ (* b (- (* t j) (* y k))) (* y1 t_8)) (* c t_5)))
                 (if (<= a 1.05e-66)
                   (*
                    y2
                    (- (* t t_6) (+ (* x (- (* a y1) (* c y0))) (* k t_1))))
                   (if (<= a 2.15e+33)
                     (*
                      c
                      (+ (* i (- (* z t) (* x y))) (+ (* y0 t_2) (* y4 t_5))))
                     (if (<= a 7.6e+214) t_10 t_3))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * y5) - (y1 * y4);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = a * ((b * ((x * y) - (z * t))) + ((y5 * ((t * y2) - (y * y3))) - (y1 * t_2)));
	double t_4 = (c * i) - (a * b);
	double t_5 = (y * y3) - (t * y2);
	double t_6 = (a * y5) - (c * y4);
	double t_7 = (i * y1) - (b * y0);
	double t_8 = (k * y2) - (j * y3);
	double t_9 = (b * y4) - (i * y5);
	double t_10 = t * ((z * t_4) + ((j * t_9) + (y2 * t_6)));
	double tmp;
	if (a <= -1.6e+118) {
		tmp = t_3;
	} else if (a <= -4.2e+86) {
		tmp = y * ((k * ((i * y5) - (b * y4))) - ((y3 * t_6) + (x * t_4)));
	} else if (a <= -6.2e+55) {
		tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((y4 * t_8) + (i * ((x * j) - (z * k)))));
	} else if (a <= -3.9e-22) {
		tmp = t_10;
	} else if (a <= -1.9e-197) {
		tmp = j * ((y3 * t_1) + ((t * t_9) + (x * t_7)));
	} else if (a <= 3.5e-274) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_7));
	} else if (a <= 9.2e-153) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_8)) + (c * t_5));
	} else if (a <= 1.05e-66) {
		tmp = y2 * ((t * t_6) - ((x * ((a * y1) - (c * y0))) + (k * t_1)));
	} else if (a <= 2.15e+33) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_2) + (y4 * t_5)));
	} else if (a <= 7.6e+214) {
		tmp = t_10;
	} 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_10
    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 = (y0 * y5) - (y1 * y4)
    t_2 = (x * y2) - (z * y3)
    t_3 = a * ((b * ((x * y) - (z * t))) + ((y5 * ((t * y2) - (y * y3))) - (y1 * t_2)))
    t_4 = (c * i) - (a * b)
    t_5 = (y * y3) - (t * y2)
    t_6 = (a * y5) - (c * y4)
    t_7 = (i * y1) - (b * y0)
    t_8 = (k * y2) - (j * y3)
    t_9 = (b * y4) - (i * y5)
    t_10 = t * ((z * t_4) + ((j * t_9) + (y2 * t_6)))
    if (a <= (-1.6d+118)) then
        tmp = t_3
    else if (a <= (-4.2d+86)) then
        tmp = y * ((k * ((i * y5) - (b * y4))) - ((y3 * t_6) + (x * t_4)))
    else if (a <= (-6.2d+55)) then
        tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((y4 * t_8) + (i * ((x * j) - (z * k)))))
    else if (a <= (-3.9d-22)) then
        tmp = t_10
    else if (a <= (-1.9d-197)) then
        tmp = j * ((y3 * t_1) + ((t * t_9) + (x * t_7)))
    else if (a <= 3.5d-274) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_7))
    else if (a <= 9.2d-153) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_8)) + (c * t_5))
    else if (a <= 1.05d-66) then
        tmp = y2 * ((t * t_6) - ((x * ((a * y1) - (c * y0))) + (k * t_1)))
    else if (a <= 2.15d+33) then
        tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_2) + (y4 * t_5)))
    else if (a <= 7.6d+214) then
        tmp = t_10
    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 = (y0 * y5) - (y1 * y4);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = a * ((b * ((x * y) - (z * t))) + ((y5 * ((t * y2) - (y * y3))) - (y1 * t_2)));
	double t_4 = (c * i) - (a * b);
	double t_5 = (y * y3) - (t * y2);
	double t_6 = (a * y5) - (c * y4);
	double t_7 = (i * y1) - (b * y0);
	double t_8 = (k * y2) - (j * y3);
	double t_9 = (b * y4) - (i * y5);
	double t_10 = t * ((z * t_4) + ((j * t_9) + (y2 * t_6)));
	double tmp;
	if (a <= -1.6e+118) {
		tmp = t_3;
	} else if (a <= -4.2e+86) {
		tmp = y * ((k * ((i * y5) - (b * y4))) - ((y3 * t_6) + (x * t_4)));
	} else if (a <= -6.2e+55) {
		tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((y4 * t_8) + (i * ((x * j) - (z * k)))));
	} else if (a <= -3.9e-22) {
		tmp = t_10;
	} else if (a <= -1.9e-197) {
		tmp = j * ((y3 * t_1) + ((t * t_9) + (x * t_7)));
	} else if (a <= 3.5e-274) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_7));
	} else if (a <= 9.2e-153) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_8)) + (c * t_5));
	} else if (a <= 1.05e-66) {
		tmp = y2 * ((t * t_6) - ((x * ((a * y1) - (c * y0))) + (k * t_1)));
	} else if (a <= 2.15e+33) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_2) + (y4 * t_5)));
	} else if (a <= 7.6e+214) {
		tmp = t_10;
	} 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 = (y0 * y5) - (y1 * y4)
	t_2 = (x * y2) - (z * y3)
	t_3 = a * ((b * ((x * y) - (z * t))) + ((y5 * ((t * y2) - (y * y3))) - (y1 * t_2)))
	t_4 = (c * i) - (a * b)
	t_5 = (y * y3) - (t * y2)
	t_6 = (a * y5) - (c * y4)
	t_7 = (i * y1) - (b * y0)
	t_8 = (k * y2) - (j * y3)
	t_9 = (b * y4) - (i * y5)
	t_10 = t * ((z * t_4) + ((j * t_9) + (y2 * t_6)))
	tmp = 0
	if a <= -1.6e+118:
		tmp = t_3
	elif a <= -4.2e+86:
		tmp = y * ((k * ((i * y5) - (b * y4))) - ((y3 * t_6) + (x * t_4)))
	elif a <= -6.2e+55:
		tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((y4 * t_8) + (i * ((x * j) - (z * k)))))
	elif a <= -3.9e-22:
		tmp = t_10
	elif a <= -1.9e-197:
		tmp = j * ((y3 * t_1) + ((t * t_9) + (x * t_7)))
	elif a <= 3.5e-274:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_7))
	elif a <= 9.2e-153:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_8)) + (c * t_5))
	elif a <= 1.05e-66:
		tmp = y2 * ((t * t_6) - ((x * ((a * y1) - (c * y0))) + (k * t_1)))
	elif a <= 2.15e+33:
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_2) + (y4 * t_5)))
	elif a <= 7.6e+214:
		tmp = t_10
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y0 * y5) - Float64(y1 * y4))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(a * Float64(Float64(b * Float64(Float64(x * y) - Float64(z * t))) + Float64(Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))) - Float64(y1 * t_2))))
	t_4 = Float64(Float64(c * i) - Float64(a * b))
	t_5 = Float64(Float64(y * y3) - Float64(t * y2))
	t_6 = Float64(Float64(a * y5) - Float64(c * y4))
	t_7 = Float64(Float64(i * y1) - Float64(b * y0))
	t_8 = Float64(Float64(k * y2) - Float64(j * y3))
	t_9 = Float64(Float64(b * y4) - Float64(i * y5))
	t_10 = Float64(t * Float64(Float64(z * t_4) + Float64(Float64(j * t_9) + Float64(y2 * t_6))))
	tmp = 0.0
	if (a <= -1.6e+118)
		tmp = t_3;
	elseif (a <= -4.2e+86)
		tmp = Float64(y * Float64(Float64(k * Float64(Float64(i * y5) - Float64(b * y4))) - Float64(Float64(y3 * t_6) + Float64(x * t_4))));
	elseif (a <= -6.2e+55)
		tmp = Float64(y1 * Float64(Float64(a * Float64(Float64(z * y3) - Float64(x * y2))) + Float64(Float64(y4 * t_8) + Float64(i * Float64(Float64(x * j) - Float64(z * k))))));
	elseif (a <= -3.9e-22)
		tmp = t_10;
	elseif (a <= -1.9e-197)
		tmp = Float64(j * Float64(Float64(y3 * t_1) + Float64(Float64(t * t_9) + Float64(x * t_7))));
	elseif (a <= 3.5e-274)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * t_7)));
	elseif (a <= 9.2e-153)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * t_8)) + Float64(c * t_5)));
	elseif (a <= 1.05e-66)
		tmp = Float64(y2 * Float64(Float64(t * t_6) - Float64(Float64(x * Float64(Float64(a * y1) - Float64(c * y0))) + Float64(k * t_1))));
	elseif (a <= 2.15e+33)
		tmp = Float64(c * Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y0 * t_2) + Float64(y4 * t_5))));
	elseif (a <= 7.6e+214)
		tmp = t_10;
	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 = (y0 * y5) - (y1 * y4);
	t_2 = (x * y2) - (z * y3);
	t_3 = a * ((b * ((x * y) - (z * t))) + ((y5 * ((t * y2) - (y * y3))) - (y1 * t_2)));
	t_4 = (c * i) - (a * b);
	t_5 = (y * y3) - (t * y2);
	t_6 = (a * y5) - (c * y4);
	t_7 = (i * y1) - (b * y0);
	t_8 = (k * y2) - (j * y3);
	t_9 = (b * y4) - (i * y5);
	t_10 = t * ((z * t_4) + ((j * t_9) + (y2 * t_6)));
	tmp = 0.0;
	if (a <= -1.6e+118)
		tmp = t_3;
	elseif (a <= -4.2e+86)
		tmp = y * ((k * ((i * y5) - (b * y4))) - ((y3 * t_6) + (x * t_4)));
	elseif (a <= -6.2e+55)
		tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((y4 * t_8) + (i * ((x * j) - (z * k)))));
	elseif (a <= -3.9e-22)
		tmp = t_10;
	elseif (a <= -1.9e-197)
		tmp = j * ((y3 * t_1) + ((t * t_9) + (x * t_7)));
	elseif (a <= 3.5e-274)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_7));
	elseif (a <= 9.2e-153)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_8)) + (c * t_5));
	elseif (a <= 1.05e-66)
		tmp = y2 * ((t * t_6) - ((x * ((a * y1) - (c * y0))) + (k * t_1)));
	elseif (a <= 2.15e+33)
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_2) + (y4 * t_5)));
	elseif (a <= 7.6e+214)
		tmp = t_10;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y1 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(t * N[(N[(z * t$95$4), $MachinePrecision] + N[(N[(j * t$95$9), $MachinePrecision] + N[(y2 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.6e+118], t$95$3, If[LessEqual[a, -4.2e+86], N[(y * N[(N[(k * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y3 * t$95$6), $MachinePrecision] + N[(x * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.2e+55], N[(y1 * N[(N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y4 * t$95$8), $MachinePrecision] + N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.9e-22], t$95$10, If[LessEqual[a, -1.9e-197], N[(j * N[(N[(y3 * t$95$1), $MachinePrecision] + N[(N[(t * t$95$9), $MachinePrecision] + N[(x * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e-274], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.2e-153], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$8), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e-66], N[(y2 * N[(N[(t * t$95$6), $MachinePrecision] - N[(N[(x * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.15e+33], N[(c * N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * t$95$2), $MachinePrecision] + N[(y4 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.6e+214], t$95$10, t$95$3]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if a < -1.60000000000000008e118 or 7.59999999999999994e214 < a

   1. Initial program 24.0%

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

   3. Simplified 24.0%

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

   4. Taylor expanded in a around inf 65.8%

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

      1. *-commutative 65.8%

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

      2. associate--l+ 65.8%

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

      3. mul-1-neg 65.8%

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

      4. *-commutative 65.8%

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

      5. mul-1-neg 65.8%

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

      6. *-commutative 65.8%

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

   6. Simplified 65.8%

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

   if -1.60000000000000008e118 < a < -4.1999999999999998e86

   1. Initial program 40.0%

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

   3. Simplified 40.0%

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

   4. Taylor expanded in y around inf 81.7%

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

      1. associate--l+ 81.7%

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

      2. mul-1-neg 81.7%

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

      3. *-commutative 81.7%

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

      4. *-commutative 81.7%

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

      5. mul-1-neg 81.7%

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

      6. *-commutative 81.7%

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

      7. *-commutative 81.7%

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

   6. Simplified 81.7%

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

   if -4.1999999999999998e86 < a < -6.19999999999999987e55

   1. Initial program 44.4%

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

   3. Simplified 44.4%

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

   4. Taylor expanded in y1 around inf 55.8%

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

      1. mul-1-neg 55.8%

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

      2. *-commutative 55.8%

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

      3. *-commutative 55.8%

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

      4. *-commutative 55.8%

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

      5. mul-1-neg 55.8%

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

      6. *-commutative 55.8%

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

   6. Simplified 55.8%

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

   if -6.19999999999999987e55 < a < -3.89999999999999998e-22 or 2.15000000000000014e33 < a < 7.59999999999999994e214

   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%

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

   4. Taylor expanded in t around inf 63.9%

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

      1. associate--l+ 63.9%

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

      2. mul-1-neg 63.9%

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

      3. *-commutative 63.9%

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

      4. *-commutative 63.9%

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

      5. *-commutative 63.9%

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

      6. *-commutative 63.9%

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

      7. *-commutative 63.9%

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

   6. Simplified 63.9%

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

   if -3.89999999999999998e-22 < a < -1.8999999999999999e-197

   1. Initial program 29.1%

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

   3. Simplified 29.1%

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

   4. Taylor expanded in j around inf 60.8%

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

      1. associate--l+ 60.8%

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

      2. mul-1-neg 60.8%

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

      3. *-commutative 60.8%

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

      4. *-commutative 60.8%

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

      5. *-commutative 60.8%

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

   6. Simplified 60.8%

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

   if -1.8999999999999999e-197 < a < 3.49999999999999982e-274

   1. Initial program 29.7%

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

   3. Simplified 29.7%

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

   4. Taylor expanded in x around inf 54.9%

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

   if 3.49999999999999982e-274 < a < 9.19999999999999988e-153

   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%

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

   4. Taylor expanded in y4 around inf 59.4%

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

   if 9.19999999999999988e-153 < a < 1.05e-66

   1. Initial program 37.1%

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

   3. Simplified 37.1%

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

   4. Taylor expanded in y2 around inf 69.0%

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

   if 1.05e-66 < a < 2.15000000000000014e33

   1. Initial program 30.1%

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

   3. Simplified 30.1%

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

   4. Taylor expanded in c around inf 65.9%

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

      1. associate--l+ 65.9%

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

      2. mul-1-neg 65.9%

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

      3. *-commutative 65.9%

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

   6. Simplified 65.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+118}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right) + \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \left(k \cdot \left(i \cdot y5 - b \cdot y4\right) - \left(y3 \cdot \left(a \cdot y5 - c \cdot y4\right) + x \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{+55}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + i \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-22}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-197}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-274}:\\ \;\;\;\;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}\;a \leq 9.2 \cdot 10^{-153}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-66}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right) - \left(x \cdot \left(a \cdot y1 - c \cdot y0\right) + k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+33}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+214}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right) + \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\right)\\ \end{array} \]

Alternative 8: 41.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot y5 - c \cdot y4\\ t_2 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_3 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_4 := y2 \cdot \left(t \cdot t_1 - \left(x \cdot \left(a \cdot y1 - c \cdot y0\right) + k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ \mathbf{if}\;y4 \leq -1.25 \cdot 10^{+105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y4 \leq -2.5 \cdot 10^{-105}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y4 \leq -2.7 \cdot 10^{-143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y4 \leq -3.9 \cdot 10^{-185}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y4 \leq 2.5 \cdot 10^{-160}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y4 \leq 3.1 \cdot 10^{-104}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 7.5 \cdot 10^{+107}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y4 \leq 1.3 \cdot 10^{+173} \lor \neg \left(y4 \leq 4.1 \cdot 10^{+207}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot y2\right) \cdot t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a y5) (* c y4)))
        (t_2
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2))))))
        (t_3
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
           (* j (- (* i y1) (* b y0))))))
        (t_4
         (*
          y2
          (-
           (* t t_1)
           (+ (* x (- (* a y1) (* c y0))) (* k (- (* y0 y5) (* y1 y4))))))))
   (if (<= y4 -1.25e+105)
     t_2
     (if (<= y4 -2.5e-105)
       t_4
       (if (<= y4 -2.7e-143)
         t_2
         (if (<= y4 -3.9e-185)
           t_4
           (if (<= y4 2.5e-160)
             t_3
             (if (<= y4 3.1e-104)
               (* c (* t (- (* z i) (* y2 y4))))
               (if (<= y4 7.5e+107)
                 t_3
                 (if (or (<= y4 1.3e+173) (not (<= y4 4.1e+207)))
                   t_2
                   (* (* t y2) t_1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y5) - (c * y4);
	double t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double t_4 = y2 * ((t * t_1) - ((x * ((a * y1) - (c * y0))) + (k * ((y0 * y5) - (y1 * y4)))));
	double tmp;
	if (y4 <= -1.25e+105) {
		tmp = t_2;
	} else if (y4 <= -2.5e-105) {
		tmp = t_4;
	} else if (y4 <= -2.7e-143) {
		tmp = t_2;
	} else if (y4 <= -3.9e-185) {
		tmp = t_4;
	} else if (y4 <= 2.5e-160) {
		tmp = t_3;
	} else if (y4 <= 3.1e-104) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (y4 <= 7.5e+107) {
		tmp = t_3;
	} else if ((y4 <= 1.3e+173) || !(y4 <= 4.1e+207)) {
		tmp = t_2;
	} else {
		tmp = (t * y2) * t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (a * y5) - (c * y4)
    t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    t_4 = y2 * ((t * t_1) - ((x * ((a * y1) - (c * y0))) + (k * ((y0 * y5) - (y1 * y4)))))
    if (y4 <= (-1.25d+105)) then
        tmp = t_2
    else if (y4 <= (-2.5d-105)) then
        tmp = t_4
    else if (y4 <= (-2.7d-143)) then
        tmp = t_2
    else if (y4 <= (-3.9d-185)) then
        tmp = t_4
    else if (y4 <= 2.5d-160) then
        tmp = t_3
    else if (y4 <= 3.1d-104) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (y4 <= 7.5d+107) then
        tmp = t_3
    else if ((y4 <= 1.3d+173) .or. (.not. (y4 <= 4.1d+207))) then
        tmp = t_2
    else
        tmp = (t * y2) * t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y5) - (c * y4);
	double t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double t_4 = y2 * ((t * t_1) - ((x * ((a * y1) - (c * y0))) + (k * ((y0 * y5) - (y1 * y4)))));
	double tmp;
	if (y4 <= -1.25e+105) {
		tmp = t_2;
	} else if (y4 <= -2.5e-105) {
		tmp = t_4;
	} else if (y4 <= -2.7e-143) {
		tmp = t_2;
	} else if (y4 <= -3.9e-185) {
		tmp = t_4;
	} else if (y4 <= 2.5e-160) {
		tmp = t_3;
	} else if (y4 <= 3.1e-104) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (y4 <= 7.5e+107) {
		tmp = t_3;
	} else if ((y4 <= 1.3e+173) || !(y4 <= 4.1e+207)) {
		tmp = t_2;
	} else {
		tmp = (t * y2) * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (a * y5) - (c * y4)
	t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	t_4 = y2 * ((t * t_1) - ((x * ((a * y1) - (c * y0))) + (k * ((y0 * y5) - (y1 * y4)))))
	tmp = 0
	if y4 <= -1.25e+105:
		tmp = t_2
	elif y4 <= -2.5e-105:
		tmp = t_4
	elif y4 <= -2.7e-143:
		tmp = t_2
	elif y4 <= -3.9e-185:
		tmp = t_4
	elif y4 <= 2.5e-160:
		tmp = t_3
	elif y4 <= 3.1e-104:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif y4 <= 7.5e+107:
		tmp = t_3
	elif (y4 <= 1.3e+173) or not (y4 <= 4.1e+207):
		tmp = t_2
	else:
		tmp = (t * y2) * t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(a * y5) - Float64(c * y4))
	t_2 = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_3 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_4 = Float64(y2 * Float64(Float64(t * t_1) - Float64(Float64(x * Float64(Float64(a * y1) - Float64(c * y0))) + Float64(k * Float64(Float64(y0 * y5) - Float64(y1 * y4))))))
	tmp = 0.0
	if (y4 <= -1.25e+105)
		tmp = t_2;
	elseif (y4 <= -2.5e-105)
		tmp = t_4;
	elseif (y4 <= -2.7e-143)
		tmp = t_2;
	elseif (y4 <= -3.9e-185)
		tmp = t_4;
	elseif (y4 <= 2.5e-160)
		tmp = t_3;
	elseif (y4 <= 3.1e-104)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (y4 <= 7.5e+107)
		tmp = t_3;
	elseif ((y4 <= 1.3e+173) || !(y4 <= 4.1e+207))
		tmp = t_2;
	else
		tmp = Float64(Float64(t * y2) * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (a * y5) - (c * y4);
	t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	t_4 = y2 * ((t * t_1) - ((x * ((a * y1) - (c * y0))) + (k * ((y0 * y5) - (y1 * y4)))));
	tmp = 0.0;
	if (y4 <= -1.25e+105)
		tmp = t_2;
	elseif (y4 <= -2.5e-105)
		tmp = t_4;
	elseif (y4 <= -2.7e-143)
		tmp = t_2;
	elseif (y4 <= -3.9e-185)
		tmp = t_4;
	elseif (y4 <= 2.5e-160)
		tmp = t_3;
	elseif (y4 <= 3.1e-104)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (y4 <= 7.5e+107)
		tmp = t_3;
	elseif ((y4 <= 1.3e+173) || ~((y4 <= 4.1e+207)))
		tmp = t_2;
	else
		tmp = (t * y2) * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y2 * N[(N[(t * t$95$1), $MachinePrecision] - N[(N[(x * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -1.25e+105], t$95$2, If[LessEqual[y4, -2.5e-105], t$95$4, If[LessEqual[y4, -2.7e-143], t$95$2, If[LessEqual[y4, -3.9e-185], t$95$4, If[LessEqual[y4, 2.5e-160], t$95$3, If[LessEqual[y4, 3.1e-104], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 7.5e+107], t$95$3, If[Or[LessEqual[y4, 1.3e+173], N[Not[LessEqual[y4, 4.1e+207]], $MachinePrecision]], t$95$2, N[(N[(t * y2), $MachinePrecision] * t$95$1), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y4 < -1.25000000000000011e105 or -2.49999999999999982e-105 < y4 < -2.70000000000000009e-143 or 7.4999999999999996e107 < y4 < 1.2999999999999999e173 or 4.1e207 < y4

   1. Initial program 29.1%

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

   3. Simplified 29.1%

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

   4. Taylor expanded in y4 around inf 69.6%

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

   if -1.25000000000000011e105 < y4 < -2.49999999999999982e-105 or -2.70000000000000009e-143 < y4 < -3.8999999999999999e-185

   1. Initial program 42.6%

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

   3. Simplified 42.6%

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

   4. Taylor expanded in y2 around inf 54.1%

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

   if -3.8999999999999999e-185 < y4 < 2.49999999999999997e-160 or 3.09999999999999976e-104 < y4 < 7.4999999999999996e107

   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%

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

   4. Taylor expanded in x around inf 52.2%

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

   if 2.49999999999999997e-160 < y4 < 3.09999999999999976e-104

   1. Initial program 36.4%

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

   3. Simplified 36.4%

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

   4. Taylor expanded in c around inf 55.0%

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

      1. associate--l+ 55.0%

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

      2. mul-1-neg 55.0%

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

      3. *-commutative 55.0%

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

   6. Simplified 55.0%

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

   7. Taylor expanded in t around -inf 64.2%

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

      1. *-commutative 64.2%

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

      2. mul-1-neg 64.2%

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

      3. unsub-neg 64.2%

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

   9. Simplified 64.2%

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

   if 1.2999999999999999e173 < y4 < 4.1e207

   1. Initial program 14.3%

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

   3. Simplified 14.3%

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

   4. Taylor expanded in t around inf 85.8%

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

      1. associate--l+ 85.8%

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

      2. mul-1-neg 85.8%

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

      3. *-commutative 85.8%

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

      4. *-commutative 85.8%

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

      5. *-commutative 85.8%

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

      6. *-commutative 85.8%

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

      7. *-commutative 85.8%

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

   6. Simplified 85.8%

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

   7. Taylor expanded in y2 around inf 72.5%

      \[\leadsto \color{blue}{\left(a \cdot y5 - c \cdot y4\right) \cdot \left(t \cdot y2\right)} \]
   8. Step-by-step derivation

      1. *-commutative 72.5%

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

      2. *-commutative 72.5%

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

   9. Simplified 72.5%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.25 \cdot 10^{+105}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -2.5 \cdot 10^{-105}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right) - \left(x \cdot \left(a \cdot y1 - c \cdot y0\right) + k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -2.7 \cdot 10^{-143}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -3.9 \cdot 10^{-185}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right) - \left(x \cdot \left(a \cdot y1 - c \cdot y0\right) + k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 2.5 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 3.1 \cdot 10^{-104}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 7.5 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 1.3 \cdot 10^{+173} \lor \neg \left(y4 \leq 4.1 \cdot 10^{+207}\right):\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot y2\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\\ \end{array} \]

Alternative 9: 39.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_2 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;y4 \leq -2.3 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq -4.5 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -7.5 \cdot 10^{-180}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq 2.5 \cdot 10^{-160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y4 \leq 1.35 \cdot 10^{-103}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 5.8 \cdot 10^{+107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y4 \leq 1.3 \cdot 10^{+173} \lor \neg \left(y4 \leq 4.1 \cdot 10^{+207}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot y2\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2))))))
        (t_2
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
           (* j (- (* i y1) (* b y0)))))))
   (if (<= y4 -2.3e+73)
     t_1
     (if (<= y4 -4.5e-62)
       (* x (* a (- (* y b) (* y1 y2))))
       (if (<= y4 -7.5e-180)
         t_1
         (if (<= y4 2.5e-160)
           t_2
           (if (<= y4 1.35e-103)
             (* c (* t (- (* z i) (* y2 y4))))
             (if (<= y4 5.8e+107)
               t_2
               (if (or (<= y4 1.3e+173) (not (<= y4 4.1e+207)))
                 t_1
                 (* (* t y2) (- (* a y5) (* c y4))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y4 <= -2.3e+73) {
		tmp = t_1;
	} else if (y4 <= -4.5e-62) {
		tmp = x * (a * ((y * b) - (y1 * y2)));
	} else if (y4 <= -7.5e-180) {
		tmp = t_1;
	} else if (y4 <= 2.5e-160) {
		tmp = t_2;
	} else if (y4 <= 1.35e-103) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (y4 <= 5.8e+107) {
		tmp = t_2;
	} else if ((y4 <= 1.3e+173) || !(y4 <= 4.1e+207)) {
		tmp = t_1;
	} else {
		tmp = (t * y2) * ((a * y5) - (c * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    if (y4 <= (-2.3d+73)) then
        tmp = t_1
    else if (y4 <= (-4.5d-62)) then
        tmp = x * (a * ((y * b) - (y1 * y2)))
    else if (y4 <= (-7.5d-180)) then
        tmp = t_1
    else if (y4 <= 2.5d-160) then
        tmp = t_2
    else if (y4 <= 1.35d-103) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (y4 <= 5.8d+107) then
        tmp = t_2
    else if ((y4 <= 1.3d+173) .or. (.not. (y4 <= 4.1d+207))) then
        tmp = t_1
    else
        tmp = (t * y2) * ((a * y5) - (c * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (y4 <= -2.3e+73) {
		tmp = t_1;
	} else if (y4 <= -4.5e-62) {
		tmp = x * (a * ((y * b) - (y1 * y2)));
	} else if (y4 <= -7.5e-180) {
		tmp = t_1;
	} else if (y4 <= 2.5e-160) {
		tmp = t_2;
	} else if (y4 <= 1.35e-103) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (y4 <= 5.8e+107) {
		tmp = t_2;
	} else if ((y4 <= 1.3e+173) || !(y4 <= 4.1e+207)) {
		tmp = t_1;
	} else {
		tmp = (t * y2) * ((a * y5) - (c * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	tmp = 0
	if y4 <= -2.3e+73:
		tmp = t_1
	elif y4 <= -4.5e-62:
		tmp = x * (a * ((y * b) - (y1 * y2)))
	elif y4 <= -7.5e-180:
		tmp = t_1
	elif y4 <= 2.5e-160:
		tmp = t_2
	elif y4 <= 1.35e-103:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif y4 <= 5.8e+107:
		tmp = t_2
	elif (y4 <= 1.3e+173) or not (y4 <= 4.1e+207):
		tmp = t_1
	else:
		tmp = (t * y2) * ((a * y5) - (c * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_2 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (y4 <= -2.3e+73)
		tmp = t_1;
	elseif (y4 <= -4.5e-62)
		tmp = Float64(x * Float64(a * Float64(Float64(y * b) - Float64(y1 * y2))));
	elseif (y4 <= -7.5e-180)
		tmp = t_1;
	elseif (y4 <= 2.5e-160)
		tmp = t_2;
	elseif (y4 <= 1.35e-103)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (y4 <= 5.8e+107)
		tmp = t_2;
	elseif ((y4 <= 1.3e+173) || !(y4 <= 4.1e+207))
		tmp = t_1;
	else
		tmp = Float64(Float64(t * y2) * Float64(Float64(a * y5) - Float64(c * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (y4 <= -2.3e+73)
		tmp = t_1;
	elseif (y4 <= -4.5e-62)
		tmp = x * (a * ((y * b) - (y1 * y2)));
	elseif (y4 <= -7.5e-180)
		tmp = t_1;
	elseif (y4 <= 2.5e-160)
		tmp = t_2;
	elseif (y4 <= 1.35e-103)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (y4 <= 5.8e+107)
		tmp = t_2;
	elseif ((y4 <= 1.3e+173) || ~((y4 <= 4.1e+207)))
		tmp = t_1;
	else
		tmp = (t * y2) * ((a * y5) - (c * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -2.3e+73], t$95$1, If[LessEqual[y4, -4.5e-62], N[(x * N[(a * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -7.5e-180], t$95$1, If[LessEqual[y4, 2.5e-160], t$95$2, If[LessEqual[y4, 1.35e-103], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 5.8e+107], t$95$2, If[Or[LessEqual[y4, 1.3e+173], N[Not[LessEqual[y4, 4.1e+207]], $MachinePrecision]], t$95$1, N[(N[(t * y2), $MachinePrecision] * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y4 < -2.3e73 or -4.50000000000000018e-62 < y4 < -7.50000000000000015e-180 or 5.79999999999999975e107 < y4 < 1.2999999999999999e173 or 4.1e207 < y4

   1. Initial program 35.7%

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

   3. Simplified 35.7%

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

   4. Taylor expanded in y4 around inf 62.5%

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

   if -2.3e73 < y4 < -4.50000000000000018e-62

   1. Initial program 27.2%

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

   3. Simplified 27.2%

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

   4. Taylor expanded in x around inf 36.8%

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

   5. Taylor expanded in a around inf 49.4%

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

      1. mul-1-neg 49.4%

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

      2. unsub-neg 49.4%

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

   7. Simplified 49.4%

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

   if -7.50000000000000015e-180 < y4 < 2.49999999999999997e-160 or 1.35000000000000005e-103 < y4 < 5.79999999999999975e107

   1. Initial program 30.0%

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

   3. Simplified 30.0%

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

   4. Taylor expanded in x around inf 51.0%

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

   if 2.49999999999999997e-160 < y4 < 1.35000000000000005e-103

   1. Initial program 36.4%

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

   3. Simplified 36.4%

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

   4. Taylor expanded in c around inf 55.0%

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

      1. associate--l+ 55.0%

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

      2. mul-1-neg 55.0%

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

      3. *-commutative 55.0%

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

   6. Simplified 55.0%

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

   7. Taylor expanded in t around -inf 64.2%

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

      1. *-commutative 64.2%

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

      2. mul-1-neg 64.2%

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

      3. unsub-neg 64.2%

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

   9. Simplified 64.2%

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

   if 1.2999999999999999e173 < y4 < 4.1e207

   1. Initial program 14.3%

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

   3. Simplified 14.3%

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

   4. Taylor expanded in t around inf 85.8%

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

      1. associate--l+ 85.8%

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

      2. mul-1-neg 85.8%

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

      3. *-commutative 85.8%

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

      4. *-commutative 85.8%

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

      5. *-commutative 85.8%

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

      6. *-commutative 85.8%

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

      7. *-commutative 85.8%

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

   6. Simplified 85.8%

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

   7. Taylor expanded in y2 around inf 72.5%

      \[\leadsto \color{blue}{\left(a \cdot y5 - c \cdot y4\right) \cdot \left(t \cdot y2\right)} \]
   8. Step-by-step derivation

      1. *-commutative 72.5%

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

      2. *-commutative 72.5%

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

   9. Simplified 72.5%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -2.3 \cdot 10^{+73}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -4.5 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -7.5 \cdot 10^{-180}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq 2.5 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 1.35 \cdot 10^{-103}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq 5.8 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y4 \leq 1.3 \cdot 10^{+173} \lor \neg \left(y4 \leq 4.1 \cdot 10^{+207}\right):\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot y2\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\\ \end{array} \]

Alternative 10: 38.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ t_2 := i \cdot y1 - b \cdot y0\\ t_3 := y \cdot y3 - t \cdot y2\\ t_4 := y0 \cdot y5 - y1 \cdot y4\\ t_5 := b \cdot y4 - i \cdot y5\\ t_6 := a \cdot y5 - c \cdot y4\\ \mathbf{if}\;a \leq -1.95 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4000000000000:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-198}:\\ \;\;\;\;j \cdot \left(y3 \cdot t_4 + \left(t \cdot t_5 + x \cdot t_2\right)\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-274}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot t_2\right)\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-152}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t_3\right)\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{-66}:\\ \;\;\;\;y2 \cdot \left(t \cdot t_6 - \left(x \cdot \left(a \cdot y1 - c \cdot y0\right) + k \cdot t_4\right)\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+33}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot t_3\right)\right)\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+213}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(j \cdot t_5 + y2 \cdot t_6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* x (* a (- (* y b) (* y1 y2)))))
        (t_2 (- (* i y1) (* b y0)))
        (t_3 (- (* y y3) (* t y2)))
        (t_4 (- (* y0 y5) (* y1 y4)))
        (t_5 (- (* b y4) (* i y5)))
        (t_6 (- (* a y5) (* c y4))))
   (if (<= a -1.95e+94)
     t_1
     (if (<= a -4000000000000.0)
       (* y4 (* k (- (* y1 y2) (* y b))))
       (if (<= a -1.02e-198)
         (* j (+ (* y3 t_4) (+ (* t t_5) (* x t_2))))
         (if (<= a 7.2e-274)
           (*
            x
            (+
             (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
             (* j t_2)))
           (if (<= a 2.05e-152)
             (*
              y4
              (+
               (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
               (* c t_3)))
             (if (<= a 8.4e-66)
               (* y2 (- (* t t_6) (+ (* x (- (* a y1) (* c y0))) (* k t_4))))
               (if (<= a 1.7e+33)
                 (*
                  c
                  (+
                   (* i (- (* z t) (* x y)))
                   (+ (* y0 (- (* x y2) (* z y3))) (* y4 t_3))))
                 (if (<= a 1.95e+213)
                   (* t (+ (* z (- (* c i) (* a b))) (+ (* j t_5) (* y2 t_6))))
                   t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (a * ((y * b) - (y1 * y2)));
	double t_2 = (i * y1) - (b * y0);
	double t_3 = (y * y3) - (t * y2);
	double t_4 = (y0 * y5) - (y1 * y4);
	double t_5 = (b * y4) - (i * y5);
	double t_6 = (a * y5) - (c * y4);
	double tmp;
	if (a <= -1.95e+94) {
		tmp = t_1;
	} else if (a <= -4000000000000.0) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (a <= -1.02e-198) {
		tmp = j * ((y3 * t_4) + ((t * t_5) + (x * t_2)));
	} else if (a <= 7.2e-274) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_2));
	} else if (a <= 2.05e-152) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3));
	} else if (a <= 8.4e-66) {
		tmp = y2 * ((t * t_6) - ((x * ((a * y1) - (c * y0))) + (k * t_4)));
	} else if (a <= 1.7e+33) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_3)));
	} else if (a <= 1.95e+213) {
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * t_5) + (y2 * t_6)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = x * (a * ((y * b) - (y1 * y2)))
    t_2 = (i * y1) - (b * y0)
    t_3 = (y * y3) - (t * y2)
    t_4 = (y0 * y5) - (y1 * y4)
    t_5 = (b * y4) - (i * y5)
    t_6 = (a * y5) - (c * y4)
    if (a <= (-1.95d+94)) then
        tmp = t_1
    else if (a <= (-4000000000000.0d0)) then
        tmp = y4 * (k * ((y1 * y2) - (y * b)))
    else if (a <= (-1.02d-198)) then
        tmp = j * ((y3 * t_4) + ((t * t_5) + (x * t_2)))
    else if (a <= 7.2d-274) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_2))
    else if (a <= 2.05d-152) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3))
    else if (a <= 8.4d-66) then
        tmp = y2 * ((t * t_6) - ((x * ((a * y1) - (c * y0))) + (k * t_4)))
    else if (a <= 1.7d+33) then
        tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_3)))
    else if (a <= 1.95d+213) then
        tmp = t * ((z * ((c * i) - (a * b))) + ((j * t_5) + (y2 * t_6)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (a * ((y * b) - (y1 * y2)));
	double t_2 = (i * y1) - (b * y0);
	double t_3 = (y * y3) - (t * y2);
	double t_4 = (y0 * y5) - (y1 * y4);
	double t_5 = (b * y4) - (i * y5);
	double t_6 = (a * y5) - (c * y4);
	double tmp;
	if (a <= -1.95e+94) {
		tmp = t_1;
	} else if (a <= -4000000000000.0) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (a <= -1.02e-198) {
		tmp = j * ((y3 * t_4) + ((t * t_5) + (x * t_2)));
	} else if (a <= 7.2e-274) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_2));
	} else if (a <= 2.05e-152) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3));
	} else if (a <= 8.4e-66) {
		tmp = y2 * ((t * t_6) - ((x * ((a * y1) - (c * y0))) + (k * t_4)));
	} else if (a <= 1.7e+33) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_3)));
	} else if (a <= 1.95e+213) {
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * t_5) + (y2 * t_6)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = x * (a * ((y * b) - (y1 * y2)))
	t_2 = (i * y1) - (b * y0)
	t_3 = (y * y3) - (t * y2)
	t_4 = (y0 * y5) - (y1 * y4)
	t_5 = (b * y4) - (i * y5)
	t_6 = (a * y5) - (c * y4)
	tmp = 0
	if a <= -1.95e+94:
		tmp = t_1
	elif a <= -4000000000000.0:
		tmp = y4 * (k * ((y1 * y2) - (y * b)))
	elif a <= -1.02e-198:
		tmp = j * ((y3 * t_4) + ((t * t_5) + (x * t_2)))
	elif a <= 7.2e-274:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_2))
	elif a <= 2.05e-152:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3))
	elif a <= 8.4e-66:
		tmp = y2 * ((t * t_6) - ((x * ((a * y1) - (c * y0))) + (k * t_4)))
	elif a <= 1.7e+33:
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_3)))
	elif a <= 1.95e+213:
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * t_5) + (y2 * t_6)))
	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(a * Float64(Float64(y * b) - Float64(y1 * y2))))
	t_2 = Float64(Float64(i * y1) - Float64(b * y0))
	t_3 = Float64(Float64(y * y3) - Float64(t * y2))
	t_4 = Float64(Float64(y0 * y5) - Float64(y1 * y4))
	t_5 = Float64(Float64(b * y4) - Float64(i * y5))
	t_6 = Float64(Float64(a * y5) - Float64(c * y4))
	tmp = 0.0
	if (a <= -1.95e+94)
		tmp = t_1;
	elseif (a <= -4000000000000.0)
		tmp = Float64(y4 * Float64(k * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (a <= -1.02e-198)
		tmp = Float64(j * Float64(Float64(y3 * t_4) + Float64(Float64(t * t_5) + Float64(x * t_2))));
	elseif (a <= 7.2e-274)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * t_2)));
	elseif (a <= 2.05e-152)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * t_3)));
	elseif (a <= 8.4e-66)
		tmp = Float64(y2 * Float64(Float64(t * t_6) - Float64(Float64(x * Float64(Float64(a * y1) - Float64(c * y0))) + Float64(k * t_4))));
	elseif (a <= 1.7e+33)
		tmp = Float64(c * Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y4 * t_3))));
	elseif (a <= 1.95e+213)
		tmp = Float64(t * Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(Float64(j * t_5) + Float64(y2 * t_6))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = x * (a * ((y * b) - (y1 * y2)));
	t_2 = (i * y1) - (b * y0);
	t_3 = (y * y3) - (t * y2);
	t_4 = (y0 * y5) - (y1 * y4);
	t_5 = (b * y4) - (i * y5);
	t_6 = (a * y5) - (c * y4);
	tmp = 0.0;
	if (a <= -1.95e+94)
		tmp = t_1;
	elseif (a <= -4000000000000.0)
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	elseif (a <= -1.02e-198)
		tmp = j * ((y3 * t_4) + ((t * t_5) + (x * t_2)));
	elseif (a <= 7.2e-274)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_2));
	elseif (a <= 2.05e-152)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3));
	elseif (a <= 8.4e-66)
		tmp = y2 * ((t * t_6) - ((x * ((a * y1) - (c * y0))) + (k * t_4)));
	elseif (a <= 1.7e+33)
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_3)));
	elseif (a <= 1.95e+213)
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * t_5) + (y2 * t_6)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(x * N[(a * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.95e+94], t$95$1, If[LessEqual[a, -4000000000000.0], N[(y4 * N[(k * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.02e-198], N[(j * N[(N[(y3 * t$95$4), $MachinePrecision] + N[(N[(t * t$95$5), $MachinePrecision] + N[(x * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.2e-274], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.05e-152], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.4e-66], N[(y2 * N[(N[(t * t$95$6), $MachinePrecision] - N[(N[(x * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e+33], N[(c * N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.95e+213], N[(t * N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * t$95$5), $MachinePrecision] + N[(y2 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -1.94999999999999993e94 or 1.9500000000000001e213 < a

   1. Initial program 23.0%

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

   3. Simplified 23.0%

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

   4. Taylor expanded in x around inf 27.4%

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

   5. Taylor expanded in a around inf 57.1%

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

      1. mul-1-neg 57.1%

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

      2. unsub-neg 57.1%

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

   7. Simplified 57.1%

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

   if -1.94999999999999993e94 < a < -4e12

   1. Initial program 38.9%

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

   3. Simplified 38.9%

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

   4. Taylor expanded in y4 around inf 39.3%

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

   5. Taylor expanded in k around inf 50.7%

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

      1. +-commutative 50.7%

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

      2. mul-1-neg 50.7%

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

      3. unsub-neg 50.7%

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

   7. Simplified 50.7%

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

   if -4e12 < a < -1.01999999999999997e-198

   1. Initial program 29.9%

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

   3. Simplified 29.9%

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

   4. Taylor expanded in j around inf 59.9%

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

      1. associate--l+ 59.9%

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

      2. mul-1-neg 59.9%

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

      3. *-commutative 59.9%

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

      4. *-commutative 59.9%

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

      5. *-commutative 59.9%

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

   6. Simplified 59.9%

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

   if -1.01999999999999997e-198 < a < 7.19999999999999965e-274

   1. Initial program 29.7%

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

   3. Simplified 29.7%

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

   4. Taylor expanded in x around inf 54.9%

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

   if 7.19999999999999965e-274 < a < 2.0500000000000001e-152

   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%

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

   4. Taylor expanded in y4 around inf 59.4%

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

   if 2.0500000000000001e-152 < a < 8.4000000000000001e-66

   1. Initial program 37.1%

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

   3. Simplified 37.1%

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

   4. Taylor expanded in y2 around inf 69.0%

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

   if 8.4000000000000001e-66 < a < 1.7e33

   1. Initial program 30.1%

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

   3. Simplified 30.1%

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

   4. Taylor expanded in c around inf 65.9%

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

      1. associate--l+ 65.9%

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

      2. mul-1-neg 65.9%

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

      3. *-commutative 65.9%

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

   6. Simplified 65.9%

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

   if 1.7e33 < a < 1.9500000000000001e213

   1. Initial program 37.6%

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

   3. Simplified 37.6%

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

   4. Taylor expanded in t around inf 60.4%

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

      1. associate--l+ 60.4%

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

      2. mul-1-neg 60.4%

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

      3. *-commutative 60.4%

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

      4. *-commutative 60.4%

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

      5. *-commutative 60.4%

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

      6. *-commutative 60.4%

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

      7. *-commutative 60.4%

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

   6. Simplified 60.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(b \cdot a - i \cdot c\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - y2 \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -4000000000000:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-198}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-274}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-152}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{-66}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right) - \left(x \cdot \left(a \cdot y1 - c \cdot y0\right) + k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+33}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+213}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \end{array} \]

Alternative 11: 38.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot y4 - i \cdot y5\\ t_2 := i \cdot y1 - b \cdot y0\\ t_3 := a \cdot y5 - c \cdot y4\\ t_4 := x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ t_5 := c \cdot i - a \cdot b\\ t_6 := y \cdot y3 - t \cdot y2\\ t_7 := a \cdot y1 - c \cdot y0\\ t_8 := y0 \cdot y5 - y1 \cdot y4\\ \mathbf{if}\;a \leq -1.6 \cdot 10^{+126}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(y3 \cdot t_7 + t \cdot t_5\right)\right)\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-198}:\\ \;\;\;\;j \cdot \left(y3 \cdot t_8 + \left(t \cdot t_1 + x \cdot t_2\right)\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-274}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot t_2\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-153}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t_6\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-65}:\\ \;\;\;\;y2 \cdot \left(t \cdot t_3 - \left(x \cdot t_7 + k \cdot t_8\right)\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+33}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot t_6\right)\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+214}:\\ \;\;\;\;t \cdot \left(z \cdot t_5 + \left(j \cdot t_1 + y2 \cdot t_3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* b y4) (* i y5)))
        (t_2 (- (* i y1) (* b y0)))
        (t_3 (- (* a y5) (* c y4)))
        (t_4 (* x (* a (- (* y b) (* y1 y2)))))
        (t_5 (- (* c i) (* a b)))
        (t_6 (- (* y y3) (* t y2)))
        (t_7 (- (* a y1) (* c y0)))
        (t_8 (- (* y0 y5) (* y1 y4))))
   (if (<= a -1.6e+126)
     t_4
     (if (<= a -4.4e-30)
       (* z (+ (* k (- (* b y0) (* i y1))) (+ (* y3 t_7) (* t t_5))))
       (if (<= a -4.4e-198)
         (* j (+ (* y3 t_8) (+ (* t t_1) (* x t_2))))
         (if (<= a 6.2e-274)
           (*
            x
            (+
             (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
             (* j t_2)))
           (if (<= a 8.5e-153)
             (*
              y4
              (+
               (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
               (* c t_6)))
             (if (<= a 1.4e-65)
               (* y2 (- (* t t_3) (+ (* x t_7) (* k t_8))))
               (if (<= a 1.6e+33)
                 (*
                  c
                  (+
                   (* i (- (* z t) (* x y)))
                   (+ (* y0 (- (* x y2) (* z y3))) (* y4 t_6))))
                 (if (<= a 1.35e+214)
                   (* t (+ (* z t_5) (+ (* j t_1) (* y2 t_3))))
                   t_4))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y4) - (i * y5);
	double t_2 = (i * y1) - (b * y0);
	double t_3 = (a * y5) - (c * y4);
	double t_4 = x * (a * ((y * b) - (y1 * y2)));
	double t_5 = (c * i) - (a * b);
	double t_6 = (y * y3) - (t * y2);
	double t_7 = (a * y1) - (c * y0);
	double t_8 = (y0 * y5) - (y1 * y4);
	double tmp;
	if (a <= -1.6e+126) {
		tmp = t_4;
	} else if (a <= -4.4e-30) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((y3 * t_7) + (t * t_5)));
	} else if (a <= -4.4e-198) {
		tmp = j * ((y3 * t_8) + ((t * t_1) + (x * t_2)));
	} else if (a <= 6.2e-274) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_2));
	} else if (a <= 8.5e-153) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_6));
	} else if (a <= 1.4e-65) {
		tmp = y2 * ((t * t_3) - ((x * t_7) + (k * t_8)));
	} else if (a <= 1.6e+33) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_6)));
	} else if (a <= 1.35e+214) {
		tmp = t * ((z * t_5) + ((j * t_1) + (y2 * t_3)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_1 = (b * y4) - (i * y5)
    t_2 = (i * y1) - (b * y0)
    t_3 = (a * y5) - (c * y4)
    t_4 = x * (a * ((y * b) - (y1 * y2)))
    t_5 = (c * i) - (a * b)
    t_6 = (y * y3) - (t * y2)
    t_7 = (a * y1) - (c * y0)
    t_8 = (y0 * y5) - (y1 * y4)
    if (a <= (-1.6d+126)) then
        tmp = t_4
    else if (a <= (-4.4d-30)) then
        tmp = z * ((k * ((b * y0) - (i * y1))) + ((y3 * t_7) + (t * t_5)))
    else if (a <= (-4.4d-198)) then
        tmp = j * ((y3 * t_8) + ((t * t_1) + (x * t_2)))
    else if (a <= 6.2d-274) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_2))
    else if (a <= 8.5d-153) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_6))
    else if (a <= 1.4d-65) then
        tmp = y2 * ((t * t_3) - ((x * t_7) + (k * t_8)))
    else if (a <= 1.6d+33) then
        tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_6)))
    else if (a <= 1.35d+214) then
        tmp = t * ((z * t_5) + ((j * t_1) + (y2 * t_3)))
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y4) - (i * y5);
	double t_2 = (i * y1) - (b * y0);
	double t_3 = (a * y5) - (c * y4);
	double t_4 = x * (a * ((y * b) - (y1 * y2)));
	double t_5 = (c * i) - (a * b);
	double t_6 = (y * y3) - (t * y2);
	double t_7 = (a * y1) - (c * y0);
	double t_8 = (y0 * y5) - (y1 * y4);
	double tmp;
	if (a <= -1.6e+126) {
		tmp = t_4;
	} else if (a <= -4.4e-30) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((y3 * t_7) + (t * t_5)));
	} else if (a <= -4.4e-198) {
		tmp = j * ((y3 * t_8) + ((t * t_1) + (x * t_2)));
	} else if (a <= 6.2e-274) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_2));
	} else if (a <= 8.5e-153) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_6));
	} else if (a <= 1.4e-65) {
		tmp = y2 * ((t * t_3) - ((x * t_7) + (k * t_8)));
	} else if (a <= 1.6e+33) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_6)));
	} else if (a <= 1.35e+214) {
		tmp = t * ((z * t_5) + ((j * t_1) + (y2 * t_3)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (b * y4) - (i * y5)
	t_2 = (i * y1) - (b * y0)
	t_3 = (a * y5) - (c * y4)
	t_4 = x * (a * ((y * b) - (y1 * y2)))
	t_5 = (c * i) - (a * b)
	t_6 = (y * y3) - (t * y2)
	t_7 = (a * y1) - (c * y0)
	t_8 = (y0 * y5) - (y1 * y4)
	tmp = 0
	if a <= -1.6e+126:
		tmp = t_4
	elif a <= -4.4e-30:
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((y3 * t_7) + (t * t_5)))
	elif a <= -4.4e-198:
		tmp = j * ((y3 * t_8) + ((t * t_1) + (x * t_2)))
	elif a <= 6.2e-274:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_2))
	elif a <= 8.5e-153:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_6))
	elif a <= 1.4e-65:
		tmp = y2 * ((t * t_3) - ((x * t_7) + (k * t_8)))
	elif a <= 1.6e+33:
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_6)))
	elif a <= 1.35e+214:
		tmp = t * ((z * t_5) + ((j * t_1) + (y2 * t_3)))
	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(b * y4) - Float64(i * y5))
	t_2 = Float64(Float64(i * y1) - Float64(b * y0))
	t_3 = Float64(Float64(a * y5) - Float64(c * y4))
	t_4 = Float64(x * Float64(a * Float64(Float64(y * b) - Float64(y1 * y2))))
	t_5 = Float64(Float64(c * i) - Float64(a * b))
	t_6 = Float64(Float64(y * y3) - Float64(t * y2))
	t_7 = Float64(Float64(a * y1) - Float64(c * y0))
	t_8 = Float64(Float64(y0 * y5) - Float64(y1 * y4))
	tmp = 0.0
	if (a <= -1.6e+126)
		tmp = t_4;
	elseif (a <= -4.4e-30)
		tmp = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(Float64(y3 * t_7) + Float64(t * t_5))));
	elseif (a <= -4.4e-198)
		tmp = Float64(j * Float64(Float64(y3 * t_8) + Float64(Float64(t * t_1) + Float64(x * t_2))));
	elseif (a <= 6.2e-274)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * t_2)));
	elseif (a <= 8.5e-153)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * t_6)));
	elseif (a <= 1.4e-65)
		tmp = Float64(y2 * Float64(Float64(t * t_3) - Float64(Float64(x * t_7) + Float64(k * t_8))));
	elseif (a <= 1.6e+33)
		tmp = Float64(c * Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y4 * t_6))));
	elseif (a <= 1.35e+214)
		tmp = Float64(t * Float64(Float64(z * t_5) + Float64(Float64(j * t_1) + Float64(y2 * t_3))));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (b * y4) - (i * y5);
	t_2 = (i * y1) - (b * y0);
	t_3 = (a * y5) - (c * y4);
	t_4 = x * (a * ((y * b) - (y1 * y2)));
	t_5 = (c * i) - (a * b);
	t_6 = (y * y3) - (t * y2);
	t_7 = (a * y1) - (c * y0);
	t_8 = (y0 * y5) - (y1 * y4);
	tmp = 0.0;
	if (a <= -1.6e+126)
		tmp = t_4;
	elseif (a <= -4.4e-30)
		tmp = z * ((k * ((b * y0) - (i * y1))) + ((y3 * t_7) + (t * t_5)));
	elseif (a <= -4.4e-198)
		tmp = j * ((y3 * t_8) + ((t * t_1) + (x * t_2)));
	elseif (a <= 6.2e-274)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_2));
	elseif (a <= 8.5e-153)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_6));
	elseif (a <= 1.4e-65)
		tmp = y2 * ((t * t_3) - ((x * t_7) + (k * t_8)));
	elseif (a <= 1.6e+33)
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_6)));
	elseif (a <= 1.35e+214)
		tmp = t * ((z * t_5) + ((j * t_1) + (y2 * t_3)));
	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[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(a * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.6e+126], t$95$4, If[LessEqual[a, -4.4e-30], N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y3 * t$95$7), $MachinePrecision] + N[(t * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.4e-198], N[(j * N[(N[(y3 * t$95$8), $MachinePrecision] + N[(N[(t * t$95$1), $MachinePrecision] + N[(x * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e-274], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e-153], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e-65], N[(y2 * N[(N[(t * t$95$3), $MachinePrecision] - N[(N[(x * t$95$7), $MachinePrecision] + N[(k * t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+33], N[(c * N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e+214], N[(t * N[(N[(z * t$95$5), $MachinePrecision] + N[(N[(j * t$95$1), $MachinePrecision] + N[(y2 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -1.5999999999999999e126 or 1.35000000000000005e214 < a

   1. Initial program 19.2%

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

   3. Simplified 19.2%

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

   4. Taylor expanded in x around inf 24.0%

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

   5. Taylor expanded in a around inf 57.9%

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

      1. mul-1-neg 57.9%

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

      2. unsub-neg 57.9%

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

   7. Simplified 57.9%

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

   if -1.5999999999999999e126 < a < -4.39999999999999967e-30

   1. Initial program 37.1%

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

   3. Simplified 37.1%

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

   4. Taylor expanded in z around -inf 55.3%

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

   if -4.39999999999999967e-30 < a < -4.4000000000000001e-198

   1. Initial program 30.7%

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

   3. Simplified 30.7%

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

   4. Taylor expanded in j around inf 61.4%

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

      1. associate--l+ 61.4%

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

      2. mul-1-neg 61.4%

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

      3. *-commutative 61.4%

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

      4. *-commutative 61.4%

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

      5. *-commutative 61.4%

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

   6. Simplified 61.4%

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

   if -4.4000000000000001e-198 < a < 6.19999999999999956e-274

   1. Initial program 29.7%

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

   3. Simplified 29.7%

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

   4. Taylor expanded in x around inf 54.9%

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

   if 6.19999999999999956e-274 < a < 8.4999999999999996e-153

   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%

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

   4. Taylor expanded in y4 around inf 59.4%

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

   if 8.4999999999999996e-153 < a < 1.4e-65

   1. Initial program 37.1%

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

   3. Simplified 37.1%

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

   4. Taylor expanded in y2 around inf 69.0%

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

   if 1.4e-65 < a < 1.60000000000000009e33

   1. Initial program 30.1%

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

   3. Simplified 30.1%

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

   4. Taylor expanded in c around inf 65.9%

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

      1. associate--l+ 65.9%

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

      2. mul-1-neg 65.9%

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

      3. *-commutative 65.9%

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

   6. Simplified 65.9%

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

   if 1.60000000000000009e33 < a < 1.35000000000000005e214

   1. Initial program 37.6%

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

   3. Simplified 37.6%

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

   4. Taylor expanded in t around inf 60.4%

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

      1. associate--l+ 60.4%

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

      2. mul-1-neg 60.4%

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

      3. *-commutative 60.4%

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

      4. *-commutative 60.4%

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

      5. *-commutative 60.4%

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

      6. *-commutative 60.4%

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

      7. *-commutative 60.4%

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

   6. Simplified 60.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(b \cdot a - i \cdot c\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - y2 \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-198}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + \left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-274}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-153}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-65}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right) - \left(x \cdot \left(a \cdot y1 - c \cdot y0\right) + k \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+33}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+214}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \end{array} \]

Alternative 12: 32.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -1.6 \cdot 10^{+216}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -6 \cdot 10^{-94}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -1.95 \cdot 10^{-185}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{elif}\;y2 \leq 1.22 \cdot 10^{+154}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 9.8 \cdot 10^{+213}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -1.6e+216)
   (* x (* a (- (* y b) (* y1 y2))))
   (if (<= y2 -6e-94)
     (* y4 (* k (- (* y1 y2) (* y b))))
     (if (<= y2 -1.95e-185)
       (* (* y c) (- (* y3 y4) (* x i)))
       (if (<= y2 1.22e+154)
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2)))))
         (if (<= y2 9.8e+213)
           (* i (* y1 (* x j)))
           (* y0 (* k (- (* z b) (* y2 y5))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.6e+216) {
		tmp = x * (a * ((y * b) - (y1 * y2)));
	} else if (y2 <= -6e-94) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (y2 <= -1.95e-185) {
		tmp = (y * c) * ((y3 * y4) - (x * i));
	} else if (y2 <= 1.22e+154) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (y2 <= 9.8e+213) {
		tmp = i * (y1 * (x * j));
	} else {
		tmp = y0 * (k * ((z * b) - (y2 * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-1.6d+216)) then
        tmp = x * (a * ((y * b) - (y1 * y2)))
    else if (y2 <= (-6d-94)) then
        tmp = y4 * (k * ((y1 * y2) - (y * b)))
    else if (y2 <= (-1.95d-185)) then
        tmp = (y * c) * ((y3 * y4) - (x * i))
    else if (y2 <= 1.22d+154) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else if (y2 <= 9.8d+213) then
        tmp = i * (y1 * (x * j))
    else
        tmp = y0 * (k * ((z * b) - (y2 * y5)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.6e+216) {
		tmp = x * (a * ((y * b) - (y1 * y2)));
	} else if (y2 <= -6e-94) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (y2 <= -1.95e-185) {
		tmp = (y * c) * ((y3 * y4) - (x * i));
	} else if (y2 <= 1.22e+154) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (y2 <= 9.8e+213) {
		tmp = i * (y1 * (x * j));
	} else {
		tmp = y0 * (k * ((z * b) - (y2 * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -1.6e+216:
		tmp = x * (a * ((y * b) - (y1 * y2)))
	elif y2 <= -6e-94:
		tmp = y4 * (k * ((y1 * y2) - (y * b)))
	elif y2 <= -1.95e-185:
		tmp = (y * c) * ((y3 * y4) - (x * i))
	elif y2 <= 1.22e+154:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	elif y2 <= 9.8e+213:
		tmp = i * (y1 * (x * j))
	else:
		tmp = y0 * (k * ((z * b) - (y2 * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -1.6e+216)
		tmp = Float64(x * Float64(a * Float64(Float64(y * b) - Float64(y1 * y2))));
	elseif (y2 <= -6e-94)
		tmp = Float64(y4 * Float64(k * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (y2 <= -1.95e-185)
		tmp = Float64(Float64(y * c) * Float64(Float64(y3 * y4) - Float64(x * i)));
	elseif (y2 <= 1.22e+154)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y2 <= 9.8e+213)
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	else
		tmp = Float64(y0 * Float64(k * Float64(Float64(z * b) - Float64(y2 * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -1.6e+216)
		tmp = x * (a * ((y * b) - (y1 * y2)));
	elseif (y2 <= -6e-94)
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	elseif (y2 <= -1.95e-185)
		tmp = (y * c) * ((y3 * y4) - (x * i));
	elseif (y2 <= 1.22e+154)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	elseif (y2 <= 9.8e+213)
		tmp = i * (y1 * (x * j));
	else
		tmp = y0 * (k * ((z * b) - (y2 * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -1.6e+216], N[(x * N[(a * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -6e-94], N[(y4 * N[(k * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.95e-185], N[(N[(y * c), $MachinePrecision] * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.22e+154], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 9.8e+213], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(k * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y2 < -1.59999999999999985e216

   1. Initial program 15.6%

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

   3. Simplified 15.6%

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

   4. Taylor expanded in x around inf 46.2%

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

   5. Taylor expanded in a around inf 58.3%

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

      1. mul-1-neg 58.3%

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

      2. unsub-neg 58.3%

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

   7. Simplified 58.3%

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

   if -1.59999999999999985e216 < y2 < -6.0000000000000003e-94

   1. Initial program 27.7%

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

   3. Simplified 27.7%

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

   4. Taylor expanded in y4 around inf 36.7%

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

   5. Taylor expanded in k around inf 44.2%

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

      1. +-commutative 44.2%

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

      2. mul-1-neg 44.2%

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

      3. unsub-neg 44.2%

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

   7. Simplified 44.2%

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

   if -6.0000000000000003e-94 < y2 < -1.95e-185

   1. Initial program 49.9%

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

   3. Simplified 49.9%

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

   4. Taylor expanded in c around inf 75.7%

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

      1. associate--l+ 75.7%

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

      2. mul-1-neg 75.7%

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

      3. *-commutative 75.7%

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

   6. Simplified 75.7%

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

   7. Taylor expanded in y around -inf 51.3%

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

      1. associate-*r* 57.2%

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

      2. *-commutative 57.2%

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

      3. mul-1-neg 57.2%

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

      4. sub-neg 57.2%

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

   9. Simplified 57.2%

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

   if -1.95e-185 < y2 < 1.22e154

   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%

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

   4. Taylor expanded in y4 around inf 51.1%

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

   if 1.22e154 < y2 < 9.79999999999999994e213

   1. Initial program 29.3%

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

   3. Simplified 35.2%

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

   4. Taylor expanded in y1 around inf 41.2%

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

      1. mul-1-neg 41.2%

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

      2. *-commutative 41.2%

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

      3. *-commutative 41.2%

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

      4. *-commutative 41.2%

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

      5. mul-1-neg 41.2%

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

      6. *-commutative 41.2%

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

   6. Simplified 41.2%

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

   7. Taylor expanded in i around inf 41.9%

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

   8. Taylor expanded in j around inf 53.6%

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

      1. *-commutative 53.6%

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

      2. associate-*l* 59.2%

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

   10. Simplified 59.2%

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

   if 9.79999999999999994e213 < 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 39.2%

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

   4. Taylor expanded in y0 around inf 25.3%

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

      1. *-commutative 25.3%

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

      2. *-commutative 25.3%

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

      3. mul-1-neg 25.3%

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

      4. *-commutative 25.3%

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

      5. *-commutative 25.3%

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

   6. Simplified 25.3%

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

   7. Taylor expanded in k around inf 64.7%

      \[\leadsto y0 \cdot \color{blue}{\left(k \cdot \left(z \cdot b - y5 \cdot y2\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.6 \cdot 10^{+216}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -6 \cdot 10^{-94}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -1.95 \cdot 10^{-185}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{elif}\;y2 \leq 1.22 \cdot 10^{+154}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 9.8 \cdot 10^{+213}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \end{array} \]

Alternative 13: 28.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ t_2 := c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{if}\;x \leq -3.6 \cdot 10^{+270}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{+212}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{+93}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-291}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{-221}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-203}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+115}:\\ \;\;\;\;t \cdot \left(b \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y (* y3 (- (* c y4) (* a y5)))))
        (t_2 (* c (* t (- (* z i) (* y2 y4))))))
   (if (<= x -3.6e+270)
     (* y1 (* a (* x (- y2))))
     (if (<= x -7.8e+212)
       t_2
       (if (<= x -2.15e+93)
         (* c (* y0 (- (* x y2) (* z y3))))
         (if (<= x -1.45e-170)
           t_1
           (if (<= x 8.8e-291)
             (* y0 (* k (- (* z b) (* y2 y5))))
             (if (<= x 6.4e-221)
               t_1
               (if (<= x 1.12e-203)
                 t_2
                 (if (<= x 1.9e+115)
                   (* t (* b (- (* j y4) (* z a))))
                   (* i (* y1 (* 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 = y * (y3 * ((c * y4) - (a * y5)));
	double t_2 = c * (t * ((z * i) - (y2 * y4)));
	double tmp;
	if (x <= -3.6e+270) {
		tmp = y1 * (a * (x * -y2));
	} else if (x <= -7.8e+212) {
		tmp = t_2;
	} else if (x <= -2.15e+93) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (x <= -1.45e-170) {
		tmp = t_1;
	} else if (x <= 8.8e-291) {
		tmp = y0 * (k * ((z * b) - (y2 * y5)));
	} else if (x <= 6.4e-221) {
		tmp = t_1;
	} else if (x <= 1.12e-203) {
		tmp = t_2;
	} else if (x <= 1.9e+115) {
		tmp = t * (b * ((j * y4) - (z * a)));
	} else {
		tmp = i * (y1 * (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 = y * (y3 * ((c * y4) - (a * y5)))
    t_2 = c * (t * ((z * i) - (y2 * y4)))
    if (x <= (-3.6d+270)) then
        tmp = y1 * (a * (x * -y2))
    else if (x <= (-7.8d+212)) then
        tmp = t_2
    else if (x <= (-2.15d+93)) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (x <= (-1.45d-170)) then
        tmp = t_1
    else if (x <= 8.8d-291) then
        tmp = y0 * (k * ((z * b) - (y2 * y5)))
    else if (x <= 6.4d-221) then
        tmp = t_1
    else if (x <= 1.12d-203) then
        tmp = t_2
    else if (x <= 1.9d+115) then
        tmp = t * (b * ((j * y4) - (z * a)))
    else
        tmp = i * (y1 * (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 = y * (y3 * ((c * y4) - (a * y5)));
	double t_2 = c * (t * ((z * i) - (y2 * y4)));
	double tmp;
	if (x <= -3.6e+270) {
		tmp = y1 * (a * (x * -y2));
	} else if (x <= -7.8e+212) {
		tmp = t_2;
	} else if (x <= -2.15e+93) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (x <= -1.45e-170) {
		tmp = t_1;
	} else if (x <= 8.8e-291) {
		tmp = y0 * (k * ((z * b) - (y2 * y5)));
	} else if (x <= 6.4e-221) {
		tmp = t_1;
	} else if (x <= 1.12e-203) {
		tmp = t_2;
	} else if (x <= 1.9e+115) {
		tmp = t * (b * ((j * y4) - (z * a)));
	} else {
		tmp = i * (y1 * (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 = y * (y3 * ((c * y4) - (a * y5)))
	t_2 = c * (t * ((z * i) - (y2 * y4)))
	tmp = 0
	if x <= -3.6e+270:
		tmp = y1 * (a * (x * -y2))
	elif x <= -7.8e+212:
		tmp = t_2
	elif x <= -2.15e+93:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif x <= -1.45e-170:
		tmp = t_1
	elif x <= 8.8e-291:
		tmp = y0 * (k * ((z * b) - (y2 * y5)))
	elif x <= 6.4e-221:
		tmp = t_1
	elif x <= 1.12e-203:
		tmp = t_2
	elif x <= 1.9e+115:
		tmp = t * (b * ((j * y4) - (z * a)))
	else:
		tmp = i * (y1 * (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(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))
	t_2 = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))))
	tmp = 0.0
	if (x <= -3.6e+270)
		tmp = Float64(y1 * Float64(a * Float64(x * Float64(-y2))));
	elseif (x <= -7.8e+212)
		tmp = t_2;
	elseif (x <= -2.15e+93)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (x <= -1.45e-170)
		tmp = t_1;
	elseif (x <= 8.8e-291)
		tmp = Float64(y0 * Float64(k * Float64(Float64(z * b) - Float64(y2 * y5))));
	elseif (x <= 6.4e-221)
		tmp = t_1;
	elseif (x <= 1.12e-203)
		tmp = t_2;
	elseif (x <= 1.9e+115)
		tmp = Float64(t * Float64(b * Float64(Float64(j * y4) - Float64(z * a))));
	else
		tmp = Float64(i * Float64(y1 * 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 = y * (y3 * ((c * y4) - (a * y5)));
	t_2 = c * (t * ((z * i) - (y2 * y4)));
	tmp = 0.0;
	if (x <= -3.6e+270)
		tmp = y1 * (a * (x * -y2));
	elseif (x <= -7.8e+212)
		tmp = t_2;
	elseif (x <= -2.15e+93)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (x <= -1.45e-170)
		tmp = t_1;
	elseif (x <= 8.8e-291)
		tmp = y0 * (k * ((z * b) - (y2 * y5)));
	elseif (x <= 6.4e-221)
		tmp = t_1;
	elseif (x <= 1.12e-203)
		tmp = t_2;
	elseif (x <= 1.9e+115)
		tmp = t * (b * ((j * y4) - (z * a)));
	else
		tmp = i * (y1 * (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[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.6e+270], N[(y1 * N[(a * N[(x * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.8e+212], t$95$2, If[LessEqual[x, -2.15e+93], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.45e-170], t$95$1, If[LessEqual[x, 8.8e-291], N[(y0 * N[(k * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.4e-221], t$95$1, If[LessEqual[x, 1.12e-203], t$95$2, If[LessEqual[x, 1.9e+115], N[(t * N[(b * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -3.6000000000000002e270

   1. Initial program 17.2%

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

   3. Simplified 25.6%

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

   4. Taylor expanded in y1 around inf 59.6%

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

      1. mul-1-neg 59.6%

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

      2. *-commutative 59.6%

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

      3. *-commutative 59.6%

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

      4. *-commutative 59.6%

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

      5. mul-1-neg 59.6%

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

      6. *-commutative 59.6%

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

   6. Simplified 59.6%

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

   7. Taylor expanded in a around inf 60.3%

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

   8. Taylor expanded in y3 around 0 60.4%

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

      1. mul-1-neg 60.4%

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

   10. Simplified 60.4%

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

   if -3.6000000000000002e270 < x < -7.8000000000000003e212 or 6.40000000000000031e-221 < x < 1.12e-203

   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%

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

   4. Taylor expanded in c around inf 26.8%

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

      1. associate--l+ 26.8%

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

      2. mul-1-neg 26.8%

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

      3. *-commutative 26.8%

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

   6. Simplified 26.8%

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

   7. Taylor expanded in t around -inf 53.2%

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

      1. *-commutative 53.2%

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

      2. mul-1-neg 53.2%

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

      3. unsub-neg 53.2%

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

   9. Simplified 53.2%

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

   if -7.8000000000000003e212 < x < -2.15e93

   1. Initial program 27.6%

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

   3. Simplified 27.6%

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

   4. Taylor expanded in c around inf 45.0%

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

      1. associate--l+ 45.0%

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

      2. mul-1-neg 45.0%

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

      3. *-commutative 45.0%

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

   6. Simplified 45.0%

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

   7. Taylor expanded in y0 around -inf 45.2%

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

   if -2.15e93 < x < -1.45e-170 or 8.8000000000000001e-291 < x < 6.40000000000000031e-221

   1. Initial program 46.5%

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

   3. Simplified 46.5%

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

   4. Taylor expanded in y around inf 47.2%

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

      1. associate--l+ 47.2%

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

      2. mul-1-neg 47.2%

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

      3. *-commutative 47.2%

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

      4. *-commutative 47.2%

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

      5. mul-1-neg 47.2%

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

      6. *-commutative 47.2%

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

      7. *-commutative 47.2%

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

   6. Simplified 47.2%

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

   7. Taylor expanded in y3 around inf 39.2%

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

   if -1.45e-170 < x < 8.8000000000000001e-291

   1. Initial program 42.5%

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

   3. Simplified 45.5%

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

   4. Taylor expanded in y0 around inf 44.7%

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

      1. *-commutative 44.7%

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

      2. *-commutative 44.7%

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

      3. mul-1-neg 44.7%

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

      4. *-commutative 44.7%

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

      5. *-commutative 44.7%

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

   6. Simplified 44.7%

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

   7. Taylor expanded in k around inf 47.8%

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

   if 1.12e-203 < x < 1.9e115

   1. Initial program 29.0%

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

   3. Simplified 29.0%

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

   4. Taylor expanded in t around inf 48.9%

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

      1. associate--l+ 48.9%

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

      2. mul-1-neg 48.9%

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

      3. *-commutative 48.9%

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

      4. *-commutative 48.9%

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

      5. *-commutative 48.9%

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

      6. *-commutative 48.9%

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

      7. *-commutative 48.9%

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

   6. Simplified 48.9%

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

   7. Taylor expanded in b around inf 37.5%

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

      1. *-commutative 37.5%

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

      2. associate-*l* 41.8%

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

      3. *-commutative 41.8%

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

      4. *-commutative 41.8%

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

   9. Simplified 41.8%

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

   if 1.9e115 < x

   1. Initial program 20.5%

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

   3. Simplified 25.6%

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

   4. Taylor expanded in y1 around inf 46.3%

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

      1. mul-1-neg 46.3%

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

      2. *-commutative 46.3%

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

      3. *-commutative 46.3%

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

      4. *-commutative 46.3%

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

      5. mul-1-neg 46.3%

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

      6. *-commutative 46.3%

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

   6. Simplified 46.3%

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

   7. Taylor expanded in i around inf 49.3%

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

   8. Taylor expanded in j around inf 46.8%

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

      1. *-commutative 46.8%

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

      2. associate-*l* 46.8%

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

   10. Simplified 46.8%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+270}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{+212}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{+93}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-170}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-291}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{-221}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-203}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+115}:\\ \;\;\;\;t \cdot \left(b \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \]

Alternative 14: 31.9% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ t_2 := c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ t_3 := y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4000000000000:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-221}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-292}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-201}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-81}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq 7.9 \cdot 10^{+177}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* i (- (* x j) (* z k)))))
        (t_2 (* c (* t (- (* z i) (* y2 y4)))))
        (t_3 (* y4 (* k (- (* y1 y2) (* y b))))))
   (if (<= t -2.9e+135)
     t_2
     (if (<= t -6.5e+68)
       t_1
       (if (<= t -4000000000000.0)
         (* y0 (* y5 (- (* j y3) (* k y2))))
         (if (<= t -1.75e-221)
           t_1
           (if (<= t 1.35e-292)
             (* y (* y3 (- (* c y4) (* a y5))))
             (if (<= t 9.2e-201)
               t_3
               (if (<= t 4e-81)
                 (* a (* y1 (- (* z y3) (* x y2))))
                 (if (<= t 7.9e+177) t_3 t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (i * ((x * j) - (z * k)));
	double t_2 = c * (t * ((z * i) - (y2 * y4)));
	double t_3 = y4 * (k * ((y1 * y2) - (y * b)));
	double tmp;
	if (t <= -2.9e+135) {
		tmp = t_2;
	} else if (t <= -6.5e+68) {
		tmp = t_1;
	} else if (t <= -4000000000000.0) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (t <= -1.75e-221) {
		tmp = t_1;
	} else if (t <= 1.35e-292) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else if (t <= 9.2e-201) {
		tmp = t_3;
	} else if (t <= 4e-81) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (t <= 7.9e+177) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y1 * (i * ((x * j) - (z * k)))
    t_2 = c * (t * ((z * i) - (y2 * y4)))
    t_3 = y4 * (k * ((y1 * y2) - (y * b)))
    if (t <= (-2.9d+135)) then
        tmp = t_2
    else if (t <= (-6.5d+68)) then
        tmp = t_1
    else if (t <= (-4000000000000.0d0)) then
        tmp = y0 * (y5 * ((j * y3) - (k * y2)))
    else if (t <= (-1.75d-221)) then
        tmp = t_1
    else if (t <= 1.35d-292) then
        tmp = y * (y3 * ((c * y4) - (a * y5)))
    else if (t <= 9.2d-201) then
        tmp = t_3
    else if (t <= 4d-81) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (t <= 7.9d+177) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (i * ((x * j) - (z * k)));
	double t_2 = c * (t * ((z * i) - (y2 * y4)));
	double t_3 = y4 * (k * ((y1 * y2) - (y * b)));
	double tmp;
	if (t <= -2.9e+135) {
		tmp = t_2;
	} else if (t <= -6.5e+68) {
		tmp = t_1;
	} else if (t <= -4000000000000.0) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (t <= -1.75e-221) {
		tmp = t_1;
	} else if (t <= 1.35e-292) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else if (t <= 9.2e-201) {
		tmp = t_3;
	} else if (t <= 4e-81) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (t <= 7.9e+177) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y1 * (i * ((x * j) - (z * k)))
	t_2 = c * (t * ((z * i) - (y2 * y4)))
	t_3 = y4 * (k * ((y1 * y2) - (y * b)))
	tmp = 0
	if t <= -2.9e+135:
		tmp = t_2
	elif t <= -6.5e+68:
		tmp = t_1
	elif t <= -4000000000000.0:
		tmp = y0 * (y5 * ((j * y3) - (k * y2)))
	elif t <= -1.75e-221:
		tmp = t_1
	elif t <= 1.35e-292:
		tmp = y * (y3 * ((c * y4) - (a * y5)))
	elif t <= 9.2e-201:
		tmp = t_3
	elif t <= 4e-81:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif t <= 7.9e+177:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * Float64(i * Float64(Float64(x * j) - Float64(z * k))))
	t_2 = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))))
	t_3 = Float64(y4 * Float64(k * Float64(Float64(y1 * y2) - Float64(y * b))))
	tmp = 0.0
	if (t <= -2.9e+135)
		tmp = t_2;
	elseif (t <= -6.5e+68)
		tmp = t_1;
	elseif (t <= -4000000000000.0)
		tmp = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))));
	elseif (t <= -1.75e-221)
		tmp = t_1;
	elseif (t <= 1.35e-292)
		tmp = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))));
	elseif (t <= 9.2e-201)
		tmp = t_3;
	elseif (t <= 4e-81)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (t <= 7.9e+177)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y1 * (i * ((x * j) - (z * k)));
	t_2 = c * (t * ((z * i) - (y2 * y4)));
	t_3 = y4 * (k * ((y1 * y2) - (y * b)));
	tmp = 0.0;
	if (t <= -2.9e+135)
		tmp = t_2;
	elseif (t <= -6.5e+68)
		tmp = t_1;
	elseif (t <= -4000000000000.0)
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	elseif (t <= -1.75e-221)
		tmp = t_1;
	elseif (t <= 1.35e-292)
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	elseif (t <= 9.2e-201)
		tmp = t_3;
	elseif (t <= 4e-81)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (t <= 7.9e+177)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y1 * N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y4 * N[(k * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e+135], t$95$2, If[LessEqual[t, -6.5e+68], t$95$1, If[LessEqual[t, -4000000000000.0], N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.75e-221], t$95$1, If[LessEqual[t, 1.35e-292], N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e-201], t$95$3, If[LessEqual[t, 4e-81], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.9e+177], t$95$3, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.8999999999999999e135 or 7.8999999999999999e177 < t

   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%

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

   4. Taylor expanded in c around inf 39.3%

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

      1. associate--l+ 39.3%

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

      2. mul-1-neg 39.3%

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

      3. *-commutative 39.3%

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

   6. Simplified 39.3%

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

   7. Taylor expanded in t around -inf 55.9%

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

      1. *-commutative 55.9%

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

      2. mul-1-neg 55.9%

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

      3. unsub-neg 55.9%

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

   9. Simplified 55.9%

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

   if -2.8999999999999999e135 < t < -6.5000000000000005e68 or -4e12 < t < -1.7499999999999999e-221

   1. Initial program 31.7%

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

   3. Simplified 37.6%

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

   4. Taylor expanded in y1 around inf 40.3%

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

      1. mul-1-neg 40.3%

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

      2. *-commutative 40.3%

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

      3. *-commutative 40.3%

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

      4. *-commutative 40.3%

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

      5. mul-1-neg 40.3%

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

      6. *-commutative 40.3%

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

   6. Simplified 40.3%

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

   7. Taylor expanded in i around inf 46.1%

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

   if -6.5000000000000005e68 < t < -4e12

   1. Initial program 9.1%

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

   3. Simplified 9.1%

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

   4. Taylor expanded in y0 around inf 54.6%

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

      1. *-commutative 54.6%

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

      2. *-commutative 54.6%

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

      3. mul-1-neg 54.6%

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

      4. *-commutative 54.6%

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

      5. *-commutative 54.6%

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

   6. Simplified 54.6%

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

   7. Taylor expanded in y5 around inf 55.7%

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

   if -1.7499999999999999e-221 < t < 1.35e-292

   1. Initial program 39.9%

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

   3. Simplified 39.9%

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

   4. Taylor expanded in y around inf 68.4%

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

      1. associate--l+ 68.4%

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

      2. mul-1-neg 68.4%

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

      3. *-commutative 68.4%

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

      4. *-commutative 68.4%

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

      5. mul-1-neg 68.4%

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

      6. *-commutative 68.4%

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

      7. *-commutative 68.4%

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

   6. Simplified 68.4%

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

   7. Taylor expanded in y3 around inf 52.9%

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

   if 1.35e-292 < t < 9.19999999999999943e-201 or 3.9999999999999998e-81 < t < 7.8999999999999999e177

   1. Initial program 31.7%

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

   3. Simplified 31.7%

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

   4. Taylor expanded in y4 around inf 46.6%

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

   5. Taylor expanded in k around inf 44.1%

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

      1. +-commutative 44.1%

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

      2. mul-1-neg 44.1%

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

      3. unsub-neg 44.1%

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

   7. Simplified 44.1%

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

   if 9.19999999999999943e-201 < t < 3.9999999999999998e-81

   1. Initial program 38.2%

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

   3. Simplified 38.2%

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

   4. Taylor expanded in y1 around inf 39.6%

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

      1. mul-1-neg 39.6%

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

      2. *-commutative 39.6%

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

      3. *-commutative 39.6%

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

      4. *-commutative 39.6%

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

      5. mul-1-neg 39.6%

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

      6. *-commutative 39.6%

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

   6. Simplified 39.6%

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

   7. Taylor expanded in a around inf 36.3%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+135}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+68}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;t \leq -4000000000000:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-221}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-292}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-201}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-81}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq 7.9 \cdot 10^{+177}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \end{array} \]

Alternative 15: 29.8% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{if}\;x \leq -1.96 \cdot 10^{+270}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{+198}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-172}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-307}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-96}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-33}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+120}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* i (- (* x j) (* z k))))))
   (if (<= x -1.96e+270)
     (* y1 (* a (* x (- y2))))
     (if (<= x -2.7e+198)
       (* c (* t (- (* z i) (* y2 y4))))
       (if (<= x -7e-6)
         t_1
         (if (<= x -7.8e-172)
           (* y (* y3 (- (* c y4) (* a y5))))
           (if (<= x -2.6e-307)
             (* y0 (* k (- (* z b) (* y2 y5))))
             (if (<= x 4.8e-96)
               (* y4 (* b (- (* t j) (* y k))))
               (if (<= x 7e-33)
                 (* a (* y1 (- (* z y3) (* x y2))))
                 (if (<= x 4.8e+120)
                   (* y4 (* j (- (* t b) (* y1 y3))))
                   t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (i * ((x * j) - (z * k)));
	double tmp;
	if (x <= -1.96e+270) {
		tmp = y1 * (a * (x * -y2));
	} else if (x <= -2.7e+198) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (x <= -7e-6) {
		tmp = t_1;
	} else if (x <= -7.8e-172) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else if (x <= -2.6e-307) {
		tmp = y0 * (k * ((z * b) - (y2 * y5)));
	} else if (x <= 4.8e-96) {
		tmp = y4 * (b * ((t * j) - (y * k)));
	} else if (x <= 7e-33) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (x <= 4.8e+120) {
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y1 * (i * ((x * j) - (z * k)))
    if (x <= (-1.96d+270)) then
        tmp = y1 * (a * (x * -y2))
    else if (x <= (-2.7d+198)) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (x <= (-7d-6)) then
        tmp = t_1
    else if (x <= (-7.8d-172)) then
        tmp = y * (y3 * ((c * y4) - (a * y5)))
    else if (x <= (-2.6d-307)) then
        tmp = y0 * (k * ((z * b) - (y2 * y5)))
    else if (x <= 4.8d-96) then
        tmp = y4 * (b * ((t * j) - (y * k)))
    else if (x <= 7d-33) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (x <= 4.8d+120) then
        tmp = y4 * (j * ((t * b) - (y1 * y3)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (i * ((x * j) - (z * k)));
	double tmp;
	if (x <= -1.96e+270) {
		tmp = y1 * (a * (x * -y2));
	} else if (x <= -2.7e+198) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (x <= -7e-6) {
		tmp = t_1;
	} else if (x <= -7.8e-172) {
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	} else if (x <= -2.6e-307) {
		tmp = y0 * (k * ((z * b) - (y2 * y5)));
	} else if (x <= 4.8e-96) {
		tmp = y4 * (b * ((t * j) - (y * k)));
	} else if (x <= 7e-33) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (x <= 4.8e+120) {
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y1 * (i * ((x * j) - (z * k)))
	tmp = 0
	if x <= -1.96e+270:
		tmp = y1 * (a * (x * -y2))
	elif x <= -2.7e+198:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif x <= -7e-6:
		tmp = t_1
	elif x <= -7.8e-172:
		tmp = y * (y3 * ((c * y4) - (a * y5)))
	elif x <= -2.6e-307:
		tmp = y0 * (k * ((z * b) - (y2 * y5)))
	elif x <= 4.8e-96:
		tmp = y4 * (b * ((t * j) - (y * k)))
	elif x <= 7e-33:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif x <= 4.8e+120:
		tmp = y4 * (j * ((t * b) - (y1 * y3)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * Float64(i * Float64(Float64(x * j) - Float64(z * k))))
	tmp = 0.0
	if (x <= -1.96e+270)
		tmp = Float64(y1 * Float64(a * Float64(x * Float64(-y2))));
	elseif (x <= -2.7e+198)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (x <= -7e-6)
		tmp = t_1;
	elseif (x <= -7.8e-172)
		tmp = Float64(y * Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))));
	elseif (x <= -2.6e-307)
		tmp = Float64(y0 * Float64(k * Float64(Float64(z * b) - Float64(y2 * y5))));
	elseif (x <= 4.8e-96)
		tmp = Float64(y4 * Float64(b * Float64(Float64(t * j) - Float64(y * k))));
	elseif (x <= 7e-33)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (x <= 4.8e+120)
		tmp = Float64(y4 * Float64(j * Float64(Float64(t * b) - Float64(y1 * y3))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y1 * (i * ((x * j) - (z * k)));
	tmp = 0.0;
	if (x <= -1.96e+270)
		tmp = y1 * (a * (x * -y2));
	elseif (x <= -2.7e+198)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (x <= -7e-6)
		tmp = t_1;
	elseif (x <= -7.8e-172)
		tmp = y * (y3 * ((c * y4) - (a * y5)));
	elseif (x <= -2.6e-307)
		tmp = y0 * (k * ((z * b) - (y2 * y5)));
	elseif (x <= 4.8e-96)
		tmp = y4 * (b * ((t * j) - (y * k)));
	elseif (x <= 7e-33)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (x <= 4.8e+120)
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y1 * N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.96e+270], N[(y1 * N[(a * N[(x * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.7e+198], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7e-6], t$95$1, If[LessEqual[x, -7.8e-172], N[(y * N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.6e-307], N[(y0 * N[(k * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.8e-96], N[(y4 * N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e-33], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.8e+120], N[(y4 * N[(j * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if x < -1.9599999999999999e270

   1. Initial program 17.2%

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

   3. Simplified 25.6%

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

   4. Taylor expanded in y1 around inf 59.6%

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

      1. mul-1-neg 59.6%

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

      2. *-commutative 59.6%

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

      3. *-commutative 59.6%

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

      4. *-commutative 59.6%

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

      5. mul-1-neg 59.6%

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

      6. *-commutative 59.6%

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

   6. Simplified 59.6%

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

   7. Taylor expanded in a around inf 60.3%

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

   8. Taylor expanded in y3 around 0 60.4%

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

      1. mul-1-neg 60.4%

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

   10. Simplified 60.4%

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

   if -1.9599999999999999e270 < x < -2.6999999999999999e198

   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%

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

   4. Taylor expanded in c around inf 37.1%

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

      1. associate--l+ 37.1%

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

      2. mul-1-neg 37.1%

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

      3. *-commutative 37.1%

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

   6. Simplified 37.1%

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

   7. Taylor expanded in t around -inf 53.3%

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

      1. *-commutative 53.3%

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

      2. mul-1-neg 53.3%

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

      3. unsub-neg 53.3%

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

   9. Simplified 53.3%

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

   if -2.6999999999999999e198 < x < -6.99999999999999989e-6 or 4.80000000000000002e120 < x

   1. Initial program 25.7%

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

   3. Simplified 31.1%

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

   4. Taylor expanded in y1 around inf 42.1%

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

      1. mul-1-neg 42.1%

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

      2. *-commutative 42.1%

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

      3. *-commutative 42.1%

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

      4. *-commutative 42.1%

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

      5. mul-1-neg 42.1%

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

      6. *-commutative 42.1%

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

   6. Simplified 42.1%

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

   7. Taylor expanded in i around inf 48.2%

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

   if -6.99999999999999989e-6 < x < -7.79999999999999946e-172

   1. Initial program 50.1%

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

   3. Simplified 50.1%

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

   4. Taylor expanded in y around inf 47.5%

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

      1. associate--l+ 47.5%

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

      2. mul-1-neg 47.5%

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

      3. *-commutative 47.5%

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

      4. *-commutative 47.5%

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

      5. mul-1-neg 47.5%

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

      6. *-commutative 47.5%

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

      7. *-commutative 47.5%

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

   6. Simplified 47.5%

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

   7. Taylor expanded in y3 around inf 41.4%

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

   if -7.79999999999999946e-172 < x < -2.59999999999999996e-307

   1. Initial program 41.8%

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

   3. Simplified 45.1%

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

   4. Taylor expanded in y0 around inf 44.2%

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

      1. *-commutative 44.2%

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

      2. *-commutative 44.2%

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

      3. mul-1-neg 44.2%

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

      4. *-commutative 44.2%

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

      5. *-commutative 44.2%

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

   6. Simplified 44.2%

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

   7. Taylor expanded in k around inf 47.5%

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

   if -2.59999999999999996e-307 < x < 4.80000000000000038e-96

   1. Initial program 42.3%

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

   3. Simplified 42.3%

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

   4. Taylor expanded in y4 around inf 53.2%

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

   5. Taylor expanded in b around inf 45.9%

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

   if 4.80000000000000038e-96 < x < 6.9999999999999997e-33

   1. Initial program 42.9%

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

   3. Simplified 42.9%

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

   4. Taylor expanded in y1 around inf 43.7%

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

      1. mul-1-neg 43.7%

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

      2. *-commutative 43.7%

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

      3. *-commutative 43.7%

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

      4. *-commutative 43.7%

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

      5. mul-1-neg 43.7%

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

      6. *-commutative 43.7%

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

   6. Simplified 43.7%

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

   7. Taylor expanded in a around inf 44.3%

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

   if 6.9999999999999997e-33 < x < 4.80000000000000002e120

   1. Initial program 17.4%

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

   3. Simplified 17.4%

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

   4. Taylor expanded in y4 around inf 61.4%

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

   5. Taylor expanded in j around inf 53.6%

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

      1. mul-1-neg 53.6%

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

      2. unsub-neg 53.6%

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

      3. *-commutative 53.6%

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

   7. Simplified 53.6%

      \[\leadsto \color{blue}{y4 \cdot \left(j \cdot \left(b \cdot t - y1 \cdot y3\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.96 \cdot 10^{+270}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{+198}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-6}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-172}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-307}:\\ \;\;\;\;y0 \cdot \left(k \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-96}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-33}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+120}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \end{array} \]

Alternative 16: 30.6% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ t_2 := c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ t_3 := \left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{if}\;t \leq -1.26 \cdot 10^{+134}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{+78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+42}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -430000000000:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq -7.1 \cdot 10^{-155}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-221}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-235}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+178}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* i (- (* x j) (* z k)))))
        (t_2 (* c (* t (- (* z i) (* y2 y4)))))
        (t_3 (* (* y c) (- (* y3 y4) (* x i)))))
   (if (<= t -1.26e+134)
     t_2
     (if (<= t -1.75e+78)
       t_1
       (if (<= t -1.15e+42)
         t_3
         (if (<= t -430000000000.0)
           (* x (* b (- (* y a) (* j y0))))
           (if (<= t -7.1e-155)
             (* y4 (* j (- (* t b) (* y1 y3))))
             (if (<= t -7.8e-221)
               t_1
               (if (<= t 2.9e-235)
                 t_3
                 (if (<= t 9.8e+178)
                   (* y4 (* k (- (* y1 y2) (* y b))))
                   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 = y1 * (i * ((x * j) - (z * k)));
	double t_2 = c * (t * ((z * i) - (y2 * y4)));
	double t_3 = (y * c) * ((y3 * y4) - (x * i));
	double tmp;
	if (t <= -1.26e+134) {
		tmp = t_2;
	} else if (t <= -1.75e+78) {
		tmp = t_1;
	} else if (t <= -1.15e+42) {
		tmp = t_3;
	} else if (t <= -430000000000.0) {
		tmp = x * (b * ((y * a) - (j * y0)));
	} else if (t <= -7.1e-155) {
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	} else if (t <= -7.8e-221) {
		tmp = t_1;
	} else if (t <= 2.9e-235) {
		tmp = t_3;
	} else if (t <= 9.8e+178) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} 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 = y1 * (i * ((x * j) - (z * k)))
    t_2 = c * (t * ((z * i) - (y2 * y4)))
    t_3 = (y * c) * ((y3 * y4) - (x * i))
    if (t <= (-1.26d+134)) then
        tmp = t_2
    else if (t <= (-1.75d+78)) then
        tmp = t_1
    else if (t <= (-1.15d+42)) then
        tmp = t_3
    else if (t <= (-430000000000.0d0)) then
        tmp = x * (b * ((y * a) - (j * y0)))
    else if (t <= (-7.1d-155)) then
        tmp = y4 * (j * ((t * b) - (y1 * y3)))
    else if (t <= (-7.8d-221)) then
        tmp = t_1
    else if (t <= 2.9d-235) then
        tmp = t_3
    else if (t <= 9.8d+178) then
        tmp = y4 * (k * ((y1 * y2) - (y * b)))
    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 = y1 * (i * ((x * j) - (z * k)));
	double t_2 = c * (t * ((z * i) - (y2 * y4)));
	double t_3 = (y * c) * ((y3 * y4) - (x * i));
	double tmp;
	if (t <= -1.26e+134) {
		tmp = t_2;
	} else if (t <= -1.75e+78) {
		tmp = t_1;
	} else if (t <= -1.15e+42) {
		tmp = t_3;
	} else if (t <= -430000000000.0) {
		tmp = x * (b * ((y * a) - (j * y0)));
	} else if (t <= -7.1e-155) {
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	} else if (t <= -7.8e-221) {
		tmp = t_1;
	} else if (t <= 2.9e-235) {
		tmp = t_3;
	} else if (t <= 9.8e+178) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} 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 = y1 * (i * ((x * j) - (z * k)))
	t_2 = c * (t * ((z * i) - (y2 * y4)))
	t_3 = (y * c) * ((y3 * y4) - (x * i))
	tmp = 0
	if t <= -1.26e+134:
		tmp = t_2
	elif t <= -1.75e+78:
		tmp = t_1
	elif t <= -1.15e+42:
		tmp = t_3
	elif t <= -430000000000.0:
		tmp = x * (b * ((y * a) - (j * y0)))
	elif t <= -7.1e-155:
		tmp = y4 * (j * ((t * b) - (y1 * y3)))
	elif t <= -7.8e-221:
		tmp = t_1
	elif t <= 2.9e-235:
		tmp = t_3
	elif t <= 9.8e+178:
		tmp = y4 * (k * ((y1 * y2) - (y * b)))
	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(y1 * Float64(i * Float64(Float64(x * j) - Float64(z * k))))
	t_2 = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))))
	t_3 = Float64(Float64(y * c) * Float64(Float64(y3 * y4) - Float64(x * i)))
	tmp = 0.0
	if (t <= -1.26e+134)
		tmp = t_2;
	elseif (t <= -1.75e+78)
		tmp = t_1;
	elseif (t <= -1.15e+42)
		tmp = t_3;
	elseif (t <= -430000000000.0)
		tmp = Float64(x * Float64(b * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (t <= -7.1e-155)
		tmp = Float64(y4 * Float64(j * Float64(Float64(t * b) - Float64(y1 * y3))));
	elseif (t <= -7.8e-221)
		tmp = t_1;
	elseif (t <= 2.9e-235)
		tmp = t_3;
	elseif (t <= 9.8e+178)
		tmp = Float64(y4 * Float64(k * Float64(Float64(y1 * y2) - Float64(y * b))));
	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 = y1 * (i * ((x * j) - (z * k)));
	t_2 = c * (t * ((z * i) - (y2 * y4)));
	t_3 = (y * c) * ((y3 * y4) - (x * i));
	tmp = 0.0;
	if (t <= -1.26e+134)
		tmp = t_2;
	elseif (t <= -1.75e+78)
		tmp = t_1;
	elseif (t <= -1.15e+42)
		tmp = t_3;
	elseif (t <= -430000000000.0)
		tmp = x * (b * ((y * a) - (j * y0)));
	elseif (t <= -7.1e-155)
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	elseif (t <= -7.8e-221)
		tmp = t_1;
	elseif (t <= 2.9e-235)
		tmp = t_3;
	elseif (t <= 9.8e+178)
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	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[(y1 * N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * c), $MachinePrecision] * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.26e+134], t$95$2, If[LessEqual[t, -1.75e+78], t$95$1, If[LessEqual[t, -1.15e+42], t$95$3, If[LessEqual[t, -430000000000.0], N[(x * N[(b * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.1e-155], N[(y4 * N[(j * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.8e-221], t$95$1, If[LessEqual[t, 2.9e-235], t$95$3, If[LessEqual[t, 9.8e+178], N[(y4 * N[(k * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.2600000000000001e134 or 9.8000000000000003e178 < t

   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%

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

   4. Taylor expanded in c around inf 39.3%

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

      1. associate--l+ 39.3%

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

      2. mul-1-neg 39.3%

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

      3. *-commutative 39.3%

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

   6. Simplified 39.3%

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

   7. Taylor expanded in t around -inf 55.9%

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

      1. *-commutative 55.9%

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

      2. mul-1-neg 55.9%

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

      3. unsub-neg 55.9%

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

   9. Simplified 55.9%

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

   if -1.2600000000000001e134 < t < -1.7500000000000001e78 or -7.1e-155 < t < -7.7999999999999997e-221

   1. Initial program 29.3%

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

   3. Simplified 32.8%

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

   4. Taylor expanded in y1 around inf 44.0%

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

      1. mul-1-neg 44.0%

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

      2. *-commutative 44.0%

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

      3. *-commutative 44.0%

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

      4. *-commutative 44.0%

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

      5. mul-1-neg 44.0%

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

      6. *-commutative 44.0%

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

   6. Simplified 44.0%

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

   7. Taylor expanded in i around inf 54.5%

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

   if -1.7500000000000001e78 < t < -1.15e42 or -7.7999999999999997e-221 < t < 2.90000000000000009e-235

   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%

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

   4. Taylor expanded in c around inf 42.6%

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

      1. associate--l+ 42.6%

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

      2. mul-1-neg 42.6%

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

      3. *-commutative 42.6%

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

   6. Simplified 42.6%

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

   7. Taylor expanded in y around -inf 53.4%

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

      1. associate-*r* 55.2%

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

      2. *-commutative 55.2%

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

      3. mul-1-neg 55.2%

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

      4. sub-neg 55.2%

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

   9. Simplified 55.2%

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

   if -1.15e42 < t < -4.3e11

   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%

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

   4. Taylor expanded in x around inf 50.0%

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

   5. Taylor expanded in b around inf 100.0%

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

   if -4.3e11 < t < -7.1e-155

   1. Initial program 34.8%

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

   3. Simplified 34.8%

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

   4. Taylor expanded in y4 around inf 65.6%

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

   5. Taylor expanded in j around inf 55.9%

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

      1. mul-1-neg 55.9%

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

      2. unsub-neg 55.9%

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

      3. *-commutative 55.9%

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

   7. Simplified 55.9%

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

   if 2.90000000000000009e-235 < t < 9.8000000000000003e178

   1. Initial program 34.4%

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

   3. Simplified 34.4%

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

   4. Taylor expanded in y4 around inf 39.8%

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

   5. Taylor expanded in k around inf 37.7%

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

      1. +-commutative 37.7%

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

      2. mul-1-neg 37.7%

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

      3. unsub-neg 37.7%

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

   7. Simplified 37.7%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{+134}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{+78}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+42}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{elif}\;t \leq -430000000000:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq -7.1 \cdot 10^{-155}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-221}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-235}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+178}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \end{array} \]

Alternative 17: 27.0% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{if}\;y5 \leq -4.8 \cdot 10^{+235}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -7.8 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq -5.4 \cdot 10^{-34}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -4.4 \cdot 10^{-129}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -1.45 \cdot 10^{-217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq 1.08 \cdot 10^{-257}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 8 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* t (- (* z i) (* y2 y4))))))
   (if (<= y5 -4.8e+235)
     (* k (* y0 (* y2 (- y5))))
     (if (<= y5 -7.8e+61)
       t_1
       (if (<= y5 -5.4e-34)
         (* a (* y1 (- (* z y3) (* x y2))))
         (if (<= y5 -4.4e-129)
           (* k (* y0 (- (* z b) (* y2 y5))))
           (if (<= y5 -1.45e-217)
             t_1
             (if (<= y5 1.08e-257)
               (* c (* y0 (- (* x y2) (* z y3))))
               (if (<= y5 8e-126) t_1 (* t (* b (- (* j y4) (* z 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 = c * (t * ((z * i) - (y2 * y4)));
	double tmp;
	if (y5 <= -4.8e+235) {
		tmp = k * (y0 * (y2 * -y5));
	} else if (y5 <= -7.8e+61) {
		tmp = t_1;
	} else if (y5 <= -5.4e-34) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y5 <= -4.4e-129) {
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	} else if (y5 <= -1.45e-217) {
		tmp = t_1;
	} else if (y5 <= 1.08e-257) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (y5 <= 8e-126) {
		tmp = t_1;
	} else {
		tmp = t * (b * ((j * y4) - (z * 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 = c * (t * ((z * i) - (y2 * y4)))
    if (y5 <= (-4.8d+235)) then
        tmp = k * (y0 * (y2 * -y5))
    else if (y5 <= (-7.8d+61)) then
        tmp = t_1
    else if (y5 <= (-5.4d-34)) then
        tmp = a * (y1 * ((z * y3) - (x * y2)))
    else if (y5 <= (-4.4d-129)) then
        tmp = k * (y0 * ((z * b) - (y2 * y5)))
    else if (y5 <= (-1.45d-217)) then
        tmp = t_1
    else if (y5 <= 1.08d-257) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (y5 <= 8d-126) then
        tmp = t_1
    else
        tmp = t * (b * ((j * y4) - (z * 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 = c * (t * ((z * i) - (y2 * y4)));
	double tmp;
	if (y5 <= -4.8e+235) {
		tmp = k * (y0 * (y2 * -y5));
	} else if (y5 <= -7.8e+61) {
		tmp = t_1;
	} else if (y5 <= -5.4e-34) {
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	} else if (y5 <= -4.4e-129) {
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	} else if (y5 <= -1.45e-217) {
		tmp = t_1;
	} else if (y5 <= 1.08e-257) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (y5 <= 8e-126) {
		tmp = t_1;
	} else {
		tmp = t * (b * ((j * y4) - (z * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (t * ((z * i) - (y2 * y4)))
	tmp = 0
	if y5 <= -4.8e+235:
		tmp = k * (y0 * (y2 * -y5))
	elif y5 <= -7.8e+61:
		tmp = t_1
	elif y5 <= -5.4e-34:
		tmp = a * (y1 * ((z * y3) - (x * y2)))
	elif y5 <= -4.4e-129:
		tmp = k * (y0 * ((z * b) - (y2 * y5)))
	elif y5 <= -1.45e-217:
		tmp = t_1
	elif y5 <= 1.08e-257:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif y5 <= 8e-126:
		tmp = t_1
	else:
		tmp = t * (b * ((j * y4) - (z * 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(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))))
	tmp = 0.0
	if (y5 <= -4.8e+235)
		tmp = Float64(k * Float64(y0 * Float64(y2 * Float64(-y5))));
	elseif (y5 <= -7.8e+61)
		tmp = t_1;
	elseif (y5 <= -5.4e-34)
		tmp = Float64(a * Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (y5 <= -4.4e-129)
		tmp = Float64(k * Float64(y0 * Float64(Float64(z * b) - Float64(y2 * y5))));
	elseif (y5 <= -1.45e-217)
		tmp = t_1;
	elseif (y5 <= 1.08e-257)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (y5 <= 8e-126)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(b * Float64(Float64(j * y4) - Float64(z * 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 = c * (t * ((z * i) - (y2 * y4)));
	tmp = 0.0;
	if (y5 <= -4.8e+235)
		tmp = k * (y0 * (y2 * -y5));
	elseif (y5 <= -7.8e+61)
		tmp = t_1;
	elseif (y5 <= -5.4e-34)
		tmp = a * (y1 * ((z * y3) - (x * y2)));
	elseif (y5 <= -4.4e-129)
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	elseif (y5 <= -1.45e-217)
		tmp = t_1;
	elseif (y5 <= 1.08e-257)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (y5 <= 8e-126)
		tmp = t_1;
	else
		tmp = t * (b * ((j * y4) - (z * 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[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -4.8e+235], N[(k * N[(y0 * N[(y2 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -7.8e+61], t$95$1, If[LessEqual[y5, -5.4e-34], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -4.4e-129], N[(k * N[(y0 * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.45e-217], t$95$1, If[LessEqual[y5, 1.08e-257], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 8e-126], t$95$1, N[(t * N[(b * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y5 < -4.7999999999999998e235

   1. Initial program 14.3%

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

   3. Simplified 21.4%

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

   4. Taylor expanded in y0 around inf 28.6%

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

      1. *-commutative 28.6%

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

      2. *-commutative 28.6%

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

      3. mul-1-neg 28.6%

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

      4. *-commutative 28.6%

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

      5. *-commutative 28.6%

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

   6. Simplified 28.6%

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

   7. Taylor expanded in y5 around inf 58.9%

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

   8. Taylor expanded in y3 around 0 78.9%

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

      1. associate-*r* 78.9%

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

      2. neg-mul-1 78.9%

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

      3. *-commutative 78.9%

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

   10. Simplified 78.9%

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

   if -4.7999999999999998e235 < y5 < -7.79999999999999975e61 or -4.40000000000000006e-129 < y5 < -1.44999999999999991e-217 or 1.07999999999999998e-257 < y5 < 7.9999999999999996e-126

   1. Initial program 26.4%

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

   3. Simplified 26.4%

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

   4. Taylor expanded in c around inf 43.0%

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

      1. associate--l+ 43.0%

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

      2. mul-1-neg 43.0%

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

      3. *-commutative 43.0%

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

   6. Simplified 43.0%

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

   7. Taylor expanded in t around -inf 46.2%

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

      1. *-commutative 46.2%

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

      2. mul-1-neg 46.2%

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

      3. unsub-neg 46.2%

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

   9. Simplified 46.2%

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

   if -7.79999999999999975e61 < y5 < -5.40000000000000034e-34

   1. Initial program 36.4%

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

   3. Simplified 45.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 55.0%

      \[\leadsto \color{blue}{y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 55.0%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      2. *-commutative 55.0%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      3. *-commutative 55.0%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      4. *-commutative 55.0%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      5. mul-1-neg 55.0%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-\left(k \cdot z - j \cdot x\right) \cdot i\right)}\right)\right) \]

      6. *-commutative 55.0%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-\color{blue}{i \cdot \left(k \cdot z - j \cdot x\right)}\right)\right)\right) \]

   6. Simplified 55.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\right)} \]

   7. Taylor expanded in a around inf 42.0%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   if -5.40000000000000034e-34 < y5 < -4.40000000000000006e-129

   1. Initial program 56.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 56.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 48.2%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 48.2%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      2. *-commutative 48.2%

         \[\leadsto y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      3. mul-1-neg 48.2%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      4. *-commutative 48.2%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      5. *-commutative 48.2%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{b \cdot \left(k \cdot z - j \cdot x\right)}\right)\right) \]

   6. Simplified 48.2%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + b \cdot \left(k \cdot z - j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in k around inf 43.9%

      \[\leadsto \color{blue}{k \cdot \left(y0 \cdot \left(b \cdot z - y5 \cdot y2\right)\right)} \]

   if -1.44999999999999991e-217 < y5 < 1.07999999999999998e-257

   1. Initial program 36.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 36.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 46.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 46.1%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 46.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. *-commutative 46.1%

         \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 46.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y0 around -inf 37.4%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]

   if 7.9999999999999996e-126 < y5

   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 31.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 44.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 44.7%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 44.7%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

      3. *-commutative 44.7%

         \[\leadsto t \cdot \left(\left(-z \cdot \left(\color{blue}{b \cdot a} - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

      4. *-commutative 44.7%

         \[\leadsto t \cdot \left(\left(-z \cdot \left(b \cdot a - \color{blue}{i \cdot c}\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

      5. *-commutative 44.7%

         \[\leadsto t \cdot \left(\left(-z \cdot \left(b \cdot a - i \cdot c\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \color{blue}{y2 \cdot \left(c \cdot y4 - a \cdot y5\right)}\right)\right) \]

      6. *-commutative 44.7%

         \[\leadsto t \cdot \left(\left(-z \cdot \left(b \cdot a - i \cdot c\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - y2 \cdot \left(\color{blue}{y4 \cdot c} - a \cdot y5\right)\right)\right) \]

      7. *-commutative 44.7%

         \[\leadsto t \cdot \left(\left(-z \cdot \left(b \cdot a - i \cdot c\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - y2 \cdot \left(y4 \cdot c - \color{blue}{y5 \cdot a}\right)\right)\right) \]

   6. Simplified 44.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(b \cdot a - i \cdot c\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - y2 \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)\right)} \]

   7. Taylor expanded in b around inf 33.6%

      \[\leadsto \color{blue}{\left(y4 \cdot j - a \cdot z\right) \cdot \left(t \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 33.6%

         \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot \left(y4 \cdot j - a \cdot z\right)} \]

      2. associate-*l* 39.2%

         \[\leadsto \color{blue}{t \cdot \left(b \cdot \left(y4 \cdot j - a \cdot z\right)\right)} \]

      3. *-commutative 39.2%

         \[\leadsto t \cdot \left(b \cdot \left(\color{blue}{j \cdot y4} - a \cdot z\right)\right) \]

      4. *-commutative 39.2%

         \[\leadsto t \cdot \left(b \cdot \left(j \cdot y4 - \color{blue}{z \cdot a}\right)\right) \]

   9. Simplified 39.2%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot \left(j \cdot y4 - z \cdot a\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -4.8 \cdot 10^{+235}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -7.8 \cdot 10^{+61}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -5.4 \cdot 10^{-34}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq -4.4 \cdot 10^{-129}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -1.45 \cdot 10^{-217}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 1.08 \cdot 10^{-257}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 8 \cdot 10^{-126}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \end{array} \]

Alternative 18: 28.7% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{if}\;x \leq -2.55 \cdot 10^{+270}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+78}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-180}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.3 \cdot 10^{-139}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* t (- (* z i) (* y2 y4))))))
   (if (<= x -2.55e+270)
     (* y1 (* a (* x (- y2))))
     (if (<= x -4e+214)
       t_1
       (if (<= x -5.5e+78)
         (* c (* y0 (- (* x y2) (* z y3))))
         (if (<= x -6.2e-180)
           t_1
           (if (<= x 6.3e-139)
             (* k (* y0 (- (* z b) (* y2 y5))))
             (if (<= x 1.25e+70) t_1 (* i (* y1 (* 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 = c * (t * ((z * i) - (y2 * y4)));
	double tmp;
	if (x <= -2.55e+270) {
		tmp = y1 * (a * (x * -y2));
	} else if (x <= -4e+214) {
		tmp = t_1;
	} else if (x <= -5.5e+78) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (x <= -6.2e-180) {
		tmp = t_1;
	} else if (x <= 6.3e-139) {
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	} else if (x <= 1.25e+70) {
		tmp = t_1;
	} else {
		tmp = i * (y1 * (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) :: tmp
    t_1 = c * (t * ((z * i) - (y2 * y4)))
    if (x <= (-2.55d+270)) then
        tmp = y1 * (a * (x * -y2))
    else if (x <= (-4d+214)) then
        tmp = t_1
    else if (x <= (-5.5d+78)) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (x <= (-6.2d-180)) then
        tmp = t_1
    else if (x <= 6.3d-139) then
        tmp = k * (y0 * ((z * b) - (y2 * y5)))
    else if (x <= 1.25d+70) then
        tmp = t_1
    else
        tmp = i * (y1 * (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 = c * (t * ((z * i) - (y2 * y4)));
	double tmp;
	if (x <= -2.55e+270) {
		tmp = y1 * (a * (x * -y2));
	} else if (x <= -4e+214) {
		tmp = t_1;
	} else if (x <= -5.5e+78) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (x <= -6.2e-180) {
		tmp = t_1;
	} else if (x <= 6.3e-139) {
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	} else if (x <= 1.25e+70) {
		tmp = t_1;
	} else {
		tmp = i * (y1 * (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 = c * (t * ((z * i) - (y2 * y4)))
	tmp = 0
	if x <= -2.55e+270:
		tmp = y1 * (a * (x * -y2))
	elif x <= -4e+214:
		tmp = t_1
	elif x <= -5.5e+78:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif x <= -6.2e-180:
		tmp = t_1
	elif x <= 6.3e-139:
		tmp = k * (y0 * ((z * b) - (y2 * y5)))
	elif x <= 1.25e+70:
		tmp = t_1
	else:
		tmp = i * (y1 * (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(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))))
	tmp = 0.0
	if (x <= -2.55e+270)
		tmp = Float64(y1 * Float64(a * Float64(x * Float64(-y2))));
	elseif (x <= -4e+214)
		tmp = t_1;
	elseif (x <= -5.5e+78)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (x <= -6.2e-180)
		tmp = t_1;
	elseif (x <= 6.3e-139)
		tmp = Float64(k * Float64(y0 * Float64(Float64(z * b) - Float64(y2 * y5))));
	elseif (x <= 1.25e+70)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(y1 * 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 = c * (t * ((z * i) - (y2 * y4)));
	tmp = 0.0;
	if (x <= -2.55e+270)
		tmp = y1 * (a * (x * -y2));
	elseif (x <= -4e+214)
		tmp = t_1;
	elseif (x <= -5.5e+78)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (x <= -6.2e-180)
		tmp = t_1;
	elseif (x <= 6.3e-139)
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	elseif (x <= 1.25e+70)
		tmp = t_1;
	else
		tmp = i * (y1 * (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[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.55e+270], N[(y1 * N[(a * N[(x * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4e+214], t$95$1, If[LessEqual[x, -5.5e+78], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.2e-180], t$95$1, If[LessEqual[x, 6.3e-139], N[(k * N[(y0 * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.25e+70], t$95$1, N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.55e270

   1. Initial program 17.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 59.6%

      \[\leadsto \color{blue}{y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 59.6%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      2. *-commutative 59.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      3. *-commutative 59.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      4. *-commutative 59.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      5. mul-1-neg 59.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-\left(k \cdot z - j \cdot x\right) \cdot i\right)}\right)\right) \]

      6. *-commutative 59.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-\color{blue}{i \cdot \left(k \cdot z - j \cdot x\right)}\right)\right)\right) \]

   6. Simplified 59.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\right)} \]

   7. Taylor expanded in a around inf 60.3%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   8. Taylor expanded in y3 around 0 60.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(a \cdot \left(y2 \cdot x\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 60.4%

         \[\leadsto \color{blue}{-y1 \cdot \left(a \cdot \left(y2 \cdot x\right)\right)} \]

   10. Simplified 60.4%

       \[\leadsto \color{blue}{-y1 \cdot \left(a \cdot \left(y2 \cdot x\right)\right)} \]

   if -2.55e270 < x < -3.9999999999999998e214 or -5.4999999999999997e78 < x < -6.1999999999999998e-180 or 6.2999999999999999e-139 < x < 1.2500000000000001e70

   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%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 40.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 40.1%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 40.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. *-commutative 40.1%

         \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 40.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 40.4%

      \[\leadsto c \cdot \color{blue}{\left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 40.4%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 40.4%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 40.4%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 40.4%

      \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   if -3.9999999999999998e214 < x < -5.4999999999999997e78

   1. Initial program 28.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 44.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 44.1%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 44.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. *-commutative 44.1%

         \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 44.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y0 around -inf 44.2%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]

   if -6.1999999999999998e-180 < x < 6.2999999999999999e-139

   1. Initial program 45.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 53.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 34.6%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 34.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      2. *-commutative 34.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      3. mul-1-neg 34.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      4. *-commutative 34.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      5. *-commutative 34.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{b \cdot \left(k \cdot z - j \cdot x\right)}\right)\right) \]

   6. Simplified 34.6%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + b \cdot \left(k \cdot z - j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in k around inf 34.2%

      \[\leadsto \color{blue}{k \cdot \left(y0 \cdot \left(b \cdot z - y5 \cdot y2\right)\right)} \]

   if 1.2500000000000001e70 < x

   1. Initial program 17.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 41.3%

      \[\leadsto \color{blue}{y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 41.3%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      2. *-commutative 41.3%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      3. *-commutative 41.3%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      4. *-commutative 41.3%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      5. mul-1-neg 41.3%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-\left(k \cdot z - j \cdot x\right) \cdot i\right)}\right)\right) \]

      6. *-commutative 41.3%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-\color{blue}{i \cdot \left(k \cdot z - j \cdot x\right)}\right)\right)\right) \]

   6. Simplified 41.3%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\right)} \]

   7. Taylor expanded in i around inf 44.9%

      \[\leadsto y1 \cdot \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   8. Taylor expanded in j around inf 43.3%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 43.3%

         \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x\right)\right) \cdot y1} \]

      2. associate-*l* 45.1%

         \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]

   10. Simplified 45.1%

       \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+270}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+214}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+78}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-180}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 6.3 \cdot 10^{-139}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+70}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \]

Alternative 19: 32.4% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ t_2 := c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{+135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -13500000000:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-168}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+177}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* i (- (* x j) (* z k)))))
        (t_2 (* c (* t (- (* z i) (* y2 y4))))))
   (if (<= t -8.2e+135)
     t_2
     (if (<= t -4.8e+68)
       t_1
       (if (<= t -13500000000.0)
         (* y0 (* y5 (- (* j y3) (* k y2))))
         (if (<= t -6.5e-189)
           t_1
           (if (<= t 4.1e-168)
             (* k (* y0 (- (* z b) (* y2 y5))))
             (if (<= t 5.2e+177) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (i * ((x * j) - (z * k)));
	double t_2 = c * (t * ((z * i) - (y2 * y4)));
	double tmp;
	if (t <= -8.2e+135) {
		tmp = t_2;
	} else if (t <= -4.8e+68) {
		tmp = t_1;
	} else if (t <= -13500000000.0) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (t <= -6.5e-189) {
		tmp = t_1;
	} else if (t <= 4.1e-168) {
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	} else if (t <= 5.2e+177) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y1 * (i * ((x * j) - (z * k)))
    t_2 = c * (t * ((z * i) - (y2 * y4)))
    if (t <= (-8.2d+135)) then
        tmp = t_2
    else if (t <= (-4.8d+68)) then
        tmp = t_1
    else if (t <= (-13500000000.0d0)) then
        tmp = y0 * (y5 * ((j * y3) - (k * y2)))
    else if (t <= (-6.5d-189)) then
        tmp = t_1
    else if (t <= 4.1d-168) then
        tmp = k * (y0 * ((z * b) - (y2 * y5)))
    else if (t <= 5.2d+177) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (i * ((x * j) - (z * k)));
	double t_2 = c * (t * ((z * i) - (y2 * y4)));
	double tmp;
	if (t <= -8.2e+135) {
		tmp = t_2;
	} else if (t <= -4.8e+68) {
		tmp = t_1;
	} else if (t <= -13500000000.0) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (t <= -6.5e-189) {
		tmp = t_1;
	} else if (t <= 4.1e-168) {
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	} else if (t <= 5.2e+177) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y1 * (i * ((x * j) - (z * k)))
	t_2 = c * (t * ((z * i) - (y2 * y4)))
	tmp = 0
	if t <= -8.2e+135:
		tmp = t_2
	elif t <= -4.8e+68:
		tmp = t_1
	elif t <= -13500000000.0:
		tmp = y0 * (y5 * ((j * y3) - (k * y2)))
	elif t <= -6.5e-189:
		tmp = t_1
	elif t <= 4.1e-168:
		tmp = k * (y0 * ((z * b) - (y2 * y5)))
	elif t <= 5.2e+177:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * Float64(i * Float64(Float64(x * j) - Float64(z * k))))
	t_2 = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))))
	tmp = 0.0
	if (t <= -8.2e+135)
		tmp = t_2;
	elseif (t <= -4.8e+68)
		tmp = t_1;
	elseif (t <= -13500000000.0)
		tmp = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))));
	elseif (t <= -6.5e-189)
		tmp = t_1;
	elseif (t <= 4.1e-168)
		tmp = Float64(k * Float64(y0 * Float64(Float64(z * b) - Float64(y2 * y5))));
	elseif (t <= 5.2e+177)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y1 * (i * ((x * j) - (z * k)));
	t_2 = c * (t * ((z * i) - (y2 * y4)));
	tmp = 0.0;
	if (t <= -8.2e+135)
		tmp = t_2;
	elseif (t <= -4.8e+68)
		tmp = t_1;
	elseif (t <= -13500000000.0)
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	elseif (t <= -6.5e-189)
		tmp = t_1;
	elseif (t <= 4.1e-168)
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	elseif (t <= 5.2e+177)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y1 * N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.2e+135], t$95$2, If[LessEqual[t, -4.8e+68], t$95$1, If[LessEqual[t, -13500000000.0], N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.5e-189], t$95$1, If[LessEqual[t, 4.1e-168], N[(k * N[(y0 * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+177], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.2e135 or 5.19999999999999959e177 < t

   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%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 39.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 39.3%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 39.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. *-commutative 39.3%

         \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 39.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 55.9%

      \[\leadsto c \cdot \color{blue}{\left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 55.9%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 55.9%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 55.9%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 55.9%

      \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   if -8.2e135 < t < -4.80000000000000016e68 or -1.35e10 < t < -6.5000000000000001e-189 or 4.0999999999999998e-168 < t < 5.19999999999999959e177

   1. Initial program 30.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 41.8%

      \[\leadsto \color{blue}{y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 41.8%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      2. *-commutative 41.8%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      3. *-commutative 41.8%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      4. *-commutative 41.8%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      5. mul-1-neg 41.8%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-\left(k \cdot z - j \cdot x\right) \cdot i\right)}\right)\right) \]

      6. *-commutative 41.8%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-\color{blue}{i \cdot \left(k \cdot z - j \cdot x\right)}\right)\right)\right) \]

   6. Simplified 41.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\right)} \]

   7. Taylor expanded in i around inf 38.8%

      \[\leadsto y1 \cdot \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if -4.80000000000000016e68 < t < -1.35e10

   1. Initial program 9.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 9.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 54.6%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 54.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      2. *-commutative 54.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      3. mul-1-neg 54.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      4. *-commutative 54.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      5. *-commutative 54.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{b \cdot \left(k \cdot z - j \cdot x\right)}\right)\right) \]

   6. Simplified 54.6%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + b \cdot \left(k \cdot z - j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in y5 around inf 55.7%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(y3 \cdot j - k \cdot y2\right) \cdot y5\right)} \]

   if -6.5000000000000001e-189 < t < 4.0999999999999998e-168

   1. Initial program 39.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 47.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 35.1%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 35.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      2. *-commutative 35.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      3. mul-1-neg 35.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      4. *-commutative 35.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      5. *-commutative 35.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{b \cdot \left(k \cdot z - j \cdot x\right)}\right)\right) \]

   6. Simplified 35.1%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + b \cdot \left(k \cdot z - j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in k around inf 38.9%

      \[\leadsto \color{blue}{k \cdot \left(y0 \cdot \left(b \cdot z - y5 \cdot y2\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+135}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+68}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;t \leq -13500000000:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-189}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-168}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+177}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \end{array} \]

Alternative 20: 31.3% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ t_2 := c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -390000:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq -5.7 \cdot 10^{-155}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-170}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+177}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* i (- (* x j) (* z k)))))
        (t_2 (* c (* t (- (* z i) (* y2 y4))))))
   (if (<= t -1.5e+135)
     t_2
     (if (<= t -2e+68)
       t_1
       (if (<= t -390000.0)
         (* y0 (* y5 (- (* j y3) (* k y2))))
         (if (<= t -5.7e-155)
           (* y4 (* j (- (* t b) (* y1 y3))))
           (if (<= t 8.5e-170)
             (* k (* y0 (- (* z b) (* y2 y5))))
             (if (<= t 5.5e+177) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (i * ((x * j) - (z * k)));
	double t_2 = c * (t * ((z * i) - (y2 * y4)));
	double tmp;
	if (t <= -1.5e+135) {
		tmp = t_2;
	} else if (t <= -2e+68) {
		tmp = t_1;
	} else if (t <= -390000.0) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (t <= -5.7e-155) {
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	} else if (t <= 8.5e-170) {
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	} else if (t <= 5.5e+177) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y1 * (i * ((x * j) - (z * k)))
    t_2 = c * (t * ((z * i) - (y2 * y4)))
    if (t <= (-1.5d+135)) then
        tmp = t_2
    else if (t <= (-2d+68)) then
        tmp = t_1
    else if (t <= (-390000.0d0)) then
        tmp = y0 * (y5 * ((j * y3) - (k * y2)))
    else if (t <= (-5.7d-155)) then
        tmp = y4 * (j * ((t * b) - (y1 * y3)))
    else if (t <= 8.5d-170) then
        tmp = k * (y0 * ((z * b) - (y2 * y5)))
    else if (t <= 5.5d+177) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (i * ((x * j) - (z * k)));
	double t_2 = c * (t * ((z * i) - (y2 * y4)));
	double tmp;
	if (t <= -1.5e+135) {
		tmp = t_2;
	} else if (t <= -2e+68) {
		tmp = t_1;
	} else if (t <= -390000.0) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (t <= -5.7e-155) {
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	} else if (t <= 8.5e-170) {
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	} else if (t <= 5.5e+177) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y1 * (i * ((x * j) - (z * k)))
	t_2 = c * (t * ((z * i) - (y2 * y4)))
	tmp = 0
	if t <= -1.5e+135:
		tmp = t_2
	elif t <= -2e+68:
		tmp = t_1
	elif t <= -390000.0:
		tmp = y0 * (y5 * ((j * y3) - (k * y2)))
	elif t <= -5.7e-155:
		tmp = y4 * (j * ((t * b) - (y1 * y3)))
	elif t <= 8.5e-170:
		tmp = k * (y0 * ((z * b) - (y2 * y5)))
	elif t <= 5.5e+177:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * Float64(i * Float64(Float64(x * j) - Float64(z * k))))
	t_2 = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))))
	tmp = 0.0
	if (t <= -1.5e+135)
		tmp = t_2;
	elseif (t <= -2e+68)
		tmp = t_1;
	elseif (t <= -390000.0)
		tmp = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))));
	elseif (t <= -5.7e-155)
		tmp = Float64(y4 * Float64(j * Float64(Float64(t * b) - Float64(y1 * y3))));
	elseif (t <= 8.5e-170)
		tmp = Float64(k * Float64(y0 * Float64(Float64(z * b) - Float64(y2 * y5))));
	elseif (t <= 5.5e+177)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y1 * (i * ((x * j) - (z * k)));
	t_2 = c * (t * ((z * i) - (y2 * y4)));
	tmp = 0.0;
	if (t <= -1.5e+135)
		tmp = t_2;
	elseif (t <= -2e+68)
		tmp = t_1;
	elseif (t <= -390000.0)
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	elseif (t <= -5.7e-155)
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	elseif (t <= 8.5e-170)
		tmp = k * (y0 * ((z * b) - (y2 * y5)));
	elseif (t <= 5.5e+177)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y1 * N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.5e+135], t$95$2, If[LessEqual[t, -2e+68], t$95$1, If[LessEqual[t, -390000.0], N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.7e-155], N[(y4 * N[(j * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-170], N[(k * N[(y0 * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+177], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.5e135 or 5.49999999999999993e177 < t

   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%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 39.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 39.3%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 39.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. *-commutative 39.3%

         \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 39.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 55.9%

      \[\leadsto c \cdot \color{blue}{\left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 55.9%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 55.9%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 55.9%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 55.9%

      \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   if -1.5e135 < t < -1.99999999999999991e68 or 8.5e-170 < t < 5.49999999999999993e177

   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 34.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 44.5%

      \[\leadsto \color{blue}{y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.5%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      2. *-commutative 44.5%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      3. *-commutative 44.5%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      4. *-commutative 44.5%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      5. mul-1-neg 44.5%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-\left(k \cdot z - j \cdot x\right) \cdot i\right)}\right)\right) \]

      6. *-commutative 44.5%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-\color{blue}{i \cdot \left(k \cdot z - j \cdot x\right)}\right)\right)\right) \]

   6. Simplified 44.5%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\right)} \]

   7. Taylor expanded in i around inf 38.4%

      \[\leadsto y1 \cdot \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if -1.99999999999999991e68 < t < -3.9e5

   1. Initial program 9.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 9.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 54.6%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 54.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      2. *-commutative 54.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      3. mul-1-neg 54.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      4. *-commutative 54.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      5. *-commutative 54.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{b \cdot \left(k \cdot z - j \cdot x\right)}\right)\right) \]

   6. Simplified 54.6%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + b \cdot \left(k \cdot z - j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in y5 around inf 55.7%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(y3 \cdot j - k \cdot y2\right) \cdot y5\right)} \]

   if -3.9e5 < t < -5.69999999999999965e-155

   1. Initial program 34.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 65.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around inf 55.9%

      \[\leadsto \color{blue}{y4 \cdot \left(j \cdot \left(t \cdot b + -1 \cdot \left(y1 \cdot y3\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 55.9%

         \[\leadsto y4 \cdot \left(j \cdot \left(t \cdot b + \color{blue}{\left(-y1 \cdot y3\right)}\right)\right) \]

      2. unsub-neg 55.9%

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(t \cdot b - y1 \cdot y3\right)}\right) \]

      3. *-commutative 55.9%

         \[\leadsto y4 \cdot \left(j \cdot \left(\color{blue}{b \cdot t} - y1 \cdot y3\right)\right) \]

   7. Simplified 55.9%

      \[\leadsto \color{blue}{y4 \cdot \left(j \cdot \left(b \cdot t - y1 \cdot y3\right)\right)} \]

   if -5.69999999999999965e-155 < t < 8.5e-170

   1. Initial program 36.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 43.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 34.1%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 34.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      2. *-commutative 34.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      3. mul-1-neg 34.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      4. *-commutative 34.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      5. *-commutative 34.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{b \cdot \left(k \cdot z - j \cdot x\right)}\right)\right) \]

   6. Simplified 34.1%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + b \cdot \left(k \cdot z - j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in k around inf 36.1%

      \[\leadsto \color{blue}{k \cdot \left(y0 \cdot \left(b \cdot z - y5 \cdot y2\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+135}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+68}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;t \leq -390000:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq -5.7 \cdot 10^{-155}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-170}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b - y2 \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+177}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \end{array} \]

Alternative 21: 30.4% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{if}\;k \leq -115000000:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;k \leq -1.35 \cdot 10^{-240}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 1.9 \cdot 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 6.6 \cdot 10^{-112}:\\ \;\;\;\;y3 \cdot \left(y0 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* y c) (- (* y3 y4) (* x i)))))
   (if (<= k -115000000.0)
     (* y4 (* k (- (* y1 y2) (* y b))))
     (if (<= k -1.35e-240)
       (* x (* a (- (* y b) (* y1 y2))))
       (if (<= k 1.9e-150)
         t_1
         (if (<= k 6.6e-112)
           (* y3 (* y0 (* j y5)))
           (if (<= k 1e+52) t_1 (* y4 (* b (- (* t j) (* y k)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * c) * ((y3 * y4) - (x * i));
	double tmp;
	if (k <= -115000000.0) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (k <= -1.35e-240) {
		tmp = x * (a * ((y * b) - (y1 * y2)));
	} else if (k <= 1.9e-150) {
		tmp = t_1;
	} else if (k <= 6.6e-112) {
		tmp = y3 * (y0 * (j * y5));
	} else if (k <= 1e+52) {
		tmp = t_1;
	} else {
		tmp = y4 * (b * ((t * j) - (y * k)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * c) * ((y3 * y4) - (x * i))
    if (k <= (-115000000.0d0)) then
        tmp = y4 * (k * ((y1 * y2) - (y * b)))
    else if (k <= (-1.35d-240)) then
        tmp = x * (a * ((y * b) - (y1 * y2)))
    else if (k <= 1.9d-150) then
        tmp = t_1
    else if (k <= 6.6d-112) then
        tmp = y3 * (y0 * (j * y5))
    else if (k <= 1d+52) then
        tmp = t_1
    else
        tmp = y4 * (b * ((t * j) - (y * k)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * c) * ((y3 * y4) - (x * i));
	double tmp;
	if (k <= -115000000.0) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (k <= -1.35e-240) {
		tmp = x * (a * ((y * b) - (y1 * y2)));
	} else if (k <= 1.9e-150) {
		tmp = t_1;
	} else if (k <= 6.6e-112) {
		tmp = y3 * (y0 * (j * y5));
	} else if (k <= 1e+52) {
		tmp = t_1;
	} else {
		tmp = y4 * (b * ((t * j) - (y * k)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y * c) * ((y3 * y4) - (x * i))
	tmp = 0
	if k <= -115000000.0:
		tmp = y4 * (k * ((y1 * y2) - (y * b)))
	elif k <= -1.35e-240:
		tmp = x * (a * ((y * b) - (y1 * y2)))
	elif k <= 1.9e-150:
		tmp = t_1
	elif k <= 6.6e-112:
		tmp = y3 * (y0 * (j * y5))
	elif k <= 1e+52:
		tmp = t_1
	else:
		tmp = y4 * (b * ((t * j) - (y * k)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * c) * Float64(Float64(y3 * y4) - Float64(x * i)))
	tmp = 0.0
	if (k <= -115000000.0)
		tmp = Float64(y4 * Float64(k * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (k <= -1.35e-240)
		tmp = Float64(x * Float64(a * Float64(Float64(y * b) - Float64(y1 * y2))));
	elseif (k <= 1.9e-150)
		tmp = t_1;
	elseif (k <= 6.6e-112)
		tmp = Float64(y3 * Float64(y0 * Float64(j * y5)));
	elseif (k <= 1e+52)
		tmp = t_1;
	else
		tmp = Float64(y4 * Float64(b * Float64(Float64(t * j) - Float64(y * k))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y * c) * ((y3 * y4) - (x * i));
	tmp = 0.0;
	if (k <= -115000000.0)
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	elseif (k <= -1.35e-240)
		tmp = x * (a * ((y * b) - (y1 * y2)));
	elseif (k <= 1.9e-150)
		tmp = t_1;
	elseif (k <= 6.6e-112)
		tmp = y3 * (y0 * (j * y5));
	elseif (k <= 1e+52)
		tmp = t_1;
	else
		tmp = y4 * (b * ((t * j) - (y * k)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y * c), $MachinePrecision] * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -115000000.0], N[(y4 * N[(k * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.35e-240], N[(x * N[(a * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.9e-150], t$95$1, If[LessEqual[k, 6.6e-112], N[(y3 * N[(y0 * N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1e+52], t$95$1, N[(y4 * N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if k < -1.15e8

   1. Initial program 32.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 47.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 53.5%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 53.5%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 53.5%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 53.5%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

   7. Simplified 53.5%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)} \]

   if -1.15e8 < k < -1.35000000000000009e-240

   1. Initial program 33.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 36.5%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in a around inf 48.7%

      \[\leadsto \color{blue}{\left(\left(y \cdot b + -1 \cdot \left(y1 \cdot y2\right)\right) \cdot a\right)} \cdot x \]
   6. Step-by-step derivation

      1. mul-1-neg 48.7%

         \[\leadsto \left(\left(y \cdot b + \color{blue}{\left(-y1 \cdot y2\right)}\right) \cdot a\right) \cdot x \]

      2. unsub-neg 48.7%

         \[\leadsto \left(\color{blue}{\left(y \cdot b - y1 \cdot y2\right)} \cdot a\right) \cdot x \]

   7. Simplified 48.7%

      \[\leadsto \color{blue}{\left(\left(y \cdot b - y1 \cdot y2\right) \cdot a\right)} \cdot x \]

   if -1.35000000000000009e-240 < k < 1.8999999999999999e-150 or 6.6000000000000002e-112 < k < 9.9999999999999999e51

   1. Initial program 33.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 37.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 37.1%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 37.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. *-commutative 37.1%

         \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 37.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y around -inf 34.0%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y4 \cdot y3 + -1 \cdot \left(i \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 37.7%

         \[\leadsto \color{blue}{\left(c \cdot y\right) \cdot \left(y4 \cdot y3 + -1 \cdot \left(i \cdot x\right)\right)} \]

      2. *-commutative 37.7%

         \[\leadsto \color{blue}{\left(y \cdot c\right)} \cdot \left(y4 \cdot y3 + -1 \cdot \left(i \cdot x\right)\right) \]

      3. mul-1-neg 37.7%

         \[\leadsto \left(y \cdot c\right) \cdot \left(y4 \cdot y3 + \color{blue}{\left(-i \cdot x\right)}\right) \]

      4. sub-neg 37.7%

         \[\leadsto \left(y \cdot c\right) \cdot \color{blue}{\left(y4 \cdot y3 - i \cdot x\right)} \]

   9. Simplified 37.7%

      \[\leadsto \color{blue}{\left(y \cdot c\right) \cdot \left(y4 \cdot y3 - i \cdot x\right)} \]

   if 1.8999999999999999e-150 < k < 6.6000000000000002e-112

   1. Initial program 21.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 50.5%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 50.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      2. *-commutative 50.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      3. mul-1-neg 50.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      4. *-commutative 50.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      5. *-commutative 50.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{b \cdot \left(k \cdot z - j \cdot x\right)}\right)\right) \]

   6. Simplified 50.5%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + b \cdot \left(k \cdot z - j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in y5 around inf 50.4%

      \[\leadsto \color{blue}{\left(y3 \cdot j - k \cdot y2\right) \cdot \left(y0 \cdot y5\right)} \]

   8. Taylor expanded in y3 around inf 57.6%

      \[\leadsto \color{blue}{\left(y3 \cdot j\right)} \cdot \left(y0 \cdot y5\right) \]

   9. Taylor expanded in y3 around 0 57.8%

      \[\leadsto \color{blue}{y0 \cdot \left(y3 \cdot \left(j \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 57.8%

          \[\leadsto \color{blue}{\left(y3 \cdot \left(j \cdot y5\right)\right) \cdot y0} \]

       2. associate-*r* 64.6%

          \[\leadsto \color{blue}{y3 \cdot \left(\left(j \cdot y5\right) \cdot y0\right)} \]

       3. *-commutative 64.6%

          \[\leadsto y3 \cdot \color{blue}{\left(y0 \cdot \left(j \cdot y5\right)\right)} \]

       4. *-commutative 64.6%

          \[\leadsto y3 \cdot \left(y0 \cdot \color{blue}{\left(y5 \cdot j\right)}\right) \]

   11. Simplified 64.6%

       \[\leadsto \color{blue}{y3 \cdot \left(y0 \cdot \left(y5 \cdot j\right)\right)} \]

   if 9.9999999999999999e51 < k

   1. Initial program 30.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 41.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around inf 44.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot b\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -115000000:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;k \leq -1.35 \cdot 10^{-240}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 1.9 \cdot 10^{-150}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{elif}\;k \leq 6.6 \cdot 10^{-112}:\\ \;\;\;\;y3 \cdot \left(y0 \cdot \left(j \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 10^{+52}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \end{array} \]

Alternative 22: 27.6% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+270}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{+199} \lor \neg \left(x \leq -7.3 \cdot 10^{-6}\right) \land x \leq 9 \cdot 10^{+70}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -2.05e+270)
   (* y1 (* a (* x (- y2))))
   (if (or (<= x -3.1e+199) (and (not (<= x -7.3e-6)) (<= x 9e+70)))
     (* c (* t (- (* z i) (* y2 y4))))
     (* i (* y1 (* 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 tmp;
	if (x <= -2.05e+270) {
		tmp = y1 * (a * (x * -y2));
	} else if ((x <= -3.1e+199) || (!(x <= -7.3e-6) && (x <= 9e+70))) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else {
		tmp = i * (y1 * (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) :: tmp
    if (x <= (-2.05d+270)) then
        tmp = y1 * (a * (x * -y2))
    else if ((x <= (-3.1d+199)) .or. (.not. (x <= (-7.3d-6))) .and. (x <= 9d+70)) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else
        tmp = i * (y1 * (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 tmp;
	if (x <= -2.05e+270) {
		tmp = y1 * (a * (x * -y2));
	} else if ((x <= -3.1e+199) || (!(x <= -7.3e-6) && (x <= 9e+70))) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else {
		tmp = i * (y1 * (x * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -2.05e+270:
		tmp = y1 * (a * (x * -y2))
	elif (x <= -3.1e+199) or (not (x <= -7.3e-6) and (x <= 9e+70)):
		tmp = c * (t * ((z * i) - (y2 * y4)))
	else:
		tmp = i * (y1 * (x * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -2.05e+270)
		tmp = Float64(y1 * Float64(a * Float64(x * Float64(-y2))));
	elseif ((x <= -3.1e+199) || (!(x <= -7.3e-6) && (x <= 9e+70)))
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	else
		tmp = Float64(i * Float64(y1 * 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)
	tmp = 0.0;
	if (x <= -2.05e+270)
		tmp = y1 * (a * (x * -y2));
	elseif ((x <= -3.1e+199) || (~((x <= -7.3e-6)) && (x <= 9e+70)))
		tmp = c * (t * ((z * i) - (y2 * y4)));
	else
		tmp = i * (y1 * (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_] := If[LessEqual[x, -2.05e+270], N[(y1 * N[(a * N[(x * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -3.1e+199], And[N[Not[LessEqual[x, -7.3e-6]], $MachinePrecision], LessEqual[x, 9e+70]]], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.04999999999999998e270

   1. Initial program 17.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 59.6%

      \[\leadsto \color{blue}{y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 59.6%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      2. *-commutative 59.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      3. *-commutative 59.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      4. *-commutative 59.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      5. mul-1-neg 59.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-\left(k \cdot z - j \cdot x\right) \cdot i\right)}\right)\right) \]

      6. *-commutative 59.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-\color{blue}{i \cdot \left(k \cdot z - j \cdot x\right)}\right)\right)\right) \]

   6. Simplified 59.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\right)} \]

   7. Taylor expanded in a around inf 60.3%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   8. Taylor expanded in y3 around 0 60.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(a \cdot \left(y2 \cdot x\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 60.4%

         \[\leadsto \color{blue}{-y1 \cdot \left(a \cdot \left(y2 \cdot x\right)\right)} \]

   10. Simplified 60.4%

       \[\leadsto \color{blue}{-y1 \cdot \left(a \cdot \left(y2 \cdot x\right)\right)} \]

   if -2.04999999999999998e270 < x < -3.09999999999999986e199 or -7.30000000000000041e-6 < x < 8.9999999999999999e70

   1. Initial program 39.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 39.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 38.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 38.1%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 38.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. *-commutative 38.1%

         \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 38.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 35.6%

      \[\leadsto c \cdot \color{blue}{\left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 35.6%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 35.6%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 35.6%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 35.6%

      \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   if -3.09999999999999986e199 < x < -7.30000000000000041e-6 or 8.9999999999999999e70 < x

   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 28.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 39.6%

      \[\leadsto \color{blue}{y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 39.6%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      2. *-commutative 39.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      3. *-commutative 39.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      4. *-commutative 39.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      5. mul-1-neg 39.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-\left(k \cdot z - j \cdot x\right) \cdot i\right)}\right)\right) \]

      6. *-commutative 39.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-\color{blue}{i \cdot \left(k \cdot z - j \cdot x\right)}\right)\right)\right) \]

   6. Simplified 39.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\right)} \]

   7. Taylor expanded in i around inf 45.4%

      \[\leadsto y1 \cdot \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   8. Taylor expanded in j around inf 36.6%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 36.6%

         \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x\right)\right) \cdot y1} \]

      2. associate-*l* 40.8%

         \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]

   10. Simplified 40.8%

       \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+270}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{+199} \lor \neg \left(x \leq -7.3 \cdot 10^{-6}\right) \land x \leq 9 \cdot 10^{+70}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \]

Alternative 23: 29.0% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{if}\;x \leq -1.85 \cdot 10^{+270}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{+214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+80}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* t (- (* z i) (* y2 y4))))))
   (if (<= x -1.85e+270)
     (* y1 (* a (* x (- y2))))
     (if (<= x -3.1e+214)
       t_1
       (if (<= x -5e+80)
         (* c (* y0 (- (* x y2) (* z y3))))
         (if (<= x 1.02e+71) t_1 (* i (* y1 (* 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 = c * (t * ((z * i) - (y2 * y4)));
	double tmp;
	if (x <= -1.85e+270) {
		tmp = y1 * (a * (x * -y2));
	} else if (x <= -3.1e+214) {
		tmp = t_1;
	} else if (x <= -5e+80) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (x <= 1.02e+71) {
		tmp = t_1;
	} else {
		tmp = i * (y1 * (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) :: tmp
    t_1 = c * (t * ((z * i) - (y2 * y4)))
    if (x <= (-1.85d+270)) then
        tmp = y1 * (a * (x * -y2))
    else if (x <= (-3.1d+214)) then
        tmp = t_1
    else if (x <= (-5d+80)) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (x <= 1.02d+71) then
        tmp = t_1
    else
        tmp = i * (y1 * (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 = c * (t * ((z * i) - (y2 * y4)));
	double tmp;
	if (x <= -1.85e+270) {
		tmp = y1 * (a * (x * -y2));
	} else if (x <= -3.1e+214) {
		tmp = t_1;
	} else if (x <= -5e+80) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (x <= 1.02e+71) {
		tmp = t_1;
	} else {
		tmp = i * (y1 * (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 = c * (t * ((z * i) - (y2 * y4)))
	tmp = 0
	if x <= -1.85e+270:
		tmp = y1 * (a * (x * -y2))
	elif x <= -3.1e+214:
		tmp = t_1
	elif x <= -5e+80:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif x <= 1.02e+71:
		tmp = t_1
	else:
		tmp = i * (y1 * (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(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))))
	tmp = 0.0
	if (x <= -1.85e+270)
		tmp = Float64(y1 * Float64(a * Float64(x * Float64(-y2))));
	elseif (x <= -3.1e+214)
		tmp = t_1;
	elseif (x <= -5e+80)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (x <= 1.02e+71)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(y1 * 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 = c * (t * ((z * i) - (y2 * y4)));
	tmp = 0.0;
	if (x <= -1.85e+270)
		tmp = y1 * (a * (x * -y2));
	elseif (x <= -3.1e+214)
		tmp = t_1;
	elseif (x <= -5e+80)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (x <= 1.02e+71)
		tmp = t_1;
	else
		tmp = i * (y1 * (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[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.85e+270], N[(y1 * N[(a * N[(x * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.1e+214], t$95$1, If[LessEqual[x, -5e+80], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.02e+71], t$95$1, N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.84999999999999997e270

   1. Initial program 17.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 59.6%

      \[\leadsto \color{blue}{y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 59.6%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      2. *-commutative 59.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      3. *-commutative 59.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      4. *-commutative 59.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      5. mul-1-neg 59.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-\left(k \cdot z - j \cdot x\right) \cdot i\right)}\right)\right) \]

      6. *-commutative 59.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-\color{blue}{i \cdot \left(k \cdot z - j \cdot x\right)}\right)\right)\right) \]

   6. Simplified 59.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\right)} \]

   7. Taylor expanded in a around inf 60.3%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   8. Taylor expanded in y3 around 0 60.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(a \cdot \left(y2 \cdot x\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 60.4%

         \[\leadsto \color{blue}{-y1 \cdot \left(a \cdot \left(y2 \cdot x\right)\right)} \]

   10. Simplified 60.4%

       \[\leadsto \color{blue}{-y1 \cdot \left(a \cdot \left(y2 \cdot x\right)\right)} \]

   if -1.84999999999999997e270 < x < -3.09999999999999979e214 or -4.99999999999999961e80 < x < 1.02000000000000003e71

   1. Initial program 38.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 38.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 37.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 37.3%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 37.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. *-commutative 37.3%

         \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 37.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 34.3%

      \[\leadsto c \cdot \color{blue}{\left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 34.3%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right)} \]

      2. mul-1-neg 34.3%

         \[\leadsto c \cdot \left(t \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \]

      3. unsub-neg 34.3%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \]

   9. Simplified 34.3%

      \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z - y4 \cdot y2\right)\right)} \]

   if -3.09999999999999979e214 < x < -4.99999999999999961e80

   1. Initial program 28.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 44.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 44.1%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 44.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. *-commutative 44.1%

         \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 44.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y0 around -inf 44.2%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]

   if 1.02000000000000003e71 < x

   1. Initial program 17.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 41.3%

      \[\leadsto \color{blue}{y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 41.3%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      2. *-commutative 41.3%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      3. *-commutative 41.3%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      4. *-commutative 41.3%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      5. mul-1-neg 41.3%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-\left(k \cdot z - j \cdot x\right) \cdot i\right)}\right)\right) \]

      6. *-commutative 41.3%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-\color{blue}{i \cdot \left(k \cdot z - j \cdot x\right)}\right)\right)\right) \]

   6. Simplified 41.3%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\right)} \]

   7. Taylor expanded in i around inf 44.9%

      \[\leadsto y1 \cdot \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   8. Taylor expanded in j around inf 43.3%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 43.3%

         \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x\right)\right) \cdot y1} \]

      2. associate-*l* 45.1%

         \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]

   10. Simplified 45.1%

       \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+270}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{+214}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+80}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+71}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \]

Alternative 24: 23.0% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y2 \cdot \left(t \cdot \left(-y4\right)\right)\right)\\ \mathbf{if}\;z \leq -7 \cdot 10^{+77}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.45 \cdot 10^{-251}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-103}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y0 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(i \cdot \left(z \cdot \left(-y1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y2 (* t (- y4))))))
   (if (<= z -7e+77)
     (* c (* i (* z t)))
     (if (<= z -1.2e-54)
       t_1
       (if (<= z -3.45e-251)
         (* i (* y1 (* x j)))
         (if (<= z 1.4e-103)
           (* y2 (* k (* y0 (- y5))))
           (if (<= z 6e+68) t_1 (* k (* i (* z (- y1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * (t * -y4));
	double tmp;
	if (z <= -7e+77) {
		tmp = c * (i * (z * t));
	} else if (z <= -1.2e-54) {
		tmp = t_1;
	} else if (z <= -3.45e-251) {
		tmp = i * (y1 * (x * j));
	} else if (z <= 1.4e-103) {
		tmp = y2 * (k * (y0 * -y5));
	} else if (z <= 6e+68) {
		tmp = t_1;
	} else {
		tmp = k * (i * (z * -y1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (y2 * (t * -y4))
    if (z <= (-7d+77)) then
        tmp = c * (i * (z * t))
    else if (z <= (-1.2d-54)) then
        tmp = t_1
    else if (z <= (-3.45d-251)) then
        tmp = i * (y1 * (x * j))
    else if (z <= 1.4d-103) then
        tmp = y2 * (k * (y0 * -y5))
    else if (z <= 6d+68) then
        tmp = t_1
    else
        tmp = k * (i * (z * -y1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * (t * -y4));
	double tmp;
	if (z <= -7e+77) {
		tmp = c * (i * (z * t));
	} else if (z <= -1.2e-54) {
		tmp = t_1;
	} else if (z <= -3.45e-251) {
		tmp = i * (y1 * (x * j));
	} else if (z <= 1.4e-103) {
		tmp = y2 * (k * (y0 * -y5));
	} else if (z <= 6e+68) {
		tmp = t_1;
	} else {
		tmp = k * (i * (z * -y1));
	}
	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 * (t * -y4))
	tmp = 0
	if z <= -7e+77:
		tmp = c * (i * (z * t))
	elif z <= -1.2e-54:
		tmp = t_1
	elif z <= -3.45e-251:
		tmp = i * (y1 * (x * j))
	elif z <= 1.4e-103:
		tmp = y2 * (k * (y0 * -y5))
	elif z <= 6e+68:
		tmp = t_1
	else:
		tmp = k * (i * (z * -y1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y2 * Float64(t * Float64(-y4))))
	tmp = 0.0
	if (z <= -7e+77)
		tmp = Float64(c * Float64(i * Float64(z * t)));
	elseif (z <= -1.2e-54)
		tmp = t_1;
	elseif (z <= -3.45e-251)
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	elseif (z <= 1.4e-103)
		tmp = Float64(y2 * Float64(k * Float64(y0 * Float64(-y5))));
	elseif (z <= 6e+68)
		tmp = t_1;
	else
		tmp = Float64(k * Float64(i * Float64(z * Float64(-y1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y2 * (t * -y4));
	tmp = 0.0;
	if (z <= -7e+77)
		tmp = c * (i * (z * t));
	elseif (z <= -1.2e-54)
		tmp = t_1;
	elseif (z <= -3.45e-251)
		tmp = i * (y1 * (x * j));
	elseif (z <= 1.4e-103)
		tmp = y2 * (k * (y0 * -y5));
	elseif (z <= 6e+68)
		tmp = t_1;
	else
		tmp = k * (i * (z * -y1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y2 * N[(t * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e+77], N[(c * N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.2e-54], t$95$1, If[LessEqual[z, -3.45e-251], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-103], N[(y2 * N[(k * N[(y0 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+68], t$95$1, N[(k * N[(i * N[(z * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.0000000000000003e77

   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%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 45.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 45.9%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 45.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. *-commutative 45.9%

         \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 45.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 39.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 39.9%

         \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right) \cdot t} \]

      2. mul-1-neg 39.9%

         \[\leadsto \left(c \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \cdot t \]

      3. unsub-neg 39.9%

         \[\leadsto \left(c \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \cdot t \]

   9. Simplified 39.9%

      \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z - y4 \cdot y2\right)\right) \cdot t} \]

   10. Taylor expanded in i around inf 34.9%

       \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]

   if -7.0000000000000003e77 < z < -1.20000000000000007e-54 or 1.40000000000000011e-103 < z < 6.0000000000000004e68

   1. Initial program 32.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 42.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 42.1%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 42.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. *-commutative 42.1%

         \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 42.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 42.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 35.0%

         \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right) \cdot t} \]

      2. mul-1-neg 35.0%

         \[\leadsto \left(c \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \cdot t \]

      3. unsub-neg 35.0%

         \[\leadsto \left(c \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \cdot t \]

   9. Simplified 35.0%

      \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z - y4 \cdot y2\right)\right) \cdot t} \]

   10. Taylor expanded in i around 0 34.5%

       \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 34.5%

          \[\leadsto \color{blue}{-c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

       2. associate-*r* 37.5%

          \[\leadsto -c \cdot \color{blue}{\left(\left(y4 \cdot t\right) \cdot y2\right)} \]

   12. Simplified 37.5%

       \[\leadsto \color{blue}{-c \cdot \left(\left(y4 \cdot t\right) \cdot y2\right)} \]

   if -1.20000000000000007e-54 < z < -3.4500000000000001e-251

   1. Initial program 35.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 40.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 55.9%

      \[\leadsto \color{blue}{y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 55.9%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      2. *-commutative 55.9%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      3. *-commutative 55.9%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      4. *-commutative 55.9%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      5. mul-1-neg 55.9%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-\left(k \cdot z - j \cdot x\right) \cdot i\right)}\right)\right) \]

      6. *-commutative 55.9%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-\color{blue}{i \cdot \left(k \cdot z - j \cdot x\right)}\right)\right)\right) \]

   6. Simplified 55.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\right)} \]

   7. Taylor expanded in i around inf 45.5%

      \[\leadsto y1 \cdot \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   8. Taylor expanded in j around inf 43.4%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 43.4%

         \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x\right)\right) \cdot y1} \]

      2. associate-*l* 47.6%

         \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]

   10. Simplified 47.6%

       \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]

   if -3.4500000000000001e-251 < z < 1.40000000000000011e-103

   1. Initial program 43.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 49.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 34.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 34.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      2. *-commutative 34.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      3. mul-1-neg 34.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      4. *-commutative 34.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      5. *-commutative 34.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{b \cdot \left(k \cdot z - j \cdot x\right)}\right)\right) \]

   6. Simplified 34.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + b \cdot \left(k \cdot z - j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in y5 around inf 25.3%

      \[\leadsto \color{blue}{\left(y3 \cdot j - k \cdot y2\right) \cdot \left(y0 \cdot y5\right)} \]

   8. Taylor expanded in y3 around 0 26.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot y2\right)\right)} \cdot \left(y0 \cdot y5\right) \]
   9. Step-by-step derivation

      1. mul-1-neg 26.8%

         \[\leadsto \color{blue}{\left(-k \cdot y2\right)} \cdot \left(y0 \cdot y5\right) \]

      2. distribute-lft-neg-out 26.8%

         \[\leadsto \color{blue}{\left(\left(-k\right) \cdot y2\right)} \cdot \left(y0 \cdot y5\right) \]

      3. *-commutative 26.8%

         \[\leadsto \color{blue}{\left(y2 \cdot \left(-k\right)\right)} \cdot \left(y0 \cdot y5\right) \]

   10. Simplified 26.8%

       \[\leadsto \color{blue}{\left(y2 \cdot \left(-k\right)\right)} \cdot \left(y0 \cdot y5\right) \]

   11. Taylor expanded in y2 around 0 26.7%

       \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(y5 \cdot y2\right)\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg 26.7%

          \[\leadsto \color{blue}{-k \cdot \left(y0 \cdot \left(y5 \cdot y2\right)\right)} \]

       2. *-commutative 26.7%

          \[\leadsto -\color{blue}{\left(y0 \cdot \left(y5 \cdot y2\right)\right) \cdot k} \]

       3. distribute-rgt-neg-in 26.7%

          \[\leadsto \color{blue}{\left(y0 \cdot \left(y5 \cdot y2\right)\right) \cdot \left(-k\right)} \]

       4. associate-*r* 26.7%

          \[\leadsto \color{blue}{\left(\left(y0 \cdot y5\right) \cdot y2\right)} \cdot \left(-k\right) \]

       5. *-commutative 26.7%

          \[\leadsto \left(\color{blue}{\left(y5 \cdot y0\right)} \cdot y2\right) \cdot \left(-k\right) \]

       6. associate-*r* 26.8%

          \[\leadsto \color{blue}{\left(y5 \cdot y0\right) \cdot \left(y2 \cdot \left(-k\right)\right)} \]

       7. *-commutative 26.8%

          \[\leadsto \color{blue}{\left(y2 \cdot \left(-k\right)\right) \cdot \left(y5 \cdot y0\right)} \]

       8. associate-*l* 26.8%

          \[\leadsto \color{blue}{y2 \cdot \left(\left(-k\right) \cdot \left(y5 \cdot y0\right)\right)} \]

   13. Simplified 26.8%

       \[\leadsto \color{blue}{y2 \cdot \left(\left(-k\right) \cdot \left(y5 \cdot y0\right)\right)} \]

   if 6.0000000000000004e68 < z

   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 22.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 39.6%

      \[\leadsto \color{blue}{y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 39.6%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      2. *-commutative 39.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      3. *-commutative 39.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      4. *-commutative 39.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      5. mul-1-neg 39.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-\left(k \cdot z - j \cdot x\right) \cdot i\right)}\right)\right) \]

      6. *-commutative 39.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-\color{blue}{i \cdot \left(k \cdot z - j \cdot x\right)}\right)\right)\right) \]

   6. Simplified 39.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\right)} \]

   7. Taylor expanded in i around inf 44.2%

      \[\leadsto y1 \cdot \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   8. Taylor expanded in j around 0 37.4%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y1 \cdot \left(i \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 37.4%

         \[\leadsto \color{blue}{-k \cdot \left(y1 \cdot \left(i \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 37.4%

         \[\leadsto \color{blue}{k \cdot \left(-y1 \cdot \left(i \cdot z\right)\right)} \]

      3. *-commutative 37.4%

         \[\leadsto k \cdot \left(-\color{blue}{\left(i \cdot z\right) \cdot y1}\right) \]

      4. associate-*l* 41.8%

         \[\leadsto k \cdot \left(-\color{blue}{i \cdot \left(z \cdot y1\right)}\right) \]

   10. Simplified 41.8%

       \[\leadsto \color{blue}{k \cdot \left(-i \cdot \left(z \cdot y1\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+77}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-54}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(t \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;z \leq -3.45 \cdot 10^{-251}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-103}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y0 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+68}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(t \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(i \cdot \left(z \cdot \left(-y1\right)\right)\right)\\ \end{array} \]

Alternative 25: 22.9% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y2 \cdot \left(t \cdot \left(-y4\right)\right)\right)\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+77}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-265}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-88}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(i \cdot \left(z \cdot \left(-y1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y2 (* t (- y4))))))
   (if (<= z -2.7e+77)
     (* c (* i (* z t)))
     (if (<= z -7e-50)
       t_1
       (if (<= z -2.6e-265)
         (* i (* y1 (* x j)))
         (if (<= z 5.6e-88)
           (* k (* y0 (* y2 (- y5))))
           (if (<= z 6.2e+68) t_1 (* k (* i (* z (- y1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * (t * -y4));
	double tmp;
	if (z <= -2.7e+77) {
		tmp = c * (i * (z * t));
	} else if (z <= -7e-50) {
		tmp = t_1;
	} else if (z <= -2.6e-265) {
		tmp = i * (y1 * (x * j));
	} else if (z <= 5.6e-88) {
		tmp = k * (y0 * (y2 * -y5));
	} else if (z <= 6.2e+68) {
		tmp = t_1;
	} else {
		tmp = k * (i * (z * -y1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (y2 * (t * -y4))
    if (z <= (-2.7d+77)) then
        tmp = c * (i * (z * t))
    else if (z <= (-7d-50)) then
        tmp = t_1
    else if (z <= (-2.6d-265)) then
        tmp = i * (y1 * (x * j))
    else if (z <= 5.6d-88) then
        tmp = k * (y0 * (y2 * -y5))
    else if (z <= 6.2d+68) then
        tmp = t_1
    else
        tmp = k * (i * (z * -y1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * (t * -y4));
	double tmp;
	if (z <= -2.7e+77) {
		tmp = c * (i * (z * t));
	} else if (z <= -7e-50) {
		tmp = t_1;
	} else if (z <= -2.6e-265) {
		tmp = i * (y1 * (x * j));
	} else if (z <= 5.6e-88) {
		tmp = k * (y0 * (y2 * -y5));
	} else if (z <= 6.2e+68) {
		tmp = t_1;
	} else {
		tmp = k * (i * (z * -y1));
	}
	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 * (t * -y4))
	tmp = 0
	if z <= -2.7e+77:
		tmp = c * (i * (z * t))
	elif z <= -7e-50:
		tmp = t_1
	elif z <= -2.6e-265:
		tmp = i * (y1 * (x * j))
	elif z <= 5.6e-88:
		tmp = k * (y0 * (y2 * -y5))
	elif z <= 6.2e+68:
		tmp = t_1
	else:
		tmp = k * (i * (z * -y1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y2 * Float64(t * Float64(-y4))))
	tmp = 0.0
	if (z <= -2.7e+77)
		tmp = Float64(c * Float64(i * Float64(z * t)));
	elseif (z <= -7e-50)
		tmp = t_1;
	elseif (z <= -2.6e-265)
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	elseif (z <= 5.6e-88)
		tmp = Float64(k * Float64(y0 * Float64(y2 * Float64(-y5))));
	elseif (z <= 6.2e+68)
		tmp = t_1;
	else
		tmp = Float64(k * Float64(i * Float64(z * Float64(-y1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y2 * (t * -y4));
	tmp = 0.0;
	if (z <= -2.7e+77)
		tmp = c * (i * (z * t));
	elseif (z <= -7e-50)
		tmp = t_1;
	elseif (z <= -2.6e-265)
		tmp = i * (y1 * (x * j));
	elseif (z <= 5.6e-88)
		tmp = k * (y0 * (y2 * -y5));
	elseif (z <= 6.2e+68)
		tmp = t_1;
	else
		tmp = k * (i * (z * -y1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y2 * N[(t * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.7e+77], N[(c * N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7e-50], t$95$1, If[LessEqual[z, -2.6e-265], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e-88], N[(k * N[(y0 * N[(y2 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+68], t$95$1, N[(k * N[(i * N[(z * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.6999999999999998e77

   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%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 45.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 45.9%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 45.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. *-commutative 45.9%

         \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 45.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 39.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 39.9%

         \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right) \cdot t} \]

      2. mul-1-neg 39.9%

         \[\leadsto \left(c \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \cdot t \]

      3. unsub-neg 39.9%

         \[\leadsto \left(c \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \cdot t \]

   9. Simplified 39.9%

      \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z - y4 \cdot y2\right)\right) \cdot t} \]

   10. Taylor expanded in i around inf 34.9%

       \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]

   if -2.6999999999999998e77 < z < -6.99999999999999993e-50 or 5.59999999999999952e-88 < z < 6.1999999999999997e68

   1. Initial program 29.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 41.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 41.8%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 41.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. *-commutative 41.8%

         \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 41.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 42.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 36.0%

         \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right) \cdot t} \]

      2. mul-1-neg 36.0%

         \[\leadsto \left(c \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \cdot t \]

      3. unsub-neg 36.0%

         \[\leadsto \left(c \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \cdot t \]

   9. Simplified 36.0%

      \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z - y4 \cdot y2\right)\right) \cdot t} \]

   10. Taylor expanded in i around 0 34.0%

       \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 34.0%

          \[\leadsto \color{blue}{-c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

       2. associate-*r* 37.1%

          \[\leadsto -c \cdot \color{blue}{\left(\left(y4 \cdot t\right) \cdot y2\right)} \]

   12. Simplified 37.1%

       \[\leadsto \color{blue}{-c \cdot \left(\left(y4 \cdot t\right) \cdot y2\right)} \]

   if -6.99999999999999993e-50 < z < -2.6000000000000001e-265

   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 38.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 53.7%

      \[\leadsto \color{blue}{y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 53.7%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      2. *-commutative 53.7%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      3. *-commutative 53.7%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      4. *-commutative 53.7%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      5. mul-1-neg 53.7%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-\left(k \cdot z - j \cdot x\right) \cdot i\right)}\right)\right) \]

      6. *-commutative 53.7%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-\color{blue}{i \cdot \left(k \cdot z - j \cdot x\right)}\right)\right)\right) \]

   6. Simplified 53.7%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\right)} \]

   7. Taylor expanded in i around inf 44.2%

      \[\leadsto y1 \cdot \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   8. Taylor expanded in j around inf 42.2%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 42.2%

         \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x\right)\right) \cdot y1} \]

      2. associate-*l* 46.0%

         \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]

   10. Simplified 46.0%

       \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]

   if -2.6000000000000001e-265 < z < 5.59999999999999952e-88

   1. Initial program 46.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 53.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 33.7%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 33.7%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      2. *-commutative 33.7%

         \[\leadsto y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      3. mul-1-neg 33.7%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      4. *-commutative 33.7%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      5. *-commutative 33.7%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{b \cdot \left(k \cdot z - j \cdot x\right)}\right)\right) \]

   6. Simplified 33.7%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + b \cdot \left(k \cdot z - j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in y5 around inf 24.4%

      \[\leadsto \color{blue}{\left(y3 \cdot j - k \cdot y2\right) \cdot \left(y0 \cdot y5\right)} \]

   8. Taylor expanded in y3 around 0 27.5%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(y5 \cdot y2\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 27.5%

         \[\leadsto \color{blue}{\left(-1 \cdot k\right) \cdot \left(y0 \cdot \left(y5 \cdot y2\right)\right)} \]

      2. neg-mul-1 27.5%

         \[\leadsto \color{blue}{\left(-k\right)} \cdot \left(y0 \cdot \left(y5 \cdot y2\right)\right) \]

      3. *-commutative 27.5%

         \[\leadsto \left(-k\right) \cdot \color{blue}{\left(\left(y5 \cdot y2\right) \cdot y0\right)} \]

   10. Simplified 27.5%

       \[\leadsto \color{blue}{\left(-k\right) \cdot \left(\left(y5 \cdot y2\right) \cdot y0\right)} \]

   if 6.1999999999999997e68 < z

   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 22.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 39.6%

      \[\leadsto \color{blue}{y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 39.6%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      2. *-commutative 39.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      3. *-commutative 39.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      4. *-commutative 39.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      5. mul-1-neg 39.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-\left(k \cdot z - j \cdot x\right) \cdot i\right)}\right)\right) \]

      6. *-commutative 39.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-\color{blue}{i \cdot \left(k \cdot z - j \cdot x\right)}\right)\right)\right) \]

   6. Simplified 39.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\right)} \]

   7. Taylor expanded in i around inf 44.2%

      \[\leadsto y1 \cdot \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   8. Taylor expanded in j around 0 37.4%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y1 \cdot \left(i \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 37.4%

         \[\leadsto \color{blue}{-k \cdot \left(y1 \cdot \left(i \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 37.4%

         \[\leadsto \color{blue}{k \cdot \left(-y1 \cdot \left(i \cdot z\right)\right)} \]

      3. *-commutative 37.4%

         \[\leadsto k \cdot \left(-\color{blue}{\left(i \cdot z\right) \cdot y1}\right) \]

      4. associate-*l* 41.8%

         \[\leadsto k \cdot \left(-\color{blue}{i \cdot \left(z \cdot y1\right)}\right) \]

   10. Simplified 41.8%

       \[\leadsto \color{blue}{k \cdot \left(-i \cdot \left(z \cdot y1\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+77}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-50}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(t \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-265}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-88}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(y2 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+68}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(t \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(i \cdot \left(z \cdot \left(-y1\right)\right)\right)\\ \end{array} \]

Alternative 26: 22.7% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y2 \cdot \left(t \cdot \left(-y4\right)\right)\right)\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+77}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-265}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-103}:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y0 \cdot \left(-y5\right)\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(i \cdot \left(z \cdot \left(-y1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y2 (* t (- y4))))))
   (if (<= z -3.1e+77)
     (* c (* i (* z t)))
     (if (<= z -2.6e-56)
       t_1
       (if (<= z -1.35e-265)
         (* i (* y1 (* x j)))
         (if (<= z 1.4e-103)
           (* (* k y2) (* y0 (- y5)))
           (if (<= z 5e+68) t_1 (* k (* i (* z (- y1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * (t * -y4));
	double tmp;
	if (z <= -3.1e+77) {
		tmp = c * (i * (z * t));
	} else if (z <= -2.6e-56) {
		tmp = t_1;
	} else if (z <= -1.35e-265) {
		tmp = i * (y1 * (x * j));
	} else if (z <= 1.4e-103) {
		tmp = (k * y2) * (y0 * -y5);
	} else if (z <= 5e+68) {
		tmp = t_1;
	} else {
		tmp = k * (i * (z * -y1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (y2 * (t * -y4))
    if (z <= (-3.1d+77)) then
        tmp = c * (i * (z * t))
    else if (z <= (-2.6d-56)) then
        tmp = t_1
    else if (z <= (-1.35d-265)) then
        tmp = i * (y1 * (x * j))
    else if (z <= 1.4d-103) then
        tmp = (k * y2) * (y0 * -y5)
    else if (z <= 5d+68) then
        tmp = t_1
    else
        tmp = k * (i * (z * -y1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * (t * -y4));
	double tmp;
	if (z <= -3.1e+77) {
		tmp = c * (i * (z * t));
	} else if (z <= -2.6e-56) {
		tmp = t_1;
	} else if (z <= -1.35e-265) {
		tmp = i * (y1 * (x * j));
	} else if (z <= 1.4e-103) {
		tmp = (k * y2) * (y0 * -y5);
	} else if (z <= 5e+68) {
		tmp = t_1;
	} else {
		tmp = k * (i * (z * -y1));
	}
	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 * (t * -y4))
	tmp = 0
	if z <= -3.1e+77:
		tmp = c * (i * (z * t))
	elif z <= -2.6e-56:
		tmp = t_1
	elif z <= -1.35e-265:
		tmp = i * (y1 * (x * j))
	elif z <= 1.4e-103:
		tmp = (k * y2) * (y0 * -y5)
	elif z <= 5e+68:
		tmp = t_1
	else:
		tmp = k * (i * (z * -y1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y2 * Float64(t * Float64(-y4))))
	tmp = 0.0
	if (z <= -3.1e+77)
		tmp = Float64(c * Float64(i * Float64(z * t)));
	elseif (z <= -2.6e-56)
		tmp = t_1;
	elseif (z <= -1.35e-265)
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	elseif (z <= 1.4e-103)
		tmp = Float64(Float64(k * y2) * Float64(y0 * Float64(-y5)));
	elseif (z <= 5e+68)
		tmp = t_1;
	else
		tmp = Float64(k * Float64(i * Float64(z * Float64(-y1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y2 * (t * -y4));
	tmp = 0.0;
	if (z <= -3.1e+77)
		tmp = c * (i * (z * t));
	elseif (z <= -2.6e-56)
		tmp = t_1;
	elseif (z <= -1.35e-265)
		tmp = i * (y1 * (x * j));
	elseif (z <= 1.4e-103)
		tmp = (k * y2) * (y0 * -y5);
	elseif (z <= 5e+68)
		tmp = t_1;
	else
		tmp = k * (i * (z * -y1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y2 * N[(t * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+77], N[(c * N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.6e-56], t$95$1, If[LessEqual[z, -1.35e-265], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-103], N[(N[(k * y2), $MachinePrecision] * N[(y0 * (-y5)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+68], t$95$1, N[(k * N[(i * N[(z * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.09999999999999999e77

   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%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 45.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 45.9%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 45.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. *-commutative 45.9%

         \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 45.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 39.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 39.9%

         \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right) \cdot t} \]

      2. mul-1-neg 39.9%

         \[\leadsto \left(c \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \cdot t \]

      3. unsub-neg 39.9%

         \[\leadsto \left(c \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \cdot t \]

   9. Simplified 39.9%

      \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z - y4 \cdot y2\right)\right) \cdot t} \]

   10. Taylor expanded in i around inf 34.9%

       \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]

   if -3.09999999999999999e77 < z < -2.59999999999999997e-56 or 1.40000000000000011e-103 < z < 5.0000000000000004e68

   1. Initial program 32.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 42.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 42.1%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 42.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. *-commutative 42.1%

         \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 42.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 42.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 35.0%

         \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right) \cdot t} \]

      2. mul-1-neg 35.0%

         \[\leadsto \left(c \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \cdot t \]

      3. unsub-neg 35.0%

         \[\leadsto \left(c \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \cdot t \]

   9. Simplified 35.0%

      \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z - y4 \cdot y2\right)\right) \cdot t} \]

   10. Taylor expanded in i around 0 34.5%

       \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 34.5%

          \[\leadsto \color{blue}{-c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

       2. associate-*r* 37.5%

          \[\leadsto -c \cdot \color{blue}{\left(\left(y4 \cdot t\right) \cdot y2\right)} \]

   12. Simplified 37.5%

       \[\leadsto \color{blue}{-c \cdot \left(\left(y4 \cdot t\right) \cdot y2\right)} \]

   if -2.59999999999999997e-56 < z < -1.3500000000000001e-265

   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 38.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 53.7%

      \[\leadsto \color{blue}{y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 53.7%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      2. *-commutative 53.7%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      3. *-commutative 53.7%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      4. *-commutative 53.7%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      5. mul-1-neg 53.7%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-\left(k \cdot z - j \cdot x\right) \cdot i\right)}\right)\right) \]

      6. *-commutative 53.7%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-\color{blue}{i \cdot \left(k \cdot z - j \cdot x\right)}\right)\right)\right) \]

   6. Simplified 53.7%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\right)} \]

   7. Taylor expanded in i around inf 44.2%

      \[\leadsto y1 \cdot \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   8. Taylor expanded in j around inf 42.2%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 42.2%

         \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x\right)\right) \cdot y1} \]

      2. associate-*l* 46.0%

         \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]

   10. Simplified 46.0%

       \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]

   if -1.3500000000000001e-265 < z < 1.40000000000000011e-103

   1. Initial program 44.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 51.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 34.8%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 34.8%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      2. *-commutative 34.8%

         \[\leadsto y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      3. mul-1-neg 34.8%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      4. *-commutative 34.8%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      5. *-commutative 34.8%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{b \cdot \left(k \cdot z - j \cdot x\right)}\right)\right) \]

   6. Simplified 34.8%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + b \cdot \left(k \cdot z - j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in y5 around inf 25.2%

      \[\leadsto \color{blue}{\left(y3 \cdot j - k \cdot y2\right) \cdot \left(y0 \cdot y5\right)} \]

   8. Taylor expanded in y3 around 0 26.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot y2\right)\right)} \cdot \left(y0 \cdot y5\right) \]
   9. Step-by-step derivation

      1. mul-1-neg 26.8%

         \[\leadsto \color{blue}{\left(-k \cdot y2\right)} \cdot \left(y0 \cdot y5\right) \]

      2. distribute-lft-neg-out 26.8%

         \[\leadsto \color{blue}{\left(\left(-k\right) \cdot y2\right)} \cdot \left(y0 \cdot y5\right) \]

      3. *-commutative 26.8%

         \[\leadsto \color{blue}{\left(y2 \cdot \left(-k\right)\right)} \cdot \left(y0 \cdot y5\right) \]

   10. Simplified 26.8%

       \[\leadsto \color{blue}{\left(y2 \cdot \left(-k\right)\right)} \cdot \left(y0 \cdot y5\right) \]

   if 5.0000000000000004e68 < z

   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 22.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 39.6%

      \[\leadsto \color{blue}{y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 39.6%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      2. *-commutative 39.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      3. *-commutative 39.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      4. *-commutative 39.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      5. mul-1-neg 39.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-\left(k \cdot z - j \cdot x\right) \cdot i\right)}\right)\right) \]

      6. *-commutative 39.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-\color{blue}{i \cdot \left(k \cdot z - j \cdot x\right)}\right)\right)\right) \]

   6. Simplified 39.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\right)} \]

   7. Taylor expanded in i around inf 44.2%

      \[\leadsto y1 \cdot \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   8. Taylor expanded in j around 0 37.4%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y1 \cdot \left(i \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 37.4%

         \[\leadsto \color{blue}{-k \cdot \left(y1 \cdot \left(i \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 37.4%

         \[\leadsto \color{blue}{k \cdot \left(-y1 \cdot \left(i \cdot z\right)\right)} \]

      3. *-commutative 37.4%

         \[\leadsto k \cdot \left(-\color{blue}{\left(i \cdot z\right) \cdot y1}\right) \]

      4. associate-*l* 41.8%

         \[\leadsto k \cdot \left(-\color{blue}{i \cdot \left(z \cdot y1\right)}\right) \]

   10. Simplified 41.8%

       \[\leadsto \color{blue}{k \cdot \left(-i \cdot \left(z \cdot y1\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+77}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-56}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(t \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-265}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-103}:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y0 \cdot \left(-y5\right)\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+68}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(t \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(i \cdot \left(z \cdot \left(-y1\right)\right)\right)\\ \end{array} \]

Alternative 27: 22.8% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y2 \cdot \left(t \cdot \left(-y4\right)\right)\right)\\ \mathbf{if}\;z \leq -5 \cdot 10^{+78}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-265}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-104}:\\ \;\;\;\;\left(-k\right) \cdot \left(y5 \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(i \cdot \left(z \cdot \left(-y1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y2 (* t (- y4))))))
   (if (<= z -5e+78)
     (* c (* i (* z t)))
     (if (<= z -2.8e-55)
       t_1
       (if (<= z -7e-265)
         (* i (* y1 (* x j)))
         (if (<= z 4.6e-104)
           (* (- k) (* y5 (* y0 y2)))
           (if (<= z 3.3e+68) t_1 (* k (* i (* z (- y1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * (t * -y4));
	double tmp;
	if (z <= -5e+78) {
		tmp = c * (i * (z * t));
	} else if (z <= -2.8e-55) {
		tmp = t_1;
	} else if (z <= -7e-265) {
		tmp = i * (y1 * (x * j));
	} else if (z <= 4.6e-104) {
		tmp = -k * (y5 * (y0 * y2));
	} else if (z <= 3.3e+68) {
		tmp = t_1;
	} else {
		tmp = k * (i * (z * -y1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (y2 * (t * -y4))
    if (z <= (-5d+78)) then
        tmp = c * (i * (z * t))
    else if (z <= (-2.8d-55)) then
        tmp = t_1
    else if (z <= (-7d-265)) then
        tmp = i * (y1 * (x * j))
    else if (z <= 4.6d-104) then
        tmp = -k * (y5 * (y0 * y2))
    else if (z <= 3.3d+68) then
        tmp = t_1
    else
        tmp = k * (i * (z * -y1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y2 * (t * -y4));
	double tmp;
	if (z <= -5e+78) {
		tmp = c * (i * (z * t));
	} else if (z <= -2.8e-55) {
		tmp = t_1;
	} else if (z <= -7e-265) {
		tmp = i * (y1 * (x * j));
	} else if (z <= 4.6e-104) {
		tmp = -k * (y5 * (y0 * y2));
	} else if (z <= 3.3e+68) {
		tmp = t_1;
	} else {
		tmp = k * (i * (z * -y1));
	}
	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 * (t * -y4))
	tmp = 0
	if z <= -5e+78:
		tmp = c * (i * (z * t))
	elif z <= -2.8e-55:
		tmp = t_1
	elif z <= -7e-265:
		tmp = i * (y1 * (x * j))
	elif z <= 4.6e-104:
		tmp = -k * (y5 * (y0 * y2))
	elif z <= 3.3e+68:
		tmp = t_1
	else:
		tmp = k * (i * (z * -y1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y2 * Float64(t * Float64(-y4))))
	tmp = 0.0
	if (z <= -5e+78)
		tmp = Float64(c * Float64(i * Float64(z * t)));
	elseif (z <= -2.8e-55)
		tmp = t_1;
	elseif (z <= -7e-265)
		tmp = Float64(i * Float64(y1 * Float64(x * j)));
	elseif (z <= 4.6e-104)
		tmp = Float64(Float64(-k) * Float64(y5 * Float64(y0 * y2)));
	elseif (z <= 3.3e+68)
		tmp = t_1;
	else
		tmp = Float64(k * Float64(i * Float64(z * Float64(-y1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y2 * (t * -y4));
	tmp = 0.0;
	if (z <= -5e+78)
		tmp = c * (i * (z * t));
	elseif (z <= -2.8e-55)
		tmp = t_1;
	elseif (z <= -7e-265)
		tmp = i * (y1 * (x * j));
	elseif (z <= 4.6e-104)
		tmp = -k * (y5 * (y0 * y2));
	elseif (z <= 3.3e+68)
		tmp = t_1;
	else
		tmp = k * (i * (z * -y1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y2 * N[(t * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+78], N[(c * N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.8e-55], t$95$1, If[LessEqual[z, -7e-265], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e-104], N[((-k) * N[(y5 * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+68], t$95$1, N[(k * N[(i * N[(z * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.99999999999999984e78

   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%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 45.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 45.9%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 45.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. *-commutative 45.9%

         \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 45.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 39.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 39.9%

         \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right) \cdot t} \]

      2. mul-1-neg 39.9%

         \[\leadsto \left(c \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \cdot t \]

      3. unsub-neg 39.9%

         \[\leadsto \left(c \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \cdot t \]

   9. Simplified 39.9%

      \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z - y4 \cdot y2\right)\right) \cdot t} \]

   10. Taylor expanded in i around inf 34.9%

       \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]

   if -4.99999999999999984e78 < z < -2.79999999999999984e-55 or 4.5999999999999999e-104 < z < 3.3e68

   1. Initial program 32.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 42.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 42.1%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 42.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. *-commutative 42.1%

         \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 42.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 42.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 35.0%

         \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right) \cdot t} \]

      2. mul-1-neg 35.0%

         \[\leadsto \left(c \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \cdot t \]

      3. unsub-neg 35.0%

         \[\leadsto \left(c \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \cdot t \]

   9. Simplified 35.0%

      \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z - y4 \cdot y2\right)\right) \cdot t} \]

   10. Taylor expanded in i around 0 34.5%

       \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 34.5%

          \[\leadsto \color{blue}{-c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

       2. associate-*r* 37.5%

          \[\leadsto -c \cdot \color{blue}{\left(\left(y4 \cdot t\right) \cdot y2\right)} \]

   12. Simplified 37.5%

       \[\leadsto \color{blue}{-c \cdot \left(\left(y4 \cdot t\right) \cdot y2\right)} \]

   if -2.79999999999999984e-55 < z < -7.00000000000000031e-265

   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 38.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 53.7%

      \[\leadsto \color{blue}{y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 53.7%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      2. *-commutative 53.7%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      3. *-commutative 53.7%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      4. *-commutative 53.7%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      5. mul-1-neg 53.7%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-\left(k \cdot z - j \cdot x\right) \cdot i\right)}\right)\right) \]

      6. *-commutative 53.7%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-\color{blue}{i \cdot \left(k \cdot z - j \cdot x\right)}\right)\right)\right) \]

   6. Simplified 53.7%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\right)} \]

   7. Taylor expanded in i around inf 44.2%

      \[\leadsto y1 \cdot \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   8. Taylor expanded in j around inf 42.2%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 42.2%

         \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x\right)\right) \cdot y1} \]

      2. associate-*l* 46.0%

         \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]

   10. Simplified 46.0%

       \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]

   if -7.00000000000000031e-265 < z < 4.5999999999999999e-104

   1. Initial program 44.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 51.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 34.8%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 34.8%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      2. *-commutative 34.8%

         \[\leadsto y0 \cdot \left(c \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      3. mul-1-neg 34.8%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      4. *-commutative 34.8%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

      5. *-commutative 34.8%

         \[\leadsto y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + \color{blue}{b \cdot \left(k \cdot z - j \cdot x\right)}\right)\right) \]

   6. Simplified 34.8%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(y2 \cdot x - z \cdot y3\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + b \cdot \left(k \cdot z - j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in y5 around inf 25.2%

      \[\leadsto \color{blue}{\left(y3 \cdot j - k \cdot y2\right) \cdot \left(y0 \cdot y5\right)} \]

   8. Taylor expanded in y3 around 0 26.7%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(y5 \cdot y2\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 26.7%

         \[\leadsto \color{blue}{-k \cdot \left(y0 \cdot \left(y5 \cdot y2\right)\right)} \]

      2. *-commutative 26.7%

         \[\leadsto -\color{blue}{\left(y0 \cdot \left(y5 \cdot y2\right)\right) \cdot k} \]

      3. distribute-rgt-neg-in 26.7%

         \[\leadsto \color{blue}{\left(y0 \cdot \left(y5 \cdot y2\right)\right) \cdot \left(-k\right)} \]

      4. associate-*r* 26.7%

         \[\leadsto \color{blue}{\left(\left(y0 \cdot y5\right) \cdot y2\right)} \cdot \left(-k\right) \]

      5. *-commutative 26.7%

         \[\leadsto \left(\color{blue}{\left(y5 \cdot y0\right)} \cdot y2\right) \cdot \left(-k\right) \]

      6. associate-*l* 28.2%

         \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y2\right)\right)} \cdot \left(-k\right) \]

   10. Simplified 28.2%

       \[\leadsto \color{blue}{\left(y5 \cdot \left(y0 \cdot y2\right)\right) \cdot \left(-k\right)} \]

   if 3.3e68 < z

   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 22.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 39.6%

      \[\leadsto \color{blue}{y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 39.6%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      2. *-commutative 39.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      3. *-commutative 39.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      4. *-commutative 39.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      5. mul-1-neg 39.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-\left(k \cdot z - j \cdot x\right) \cdot i\right)}\right)\right) \]

      6. *-commutative 39.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-\color{blue}{i \cdot \left(k \cdot z - j \cdot x\right)}\right)\right)\right) \]

   6. Simplified 39.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\right)} \]

   7. Taylor expanded in i around inf 44.2%

      \[\leadsto y1 \cdot \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   8. Taylor expanded in j around 0 37.4%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y1 \cdot \left(i \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 37.4%

         \[\leadsto \color{blue}{-k \cdot \left(y1 \cdot \left(i \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 37.4%

         \[\leadsto \color{blue}{k \cdot \left(-y1 \cdot \left(i \cdot z\right)\right)} \]

      3. *-commutative 37.4%

         \[\leadsto k \cdot \left(-\color{blue}{\left(i \cdot z\right) \cdot y1}\right) \]

      4. associate-*l* 41.8%

         \[\leadsto k \cdot \left(-\color{blue}{i \cdot \left(z \cdot y1\right)}\right) \]

   10. Simplified 41.8%

       \[\leadsto \color{blue}{k \cdot \left(-i \cdot \left(z \cdot y1\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+78}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-55}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(t \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-265}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-104}:\\ \;\;\;\;\left(-k\right) \cdot \left(y5 \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+68}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(t \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(i \cdot \left(z \cdot \left(-y1\right)\right)\right)\\ \end{array} \]

Alternative 28: 20.5% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{if}\;y1 \leq -1.4 \cdot 10^{+73}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -6.5 \cdot 10^{-200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y1 \leq 1.2 \cdot 10^{-177}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 5.2 \cdot 10^{+36}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* y1 (* x j)))))
   (if (<= y1 -1.4e+73)
     (* a (* y3 (* z y1)))
     (if (<= y1 -6.5e-200)
       t_1
       (if (<= y1 1.2e-177)
         (* x (* a (* y b)))
         (if (<= y1 5.2e+36) (* i (* c (* z t))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y1 * (x * j));
	double tmp;
	if (y1 <= -1.4e+73) {
		tmp = a * (y3 * (z * y1));
	} else if (y1 <= -6.5e-200) {
		tmp = t_1;
	} else if (y1 <= 1.2e-177) {
		tmp = x * (a * (y * b));
	} else if (y1 <= 5.2e+36) {
		tmp = i * (c * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (y1 * (x * j))
    if (y1 <= (-1.4d+73)) then
        tmp = a * (y3 * (z * y1))
    else if (y1 <= (-6.5d-200)) then
        tmp = t_1
    else if (y1 <= 1.2d-177) then
        tmp = x * (a * (y * b))
    else if (y1 <= 5.2d+36) then
        tmp = i * (c * (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y1 * (x * j));
	double tmp;
	if (y1 <= -1.4e+73) {
		tmp = a * (y3 * (z * y1));
	} else if (y1 <= -6.5e-200) {
		tmp = t_1;
	} else if (y1 <= 1.2e-177) {
		tmp = x * (a * (y * b));
	} else if (y1 <= 5.2e+36) {
		tmp = i * (c * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (y1 * (x * j))
	tmp = 0
	if y1 <= -1.4e+73:
		tmp = a * (y3 * (z * y1))
	elif y1 <= -6.5e-200:
		tmp = t_1
	elif y1 <= 1.2e-177:
		tmp = x * (a * (y * b))
	elif y1 <= 5.2e+36:
		tmp = i * (c * (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(y1 * Float64(x * j)))
	tmp = 0.0
	if (y1 <= -1.4e+73)
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	elseif (y1 <= -6.5e-200)
		tmp = t_1;
	elseif (y1 <= 1.2e-177)
		tmp = Float64(x * Float64(a * Float64(y * b)));
	elseif (y1 <= 5.2e+36)
		tmp = Float64(i * Float64(c * Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (y1 * (x * j));
	tmp = 0.0;
	if (y1 <= -1.4e+73)
		tmp = a * (y3 * (z * y1));
	elseif (y1 <= -6.5e-200)
		tmp = t_1;
	elseif (y1 <= 1.2e-177)
		tmp = x * (a * (y * b));
	elseif (y1 <= 5.2e+36)
		tmp = i * (c * (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -1.4e+73], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -6.5e-200], t$95$1, If[LessEqual[y1, 1.2e-177], N[(x * N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 5.2e+36], N[(i * N[(c * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y1 < -1.40000000000000004e73

   1. Initial program 24.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 51.8%

      \[\leadsto \color{blue}{y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 51.8%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      2. *-commutative 51.8%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      3. *-commutative 51.8%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      4. *-commutative 51.8%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      5. mul-1-neg 51.8%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-\left(k \cdot z - j \cdot x\right) \cdot i\right)}\right)\right) \]

      6. *-commutative 51.8%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-\color{blue}{i \cdot \left(k \cdot z - j \cdot x\right)}\right)\right)\right) \]

   6. Simplified 51.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\right)} \]

   7. Taylor expanded in a around inf 39.4%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   8. Taylor expanded in y3 around inf 31.6%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 31.6%

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(z \cdot y3\right)}\right) \]

      2. associate-*r* 35.3%

         \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot z\right) \cdot y3\right)} \]

   10. Simplified 35.3%

       \[\leadsto \color{blue}{a \cdot \left(\left(y1 \cdot z\right) \cdot y3\right)} \]

   if -1.40000000000000004e73 < y1 < -6.5000000000000002e-200 or 5.2000000000000003e36 < y1

   1. Initial program 25.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 43.2%

      \[\leadsto \color{blue}{y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.2%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      2. *-commutative 43.2%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      3. *-commutative 43.2%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      4. *-commutative 43.2%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      5. mul-1-neg 43.2%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-\left(k \cdot z - j \cdot x\right) \cdot i\right)}\right)\right) \]

      6. *-commutative 43.2%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-\color{blue}{i \cdot \left(k \cdot z - j \cdot x\right)}\right)\right)\right) \]

   6. Simplified 43.2%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\right)} \]

   7. Taylor expanded in i around inf 36.9%

      \[\leadsto y1 \cdot \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   8. Taylor expanded in j around inf 29.4%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 29.4%

         \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x\right)\right) \cdot y1} \]

      2. associate-*l* 33.9%

         \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]

   10. Simplified 33.9%

       \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]

   if -6.5000000000000002e-200 < y1 < 1.1999999999999999e-177

   1. Initial program 51.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 51.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 31.8%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in b around inf 25.5%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot a - y0 \cdot j\right)\right)} \cdot x \]

   6. Taylor expanded in y around inf 29.6%

      \[\leadsto \color{blue}{\left(a \cdot \left(y \cdot b\right)\right)} \cdot x \]

   if 1.1999999999999999e-177 < y1 < 5.2000000000000003e36

   1. Initial program 34.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 41.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 41.5%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 41.5%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. *-commutative 41.5%

         \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 41.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 42.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 38.5%

         \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right) \cdot t} \]

      2. mul-1-neg 38.5%

         \[\leadsto \left(c \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \cdot t \]

      3. unsub-neg 38.5%

         \[\leadsto \left(c \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \cdot t \]

   9. Simplified 38.5%

      \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z - y4 \cdot y2\right)\right) \cdot t} \]

   10. Taylor expanded in i around inf 28.1%

       \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 28.1%

          \[\leadsto \color{blue}{\left(c \cdot i\right) \cdot \left(t \cdot z\right)} \]

       2. *-commutative 28.1%

          \[\leadsto \color{blue}{\left(i \cdot c\right)} \cdot \left(t \cdot z\right) \]

       3. associate-*l* 30.1%

          \[\leadsto \color{blue}{i \cdot \left(c \cdot \left(t \cdot z\right)\right)} \]

   12. Simplified 30.1%

       \[\leadsto \color{blue}{i \cdot \left(c \cdot \left(t \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.4 \cdot 10^{+73}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -6.5 \cdot 10^{-200}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 1.2 \cdot 10^{-177}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 5.2 \cdot 10^{+36}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \]

Alternative 29: 21.5% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -1.45 \cdot 10^{+94}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq 3 \cdot 10^{-213}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 6.5 \cdot 10^{+36}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -1.45e+94)
   (* a (* y3 (* z y1)))
   (if (<= y1 3e-213)
     (* a (* y (* x b)))
     (if (<= y1 6.5e+36) (* i (* c (* z t))) (* i (* y1 (* 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 tmp;
	if (y1 <= -1.45e+94) {
		tmp = a * (y3 * (z * y1));
	} else if (y1 <= 3e-213) {
		tmp = a * (y * (x * b));
	} else if (y1 <= 6.5e+36) {
		tmp = i * (c * (z * t));
	} else {
		tmp = i * (y1 * (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) :: tmp
    if (y1 <= (-1.45d+94)) then
        tmp = a * (y3 * (z * y1))
    else if (y1 <= 3d-213) then
        tmp = a * (y * (x * b))
    else if (y1 <= 6.5d+36) then
        tmp = i * (c * (z * t))
    else
        tmp = i * (y1 * (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 tmp;
	if (y1 <= -1.45e+94) {
		tmp = a * (y3 * (z * y1));
	} else if (y1 <= 3e-213) {
		tmp = a * (y * (x * b));
	} else if (y1 <= 6.5e+36) {
		tmp = i * (c * (z * t));
	} else {
		tmp = i * (y1 * (x * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -1.45e+94:
		tmp = a * (y3 * (z * y1))
	elif y1 <= 3e-213:
		tmp = a * (y * (x * b))
	elif y1 <= 6.5e+36:
		tmp = i * (c * (z * t))
	else:
		tmp = i * (y1 * (x * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -1.45e+94)
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	elseif (y1 <= 3e-213)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (y1 <= 6.5e+36)
		tmp = Float64(i * Float64(c * Float64(z * t)));
	else
		tmp = Float64(i * Float64(y1 * 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)
	tmp = 0.0;
	if (y1 <= -1.45e+94)
		tmp = a * (y3 * (z * y1));
	elseif (y1 <= 3e-213)
		tmp = a * (y * (x * b));
	elseif (y1 <= 6.5e+36)
		tmp = i * (c * (z * t));
	else
		tmp = i * (y1 * (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_] := If[LessEqual[y1, -1.45e+94], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3e-213], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 6.5e+36], N[(i * N[(c * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y1 < -1.4499999999999999e94

   1. Initial program 23.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 54.8%

      \[\leadsto \color{blue}{y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 54.8%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      2. *-commutative 54.8%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      3. *-commutative 54.8%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      4. *-commutative 54.8%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      5. mul-1-neg 54.8%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-\left(k \cdot z - j \cdot x\right) \cdot i\right)}\right)\right) \]

      6. *-commutative 54.8%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-\color{blue}{i \cdot \left(k \cdot z - j \cdot x\right)}\right)\right)\right) \]

   6. Simplified 54.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\right)} \]

   7. Taylor expanded in a around inf 42.5%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   8. Taylor expanded in y3 around inf 33.9%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 33.9%

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(z \cdot y3\right)}\right) \]

      2. associate-*r* 38.1%

         \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot z\right) \cdot y3\right)} \]

   10. Simplified 38.1%

       \[\leadsto \color{blue}{a \cdot \left(\left(y1 \cdot z\right) \cdot y3\right)} \]

   if -1.4499999999999999e94 < y1 < 2.99999999999999986e-213

   1. Initial program 38.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 38.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 35.5%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in b around inf 27.5%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot a - y0 \cdot j\right)\right)} \cdot x \]

   6. Taylor expanded in y around inf 21.7%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

   if 2.99999999999999986e-213 < y1 < 6.4999999999999998e36

   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%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 39.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 39.2%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 39.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. *-commutative 39.2%

         \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 39.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 39.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 35.2%

         \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right) \cdot t} \]

      2. mul-1-neg 35.2%

         \[\leadsto \left(c \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \cdot t \]

      3. unsub-neg 35.2%

         \[\leadsto \left(c \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \cdot t \]

   9. Simplified 35.2%

      \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z - y4 \cdot y2\right)\right) \cdot t} \]

   10. Taylor expanded in i around inf 27.9%

       \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 26.2%

          \[\leadsto \color{blue}{\left(c \cdot i\right) \cdot \left(t \cdot z\right)} \]

       2. *-commutative 26.2%

          \[\leadsto \color{blue}{\left(i \cdot c\right)} \cdot \left(t \cdot z\right) \]

       3. associate-*l* 29.6%

          \[\leadsto \color{blue}{i \cdot \left(c \cdot \left(t \cdot z\right)\right)} \]

   12. Simplified 29.6%

       \[\leadsto \color{blue}{i \cdot \left(c \cdot \left(t \cdot z\right)\right)} \]

   if 6.4999999999999998e36 < y1

   1. Initial program 18.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 52.6%

      \[\leadsto \color{blue}{y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 52.6%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      2. *-commutative 52.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      3. *-commutative 52.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      4. *-commutative 52.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      5. mul-1-neg 52.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-\left(k \cdot z - j \cdot x\right) \cdot i\right)}\right)\right) \]

      6. *-commutative 52.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-\color{blue}{i \cdot \left(k \cdot z - j \cdot x\right)}\right)\right)\right) \]

   6. Simplified 52.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\right)} \]

   7. Taylor expanded in i around inf 41.7%

      \[\leadsto y1 \cdot \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   8. Taylor expanded in j around inf 36.5%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 36.5%

         \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x\right)\right) \cdot y1} \]

      2. associate-*l* 43.4%

         \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]

   10. Simplified 43.4%

       \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 31.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.45 \cdot 10^{+94}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq 3 \cdot 10^{-213}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 6.5 \cdot 10^{+36}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \]

Alternative 30: 21.4% accurate, 7.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -1.8 \cdot 10^{+102}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq 9 \cdot 10^{-19}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(t \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -1.8e+102)
   (* a (* y3 (* z y1)))
   (if (<= y1 9e-19) (* c (* y2 (* t (- y4)))) (* i (* y1 (* 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 tmp;
	if (y1 <= -1.8e+102) {
		tmp = a * (y3 * (z * y1));
	} else if (y1 <= 9e-19) {
		tmp = c * (y2 * (t * -y4));
	} else {
		tmp = i * (y1 * (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) :: tmp
    if (y1 <= (-1.8d+102)) then
        tmp = a * (y3 * (z * y1))
    else if (y1 <= 9d-19) then
        tmp = c * (y2 * (t * -y4))
    else
        tmp = i * (y1 * (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 tmp;
	if (y1 <= -1.8e+102) {
		tmp = a * (y3 * (z * y1));
	} else if (y1 <= 9e-19) {
		tmp = c * (y2 * (t * -y4));
	} else {
		tmp = i * (y1 * (x * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -1.8e+102:
		tmp = a * (y3 * (z * y1))
	elif y1 <= 9e-19:
		tmp = c * (y2 * (t * -y4))
	else:
		tmp = i * (y1 * (x * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -1.8e+102)
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	elseif (y1 <= 9e-19)
		tmp = Float64(c * Float64(y2 * Float64(t * Float64(-y4))));
	else
		tmp = Float64(i * Float64(y1 * 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)
	tmp = 0.0;
	if (y1 <= -1.8e+102)
		tmp = a * (y3 * (z * y1));
	elseif (y1 <= 9e-19)
		tmp = c * (y2 * (t * -y4));
	else
		tmp = i * (y1 * (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_] := If[LessEqual[y1, -1.8e+102], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 9e-19], N[(c * N[(y2 * N[(t * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(y1 * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y1 < -1.8000000000000001e102

   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 30.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 56.3%

      \[\leadsto \color{blue}{y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 56.3%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      2. *-commutative 56.3%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      3. *-commutative 56.3%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      4. *-commutative 56.3%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      5. mul-1-neg 56.3%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-\left(k \cdot z - j \cdot x\right) \cdot i\right)}\right)\right) \]

      6. *-commutative 56.3%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-\color{blue}{i \cdot \left(k \cdot z - j \cdot x\right)}\right)\right)\right) \]

   6. Simplified 56.3%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\right)} \]

   7. Taylor expanded in a around inf 43.1%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   8. Taylor expanded in y3 around inf 33.8%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 33.8%

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(z \cdot y3\right)}\right) \]

      2. associate-*r* 38.4%

         \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot z\right) \cdot y3\right)} \]

   10. Simplified 38.4%

       \[\leadsto \color{blue}{a \cdot \left(\left(y1 \cdot z\right) \cdot y3\right)} \]

   if -1.8000000000000001e102 < y1 < 9.00000000000000026e-19

   1. Initial program 40.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 40.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 34.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 34.8%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 34.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. *-commutative 34.8%

         \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 34.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 31.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 28.2%

         \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right) \cdot t} \]

      2. mul-1-neg 28.2%

         \[\leadsto \left(c \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \cdot t \]

      3. unsub-neg 28.2%

         \[\leadsto \left(c \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \cdot t \]

   9. Simplified 28.2%

      \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z - y4 \cdot y2\right)\right) \cdot t} \]

   10. Taylor expanded in i around 0 23.9%

       \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 23.9%

          \[\leadsto \color{blue}{-c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

       2. associate-*r* 25.8%

          \[\leadsto -c \cdot \color{blue}{\left(\left(y4 \cdot t\right) \cdot y2\right)} \]

   12. Simplified 25.8%

       \[\leadsto \color{blue}{-c \cdot \left(\left(y4 \cdot t\right) \cdot y2\right)} \]

   if 9.00000000000000026e-19 < y1

   1. Initial program 16.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 47.7%

      \[\leadsto \color{blue}{y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 47.7%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      2. *-commutative 47.7%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      3. *-commutative 47.7%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      4. *-commutative 47.7%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      5. mul-1-neg 47.7%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-\left(k \cdot z - j \cdot x\right) \cdot i\right)}\right)\right) \]

      6. *-commutative 47.7%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-\color{blue}{i \cdot \left(k \cdot z - j \cdot x\right)}\right)\right)\right) \]

   6. Simplified 47.7%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\right)} \]

   7. Taylor expanded in i around inf 41.8%

      \[\leadsto y1 \cdot \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   8. Taylor expanded in j around inf 34.7%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 34.7%

         \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x\right)\right) \cdot y1} \]

      2. associate-*l* 40.3%

         \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]

   10. Simplified 40.3%

       \[\leadsto \color{blue}{i \cdot \left(\left(j \cdot x\right) \cdot y1\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.8 \cdot 10^{+102}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq 9 \cdot 10^{-19}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(t \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j\right)\right)\\ \end{array} \]

Alternative 31: 21.2% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-124} \lor \neg \left(x \leq 2.3 \cdot 10^{-13}\right):\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= x -2.5e-124) (not (<= x 2.3e-13)))
   (* a (* y (* x b)))
   (* a (* y3 (* z y1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((x <= -2.5e-124) || !(x <= 2.3e-13)) {
		tmp = a * (y * (x * b));
	} else {
		tmp = a * (y3 * (z * y1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((x <= (-2.5d-124)) .or. (.not. (x <= 2.3d-13))) then
        tmp = a * (y * (x * b))
    else
        tmp = a * (y3 * (z * y1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((x <= -2.5e-124) || !(x <= 2.3e-13)) {
		tmp = a * (y * (x * b));
	} else {
		tmp = a * (y3 * (z * y1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (x <= -2.5e-124) or not (x <= 2.3e-13):
		tmp = a * (y * (x * b))
	else:
		tmp = a * (y3 * (z * y1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((x <= -2.5e-124) || !(x <= 2.3e-13))
		tmp = Float64(a * Float64(y * Float64(x * b)));
	else
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((x <= -2.5e-124) || ~((x <= 2.3e-13)))
		tmp = a * (y * (x * b));
	else
		tmp = a * (y3 * (z * y1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[x, -2.5e-124], N[Not[LessEqual[x, 2.3e-13]], $MachinePrecision]], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5000000000000001e-124 or 2.29999999999999979e-13 < x

   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%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 41.8%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in b around inf 30.3%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot a - y0 \cdot j\right)\right)} \cdot x \]

   6. Taylor expanded in y around inf 30.1%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

   if -2.5000000000000001e-124 < x < 2.29999999999999979e-13

   1. Initial program 45.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 51.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 37.6%

      \[\leadsto \color{blue}{y1 \cdot \left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 37.6%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      2. *-commutative 37.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(x \cdot y2 - \color{blue}{z \cdot y3}\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      3. *-commutative 37.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(\color{blue}{y2 \cdot x} - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      4. *-commutative 37.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - \color{blue}{j \cdot y3}\right) + -1 \cdot \left(\left(k \cdot z - j \cdot x\right) \cdot i\right)\right)\right) \]

      5. mul-1-neg 37.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \color{blue}{\left(-\left(k \cdot z - j \cdot x\right) \cdot i\right)}\right)\right) \]

      6. *-commutative 37.6%

         \[\leadsto y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-\color{blue}{i \cdot \left(k \cdot z - j \cdot x\right)}\right)\right)\right) \]

   6. Simplified 37.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(-a \cdot \left(y2 \cdot x - z \cdot y3\right)\right) + \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(-i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\right)} \]

   7. Taylor expanded in a around inf 25.4%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

   8. Taylor expanded in y3 around inf 20.0%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 20.0%

         \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(z \cdot y3\right)}\right) \]

      2. associate-*r* 22.1%

         \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot z\right) \cdot y3\right)} \]

   10. Simplified 22.1%

       \[\leadsto \color{blue}{a \cdot \left(\left(y1 \cdot z\right) \cdot y3\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 27.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-124} \lor \neg \left(x \leq 2.3 \cdot 10^{-13}\right):\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \end{array} \]

Alternative 32: 21.7% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-124} \lor \neg \left(x \leq 1.65 \cdot 10^{+65}\right):\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= x -1.05e-124) (not (<= x 1.65e+65)))
   (* a (* y (* x b)))
   (* c (* i (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((x <= -1.05e-124) || !(x <= 1.65e+65)) {
		tmp = a * (y * (x * b));
	} else {
		tmp = c * (i * (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((x <= (-1.05d-124)) .or. (.not. (x <= 1.65d+65))) then
        tmp = a * (y * (x * b))
    else
        tmp = c * (i * (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((x <= -1.05e-124) || !(x <= 1.65e+65)) {
		tmp = a * (y * (x * b));
	} else {
		tmp = c * (i * (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (x <= -1.05e-124) or not (x <= 1.65e+65):
		tmp = a * (y * (x * b))
	else:
		tmp = c * (i * (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((x <= -1.05e-124) || !(x <= 1.65e+65))
		tmp = Float64(a * Float64(y * Float64(x * b)));
	else
		tmp = Float64(c * Float64(i * Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((x <= -1.05e-124) || ~((x <= 1.65e+65)))
		tmp = a * (y * (x * b));
	else
		tmp = c * (i * (z * t));
	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[x, -1.05e-124], N[Not[LessEqual[x, 1.65e+65]], $MachinePrecision]], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.05e-124 or 1.65000000000000012e65 < x

   1. Initial program 24.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 43.1%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in b around inf 31.6%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot a - y0 \cdot j\right)\right)} \cdot x \]

   6. Taylor expanded in y around inf 32.0%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

   if -1.05e-124 < x < 1.65000000000000012e65

   1. Initial program 41.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 41.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 39.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 39.4%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 39.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. *-commutative 39.4%

         \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 39.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 34.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 29.9%

         \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right) \cdot t} \]

      2. mul-1-neg 29.9%

         \[\leadsto \left(c \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \cdot t \]

      3. unsub-neg 29.9%

         \[\leadsto \left(c \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \cdot t \]

   9. Simplified 29.9%

      \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z - y4 \cdot y2\right)\right) \cdot t} \]

   10. Taylor expanded in i around inf 21.3%

       \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 27.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-124} \lor \neg \left(x \leq 1.65 \cdot 10^{+65}\right):\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 33: 21.6% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{-124} \lor \neg \left(x \leq 1.5 \cdot 10^{+65}\right):\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= x -2.05e-124) (not (<= x 1.5e+65)))
   (* a (* y (* x b)))
   (* i (* c (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((x <= -2.05e-124) || !(x <= 1.5e+65)) {
		tmp = a * (y * (x * b));
	} else {
		tmp = i * (c * (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((x <= (-2.05d-124)) .or. (.not. (x <= 1.5d+65))) then
        tmp = a * (y * (x * b))
    else
        tmp = i * (c * (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((x <= -2.05e-124) || !(x <= 1.5e+65)) {
		tmp = a * (y * (x * b));
	} else {
		tmp = i * (c * (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (x <= -2.05e-124) or not (x <= 1.5e+65):
		tmp = a * (y * (x * b))
	else:
		tmp = i * (c * (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((x <= -2.05e-124) || !(x <= 1.5e+65))
		tmp = Float64(a * Float64(y * Float64(x * b)));
	else
		tmp = Float64(i * Float64(c * Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((x <= -2.05e-124) || ~((x <= 1.5e+65)))
		tmp = a * (y * (x * b));
	else
		tmp = i * (c * (z * t));
	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[x, -2.05e-124], N[Not[LessEqual[x, 1.5e+65]], $MachinePrecision]], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(c * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.0500000000000002e-124 or 1.5000000000000001e65 < x

   1. Initial program 24.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 43.1%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in b around inf 31.6%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot a - y0 \cdot j\right)\right)} \cdot x \]

   6. Taylor expanded in y around inf 32.0%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

   if -2.0500000000000002e-124 < x < 1.5000000000000001e65

   1. Initial program 41.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 41.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 39.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 39.4%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 39.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      3. *-commutative 39.4%

         \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 39.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in t around -inf 34.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 29.9%

         \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z + -1 \cdot \left(y4 \cdot y2\right)\right)\right) \cdot t} \]

      2. mul-1-neg 29.9%

         \[\leadsto \left(c \cdot \left(i \cdot z + \color{blue}{\left(-y4 \cdot y2\right)}\right)\right) \cdot t \]

      3. unsub-neg 29.9%

         \[\leadsto \left(c \cdot \color{blue}{\left(i \cdot z - y4 \cdot y2\right)}\right) \cdot t \]

   9. Simplified 29.9%

      \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z - y4 \cdot y2\right)\right) \cdot t} \]

   10. Taylor expanded in i around inf 21.3%

       \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 19.5%

          \[\leadsto \color{blue}{\left(c \cdot i\right) \cdot \left(t \cdot z\right)} \]

       2. *-commutative 19.5%

          \[\leadsto \color{blue}{\left(i \cdot c\right)} \cdot \left(t \cdot z\right) \]

       3. associate-*l* 21.3%

          \[\leadsto \color{blue}{i \cdot \left(c \cdot \left(t \cdot z\right)\right)} \]

   12. Simplified 21.3%

       \[\leadsto \color{blue}{i \cdot \left(c \cdot \left(t \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 27.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{-124} \lor \neg \left(x \leq 1.5 \cdot 10^{+65}\right):\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 34: 16.8% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y \cdot \left(x \cdot b\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* y (* x b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y * (x * b));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * (y * (x * b))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y * (x * b));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (y * (x * b))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(y * Float64(x * b)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (y * (x * b));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 32.1%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

3. Simplified 32.1%

   \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

4. Taylor expanded in x around inf 34.0%

   \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

5. Taylor expanded in b around inf 25.2%

   \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot a - y0 \cdot j\right)\right)} \cdot x \]

6. Taylor expanded in y around inf 21.0%

   \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

7. Final simplification 21.0%

   \[\leadsto a \cdot \left(y \cdot \left(x \cdot b\right)\right) \]

Developer target: 27.2% 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 2023200 
(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)))))